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  • Main Page
    *[[Info_z-transform|Z-transform]], [[Info_inverse_z-transform|Inverse Z-transform]] *[[Discrete-time_Fourier_transform_info|Discrete-time Fourier transform (DTFT)]]
    2 KB (209 words) - 13:07, 9 September 2022
  • ECE 301 Fall 2007 mboutin Difference Between Fourier and Laplace
    [[Category: Fourier]] [[Category: Fourier Transform]]
    2 KB (268 words) - 12:14, 10 December 2008
  • ECE 301 (SanSummer2008)
    ...representation of continuous-time periodic signals_(ECE301Summer2008asan)|Fourier Series representation of continuous-time periodic signals]] ...ourier Series Representation of CT periodic signals_(ECE301Summer2008asan)|Fourier Series Representation of CT periodic signals]]
    7 KB (921 words) - 06:08, 21 October 2011
  • ECE301:SanSummer08:Exam II (ECE301Summer2008asan)
    1)a)If a discrete time singal x[n] is periodic with period N, then the Fourier series coefficients <math>a_k</math> of the signal x[n] is also periodic wi ...er a continuous-time periodic signal x(t) with period T = 5 whose non-zero Fourier series coefficients <math>a_k</math> are given by
    4 KB (815 words) - 10:57, 21 November 2008
  • ECE 301 Fall 2007 mboutin Definitions
    ==[[ECE 301 Fall 2007 mboutin Fourier Series|Fourier Series]]== {{:ECE 301 Fall 2007 mboutin Fourier Series}}
    3 KB (297 words) - 16:56, 23 April 2013
  • ECE 301 Fall 2007 mboutin Duality
    ...sform pair over and over... Note: I can not find a way to display a proper fourier symbol, so I went with the "\displaystyle {\bf F}" as seen below. ..., it becomes clear that it is only necessary to take the dual of a Fourier Transform Pair once. After taking the dual once, one might as well use time reversal.
    1 KB (241 words) - 10:13, 10 December 2008
  • ECE 301 Fall 2007 mboutin Fourier Transform Table
    [[Category: Fourier]] [[Category: Fourier Transform]]
    2 KB (321 words) - 11:28, 10 December 2008
  • ECE 301 Fall 2007 mboutin Common Questions on FS/FT Answered By Mimi
    [[Category: Fourier]] [[Category: Fourier Series]]
    1 KB (186 words) - 17:25, 23 April 2013
  • ECE 301 Fall 2007 mboutin Guide to Partial Fraction Expansion
    ...on allows us to fit functions to the known ones given by the known Fourier Transform pairs table. ...obtaining the capital letters quickly are from learning to do the Laplace Transform in ECE 202.
    4 KB (616 words) - 17:26, 23 April 2013
  • ECE 301 Fall 2007 mboutin Joseph Fourier
    [[Category: Fourier]] Jean Baptiste Joseph Fourier (1768 - 1830)
    3 KB (390 words) - 12:10, 11 December 2008
  • ECE 301 Fall 2007 mboutin Homework 4
    [[Category: Fourier]] [[Category: Fourier Transforms]]
    2 KB (263 words) - 12:19, 11 December 2008
  • ECE 301 Fall 2007 mboutin Homework 5
    ...math> is actually <math> \omega\ </math> when you want to take the inverse transform and therefore it is a variable and not a constant. So when you write the in ...division by zero. I also don't understand why the integral for the inverse transform is taken of <math> -\pi\ </math> to <math> \pi\ </math> when the solution k
    4 KB (688 words) - 12:34, 11 December 2008
  • ECE 301 Fall 2007 mboutin Meaning of Fourier Transform
    [[Category: Fourier]] [[Category: Fourier Transform]]
    3 KB (431 words) - 17:29, 23 April 2013
  • ECE 301 Fall 2007 mboutin Multidimension Fourier Transform
    [[Category: Fourier]] [[Category: Fourier Transform]]
    2 KB (303 words) - 10:13, 12 December 2008
  • ECE 301 Fall 2007 mboutin Frequency and Impulse Response Example
    1: Take the Fourier transform of the equation, ...uide to Partial Fraction Expansion]]) to facilitate use of inverse Fourier transform,
    2 KB (248 words) - 08:31, 9 March 2011
  • ECE 301 Fall 2007 mboutin Difference Equation in Class Example
    [[Category: Fourier]] [[Category: Fourier Transforms]]
    2 KB (379 words) - 08:35, 9 March 2011
  • ECE 301 Fall 2007 mboutin Sampling Theorem
    ...ontent exists in the signal at a higher frequency. If you take the Fourier transform of a signal and can find a point at which the signal is equal to zero at th : Below is a Fourier transform of a signal, you can see that is is bandlimited because it has a point equa
    3 KB (591 words) - 17:24, 23 April 2013
  • ECE 301 Fall 2007 mboutin Sampling Theorem Def
    ...qual to two times the absolute value of the frequency at which the Fourier transform of the signal is zero for values greater than said frequency) you are guara ...</math>, where <math> \omega_m\ </math> is the frequency where the Fourier transform of the signal equals zero for all frequencies greater than <math> \omega_m\
    4 KB (689 words) - 12:48, 12 December 2008
  • Lecture Schedule (ECE438BoutinSpring09)
    ...ign="right" style="padding-right: 1em;" | Monday || 01/26/09 || CT Fourier transform || 1.3.2 || DT systems ...="right" style="padding-right: 1em;" | Wednesday || 01/28/09 || DT Fourier transform, <span style="color:red"> HW1 due </span> || 1.3.3 ||
    6 KB (689 words) - 07:59, 2 August 2010
  • Table of Formulas and Properties ECE301Fall2008mboutin
    ...ing-right: 1em;" | [[DT Fourier Transform_ECE301Fall2008mboutin]] || {{:DT Fourier Transform_ECE301Fall2008mboutin}} ...| [[DT Inverse Fourier Transform_ECE301Fall2008mboutin]] || {{:DT Inverse Fourier Transform_ECE301Fall2008mboutin}}
    8 KB (989 words) - 07:20, 5 February 2009
  • Hw3 comments (ECE438BoutinSpring09)
    - Using sinc and rect functions along with Fourier transform properties is key to solving some of the problems <br> ...o not confuse them with each other. The DTFT is the discrete time Fourier transform of x[n], which is the sampled signal of continuous time signal x(t) <br>
    546 B (93 words) - 20:27, 18 February 2009
  • HW 3 Question 2
    ...tips for a different way to do this problem or on how to find the fourier transform of the sinc function? Thanks! --[[User:Kklacik|Kklacik]] 16:35, 10 Februar
    572 B (91 words) - 15:28, 10 February 2009
  • CourseNotes16 (BoutinSpring2009)
    == 1.6.4 FFT "Fast Fourier transform" ==
    2 KB (376 words) - 06:44, 16 September 2013
  • Reading guide (ECE438BoutinSpring2009)
    * PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409, ...llak/ee438/FALL01/Fourier_notes1.pdf Prof. Pollak's supplementary notes on Fourier series]
    8 KB (1,226 words) - 11:40, 1 May 2009
  • ECE438 (BoutinFall2009)
    | [[student_summary_CT_DT_Fourier_transform_ECE438F09|CT and DT Fourier transform]] | [[student_summary_z_transform_ECE438F09|z-transform]]
    7 KB (1,067 words) - 12:05, 25 June 2010
  • Mimi's key points ECE301Fall2008mboutin
    === Fourier series === ===CT Fourier transform ===
    2 KB (243 words) - 08:04, 21 November 2008
  • HW4.1 Nicholas Gentry ECE301Fall2008mboutin
    [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (384 words) - 10:55, 16 September 2013
  • HW4.1 Paul Scheffler ECE301Fall2008mboutin
    [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    863 B (144 words) - 10:54, 16 September 2013
  • HW4.2 Tyler Houlihan ECE301Fall2008mboutin
    == Definition of fourier transform for DT signal == These are the fourier coefficients, which must be calculated from the function in this case, rath
    2 KB (374 words) - 14:27, 25 September 2008
  • HW4.4 Tyler Houlihan ECE301Fall2008mboutin
    So take laplace transform of this function to get <math>H(s)\,</math>, the system function. I have to multiply each of these fourier coefficients by my <math>H[z]\,</math>, also noting that my <math>\,\omega
    1 KB (235 words) - 15:29, 25 September 2008
  • Homework 5 ECE301Fall2008mboutin
    ==Fourier Transform== ==Inverse Fourier Transform==
    6 KB (711 words) - 11:28, 16 September 2013
  • HW5.2 Jacob Pfister ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (270 words) - 12:24, 16 September 2013
  • HW5.3 Jacob Pfister ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (252 words) - 12:41, 16 September 2013
  • HW5.3 Naman Chopra ECE301Fall2008mboutin
    Specify a Fourier transform X(w) and compute its inverse Fourier transform using the integral formula. (Make it difficult).
    123 B (19 words) - 11:20, 3 October 2008
  • HW5.2 Naman Chopra ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    913 B (139 words) - 12:24, 16 September 2013
  • HW5.2 Jeff Kubascik ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (279 words) - 12:25, 16 September 2013
  • HW5.3 Jeff Kubascik ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    2 KB (384 words) - 12:42, 16 September 2013
  • HW5.2 Ronny Wijaya ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (215 words) - 12:26, 16 September 2013
  • HW5.3 Ronny Wijaya ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    966 B (151 words) - 12:42, 16 September 2013
  • HW5.2 Wei Jian Chan ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (213 words) - 12:26, 16 September 2013
  • HW5.3 Wei Jian Chan ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (167 words) - 12:42, 16 September 2013
  • HW5.3 Bavorndej Chanyasak ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    905 B (142 words) - 12:45, 16 September 2013
  • HW5.2 Nicholas Block ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    759 B (126 words) - 12:27, 16 September 2013
  • HW5.3 Nicholas Block ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (206 words) - 12:44, 16 September 2013
  • HW5.2 Max Paganini ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (171 words) - 12:28, 16 September 2013
  • HW5.2 Steve Anderson ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (260 words) - 12:28, 16 September 2013
  • HW5.2 Eric Zarowny ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (191 words) - 12:29, 16 September 2013
  • HW5.2 Daniel Morris ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (281 words) - 12:29, 16 September 2013
  • HW5.2 Scott Hamilton ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (263 words) - 12:30, 16 September 2013
  • HW5.3 Eric Zarowny ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1,011 B (164 words) - 12:46, 16 September 2013
  • HW5.3 Steve Anderson ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (156 words) - 12:46, 16 September 2013
  • HW5.3 Scott Hamilton ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    2 KB (379 words) - 12:47, 16 September 2013
  • HW5.2 Josh Long ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (292 words) - 12:27, 16 September 2013
  • HW5.2 Sangwan Han ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (199 words) - 12:31, 16 September 2013
  • HW5.2 Bavorndej Chanyasak ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (183 words) - 12:31, 16 September 2013
  • HW5.3 Daniel Morris ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (187 words) - 12:43, 16 September 2013
  • HW5.2 David Record ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    881 B (135 words) - 12:31, 16 September 2013
  • HW5.3 Sangwan Han ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    847 B (132 words) - 12:46, 16 September 2013
  • HW5.3 Josh Long ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (240 words) - 12:45, 16 September 2013
  • HW5.4 Jun HYeong Park ECE301Fall2008mboutin
    I feel that computing Fourier Transform of summation problem.
    108 B (16 words) - 17:25, 7 October 2008
  • HW5.2 Jun Hyeong Park ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (188 words) - 12:33, 16 September 2013
  • HW5.2 Brian Thomas ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (309 words) - 12:33, 16 September 2013
  • HW5.4 Jun Hyeong Park ECE301Fall2008mboutin
    It was too hard to get fourier transform of summation term.
    97 B (16 words) - 18:19, 7 October 2008
  • HW5.2 Joseph Mazzei ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (176 words) - 12:32, 16 September 2013
  • HW5.3 Jun Hyeong Park ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    848 B (136 words) - 12:49, 16 September 2013
  • HW5.3 Brian Thomas ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    2 KB (368 words) - 12:49, 16 September 2013
  • HW5.4 Brian Thomas ECE301Fall2008mboutin
    ...he sin's and cos's to exponentials, and chug away. However, the beautiful transform equation turns into alphabet soup after all this happens, and it's really h
    667 B (107 words) - 18:49, 7 October 2008
  • HW5.2 Jonathan Morales ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (233 words) - 12:34, 16 September 2013
  • HW5.2 Jessica Sparks ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1,015 B (175 words) - 12:34, 16 September 2013
  • HW5.3 Jessica Sparks ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    943 B (144 words) - 12:50, 16 September 2013
  • HW5.1 Allen Humphreys ECE301Fall2008mboutin
    ...operties of integrating an absolute value and the linearity of the Fourier transform. Apply the inverse fourier transform integral:
    8 KB (1,324 words) - 18:59, 8 October 2008
  • HW5.2 Xujun Huang ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (266 words) - 12:35, 16 September 2013
  • HW5.3 Xujun Huang ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    921 B (156 words) - 12:50, 16 September 2013
  • HW5.2 Ryan Scott ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (177 words) - 12:35, 16 September 2013
  • HW5.3 Max Paganini ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (168 words) - 12:51, 16 September 2013
  • HW5.3 Ryan Scott ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    846 B (122 words) - 12:51, 16 September 2013
  • HW5.2 Caleb Tan ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    845 B (149 words) - 12:36, 16 September 2013
  • HW5.3 Joseph Mazzei ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    981 B (144 words) - 12:47, 16 September 2013
  • HW5.2 Chris Cadwallader ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    842 B (140 words) - 12:30, 16 September 2013
  • HW5.3 Caleb Tan ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    906 B (151 words) - 12:51, 16 September 2013
  • HW5.2 Tyler Houlihan ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (192 words) - 12:35, 16 September 2013
  • HW5.4 Caleb Tan ECE301Fall2008mboutin
    ...cept of a CT Fourier transform. When it is in DT it is easy to express the Fourier coefficients. We just need to express all the coefficients in one period. B
    320 B (61 words) - 14:03, 8 October 2008
  • HW5.4 Chris Cadwallader ECE301Fall2008mboutin
    Im having difficulty with D.T. Fourier Transforms Im having a hard time visualizing how you can transform from a DT signal to the frequency domain with a summation and back again wi
    426 B (77 words) - 14:22, 8 October 2008
  • Lecture17 ECE301Fall2008mboutin
    Fourier Transforms and the frequency response of a system. ...response has a fundamental relationship to the unit step response through Fourier Transforms as follows
    3 KB (449 words) - 17:07, 8 October 2008
  • HW5.3 Tyler Houlihan ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    929 B (140 words) - 12:48, 16 September 2013
  • HW5.2 Eric Smith ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (179 words) - 12:32, 16 September 2013
  • HW5.2 Adrian Delancy ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (353 words) - 12:23, 16 September 2013
  • HW5.2 Adam Forkner ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (181 words) - 12:36, 16 September 2013
  • HW5.4 Wei Jian Chan ECE301Fall2008mboutin
    Fourier Series Transformation - I had problems in determining which frequency is th Fourier Transform -
    402 B (70 words) - 16:57, 8 October 2008
  • HW5.2 I-Cheng Chen ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (218 words) - 12:25, 16 September 2013
  • HW5.2 Tyler Johnson ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (218 words) - 12:22, 16 September 2013
  • HW5.3 Adam Forkner ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    919 B (145 words) - 12:52, 16 September 2013
  • HW5.2 Carlos Leon ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (280 words) - 12:37, 16 September 2013
  • HW5.3 Eric Smith ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    757 B (115 words) - 12:48, 16 September 2013
  • HW5.3 David Record ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (184 words) - 12:47, 16 September 2013
  • HW5.2 David Hartmann ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (177 words) - 12:24, 16 September 2013
  • HW5.3 Tyler Johnson ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (239 words) - 12:39, 16 September 2013
  • HW5.3 Carlos Leon ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    917 B (138 words) - 12:52, 16 September 2013
  • HW5.2 Daniel Barjum ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    965 B (145 words) - 12:37, 16 September 2013
  • HW5.3 Adrian Delancy ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (160 words) - 12:40, 16 September 2013
  • HW5.3 I-Cheng Chen ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (201 words) - 12:44, 16 September 2013
  • HW5.3 David Hartmann ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (220 words) - 12:40, 16 September 2013
  • HW5.4 David Hartmann ECE301Fall2008mboutin
    I still have difficulty calculating Fourier Transform coefficients.
    67 B (8 words) - 18:37, 8 October 2008
  • HW5.3 Daniel Barjum ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (203 words) - 12:53, 16 September 2013
  • HW5.2 Naman Verma ECE301Fall2008mboutin
    [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (206 words) - 12:36, 16 September 2013
  • HW5.3 Naman Verma ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (161 words) - 12:52, 16 September 2013
  • HW5.3 Chris Cadwallader ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    803 B (124 words) - 12:49, 16 September 2013
  • Incorrect CT FT periodic signal 1 ECE301Fall2008mboutin
    '''Question:''' Compute the Fourier transform of the signal x(t) equal to: The Fourier Transform of a signal in Continuous Time is defined by:
    1 KB (188 words) - 11:09, 17 October 2008
  • Correct CT FT 1 ECE301Fall2008mboutin
    '''Question:''' Compute the Fourier transform of the signal
    882 B (162 words) - 13:42, 24 October 2008
  • Homework 7 ECE301Fall2008mboutin
    * [[David Record - Fourier Transform Quiz Explanation _ECE301Fall2008mboutin]] * [[Fourier Transform of x(at+b) when the transform of x(t) is known_ECE301Fall2008mboutin]] (Brian Thomas)
    3 KB (406 words) - 11:28, 16 September 2013
  • Examples ECE301Fall2008mboutin
    [[Category:Fourier transform]] Compute the Fourier Transform of <math>x(t)=e^{-t}u(t)</math>.
    4 KB (753 words) - 16:48, 23 April 2013
  • Midterm Exam Div 2 Fall 2006 Solution ECE301Fall2008mboutin
    ...he right way: taking the inverse Fourier transform, instead of the Fourier transform. The explanation is crystal clear and logical. No important step is missing ...on. The Transformed output is a imaginary and even signal,thus the Fourier transform is wrong.
    11 KB (1,951 words) - 03:48, 25 March 2011
  • Austin Melnyk - HW 7 Contribution ECE301Fall2008mboutin
    ...the exam that is coming up is to remember that you cannot take the fourier transform of a signal using the table in the book when the signal is in CT form. ...means use the set transforms in the book or formula sheet to write out the transform.
    970 B (186 words) - 18:20, 22 October 2008
  • David Record - Fourier Transform Quiz Explanation ECE301Fall2008mboutin
    == Explanation of Wednesday October 22nd In-Class Quiz on Fourier TRansform== ...d been time inverted and time shifted by using the definition of a Fourier Transform. The quiz consisted of two very similar questions. The first was to be answ
    2 KB (296 words) - 15:39, 30 November 2010
  • Fourier Transform of x(at+b) when the transform of x(t) is known ECE301Fall2008mboutin
    ...being sure, perhaps it would be better to use the definition of a Fourier transform to solve this.
    2 KB (302 words) - 09:07, 23 October 2008
  • Sangwan Han - Brief explanation and Example question for Fourier Transform ECE301Fall2008mboutin
    == Brief explanation about Fourier Transform == for the CT Fourier Transform, there are two important formulas that we have to know which are,
    2 KB (345 words) - 10:01, 23 October 2008
  • Justin Kietzman - Time Shifting property of F.T and you ECE301Fall2008mboutin
    We can solve by the definition of a Fourier Transform
    1 KB (256 words) - 09:42, 23 October 2008
  • Zachary Curosh - Frequency Response and Difference Equations ECE301Fall2008mboutin
    ...equation of the above form, one can apply simple mathematical and Fourier Transform properties to get an equation of the form
    2 KB (401 words) - 17:16, 21 April 2013
  • The Importance of Foresight in Solving Certain types of F.T. Problems ECE301Fall2008mboutin
    ...ut thinking, you rush into the problem using the definition of the Fourier Transform...
    3 KB (665 words) - 19:39, 23 October 2008
  • Joshua Long ECE301Fall2008mboutin
    ...on allows us to fit functions to the known ones given by the known Fourier Transform pairs table.
    2 KB (284 words) - 10:14, 24 October 2008
  • Tyler Houlihan - Difference equations - a few examples with Partial Fraction Expansion explanation ECE301Fall2008mboutin
    1) Take the fourier transform of every term: Now finally to find <math>\,h[n]</math>, take the inverse Fourier Transform:
    4 KB (633 words) - 11:13, 24 October 2008
  • Monil Goklani - AM Modulation ECE301Fall2008mboutin
    ...suppose the input signal was multiplied by a cosine wave then the fourier transform of the wave would look as follows
    448 B (80 words) - 10:24, 24 October 2008
  • Bavorndej Chanyasak - Frequency Response ECE301Fall2008mboutin
    First, we do the Fourier transform on both sides, which yields:
    1 KB (197 words) - 10:50, 24 October 2008
  • Thomas Wroblewski - HW7 Contribution ECE301Fall2008mboutin
    ...thought it would be a good idea to do some examples of how to do a Fourier Transform to help clarify the process. Using the Fourier Transform Equation:
    3 KB (504 words) - 13:03, 24 October 2008
  • HW 7 Allen Humphreys ECE301Fall2008mboutin
    ==Continuous Time Fourier Transform Pair for Aperiodic and Periodic Signals== The Fourier transform exists if the signal is absolutely integrable or if the signal has a finite
    3 KB (465 words) - 14:38, 24 October 2008
  • Jonathan Morales - Differentiation in time ECE301Fall2008mboutin
    '''Proof''': Differentiating the inverse Fourier Transform <math>X(\omega) \,\ </math> with respect to t we get.
    670 B (123 words) - 14:09, 24 October 2008
  • Joseph Mazzei - Main Points for Exam 2 ECE301Fall2008mboutin
    == CT Fourier Transform == *[[CT Fourier Transform_ECE301Fall2008mboutin]] {{:CT Fourier Transform}}
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  • Carlos Leon ECE301Fall2008mboutin
    Fourier Transform of delta functions
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  • Emily Blount: DT and CT frequency response for systems characterized by Linear, Constant coefficients, Difference Equations ECE301Fall2008mboutin
    Then the Fourier Transform: Then the Fourier Transform:
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  • Wei Jian Chan: Chapter 7 key points ECE301Fall2008mboutin
    Consider <math>x(t)\,</math> as a signal with Fourier transform of <math>X(\omega)=0</math> when <math>|\omega|>\omega_m</math>. <math>x(t)
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  • HW8 - Zachary Curosh: Impulse-train Sampling ECE301Fall2008mboutin
    This answer can be found simply by using the Fourier Transform of the <math>X_p(\omega) </math>.
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  • Sourabh Ranka: Sampling Theorem ECE301Fall2008mboutin
    ...inuous-time signal and X(j<math>\omega\,</math>) be the continuous Fourier transform of that signal. Then,
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  • SangMo Je: HW ECE301Fall2008mboutin
    ...a continuous-time signal and <math>X(W)\,</math> be the continuous Fourier transform of that signal
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  • SangMo Je: Nyquist–Shannon sampling theorem ECE301Fall2008mboutin
    ...a continuous-time signal and <math>X(w)\,</math> be the continuous Fourier transform of that signal (which exists if <math>x(t)\,</math> is square-integrable)
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  • David Record: Sampling- A bridge between CT and DT ECE301Fall2008mboutin
    Taking the Fourier Transform of this function yields,
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  • Daniel Morris: Amplitude modulation with Sinusoidal Carrier ECE301Fall2008mboutin
    so <math>y(t)=x(t)c(t)</math>. Then by taking the Fourier Transform of both sides of this equations yields <math>y(\omega)</math>. Also, for co
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  • Justin Kietzman ECE301Fall2008mboutin
    ...rm. In fact, the Fourier Transform is just the restriction of the Laplace transform to the imaginary axis, in other words, s=jw. ===Trying a Laplace Transform===
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  • Monil Goklani ECE301Fall2008mboutin
    then the fourier transform of the wave would look as follows
    971 B (172 words) - 17:48, 17 November 2008
  • Jessica Sparks ECE301Fall2008mboutin
    ...>|{\omega}| > \omega_M</math> where <math>X(j\omega)</math> is the Fourier Transform of the signal we are sampling. This means that <math>X(j\omega)</math> can ...they would interfere with eachother and make something new so when Inverse Fourier Transforming the signal you would not get back the original signal.
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  • Sourabh Ranka ECE301Fall2008mboutin
    taking the fourier transform
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  • Max Paganini: Properties of Region of Convergence (ROC) ECE301Fall2008mboutin
    ROC of the Laplace Transform consists of vertical strips in the complex plane (could be empty or could b ...th> consists of those <math> s = a + j\omega </math> for which the Fourier Transform of <math> x(t)e^{-at} </math> converges.
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  • Homework 10 ECE301Fall2008mboutin
    == '''Fundamentals of Laplace Transform''' == Here is how to compute the Laplace Transform of <math>x(t)</math>:
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  • Homework ECE301Fall2008mboutin
    ...C of X(s) consists of those <math>s=a+j\omega</math> for which the Fourier transform of <math>x(t)e^{-at}</math> converges. This condition only depends of a.
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  • HW10 Jun Hyeong Park ECE301Fall2008mboutin
    == Laplace Transform == The laplace transform of a general signal <math> x(t) </math> is defined as
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  • HW10 Sourabh Ranka ECE301Fall2008mboutin
    ==Laplace Transform== The Laplace transform of a function ''f''(''t''), defined for all real numbers, is the function '
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  • HW10 Zachary Curosh - Laplace Transform and Basic Properties ECE301Fall2008mboutin
    == The Laplace Transform == ...axis, <math>j\omega\!</math>, (as the Fourier Transform does) the Laplace Transform considers all complex values represented by the general complex variable <m
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  • HW10 SangMo je ECE301Fall2008mboutin
    == definition of laplace transform == The Laplace transform of a function ''f''(''t''), defined for all real numbers ''t'' ≥ 0, is th
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  • HW10 Seung Seob Lee ECE301Fall2008mboutin
    == The relationship between Fourier and Laplace transform == The continuous-time Fourier transform provides us with a representation for signals as linear combinations of com
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  • HW10 Daniel Barjum: Example illustration relationship between Fourier and Laplace transform ECE301Fall2008mboutin
    [[Category:Fourier transform]] [[Category:Laplace transform]]
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  • HW10 Vivek Ravi Region of Convergence for Laplace Transforms ECE301Fall2008mboutin
    In a nutshell Laplace transform is a generalization of Fourier transform. Laplace transforms can be applied to the analysis of many unstable systems The Laplace transform of a general signal x(t) is defined as
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  • HW11 Zachary Curosh - Z-transform and Basic Properties ECE301Fall2008mboutin
    [[Category:z transform]] == The Z-Transform ==
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  • HW11 SangMo Je ECE301Fall2008mboutin
    == Basic definition of the Z-Transform == The Z-transform of a sequence is defined as <math>H(z) = \sum^{\infty}_{n = -\infty} h[n]z^
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  • Exam3 ECE301Fall2008mboutin
    CT Fourier Transform Pair DT Fourier Transform Pair
    21 KB (3,312 words) - 11:58, 5 December 2008
  • Chapter 10 ECE301Fall2008mboutin
    1. '''The z-Transform''' ...ore general case of transform called z-Transform. The development of the z-Transform is outlined in Chapter 10.1 of the Oppenheim and Wilsky text.
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  • Final ECE301Fall2008mboutin
    ...transforms, bi-lateral Laplace transforms, Z transforms, and discrete time Fourier transforms and an ability to compute the transforms and inverse transforms ===[[Chapter 3_ECE301Fall2008mboutin]]: Fourier Series Representation of Period Signals===
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  • Chapter 9 ECE301Fall2008mboutin
    1. '''The Laplace Transform''' "Here I come to save the day!" ...and if <math> \sigma = 0 </math> then this equation reduces to the Fourier Transform of <math>x(t)</math>. Indeed, the LT can be viewed as the FT of the signal
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  • Chapter 7 ECE301Fall2008mboutin
    ...if x(t) is band-limited, one must exam <math>X(\omega)</math> the Fourier transform of x(t).
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  • 4.1 ECE301Fall2008mboutin
    ...operties of integrating an absolute value and the linearity of the Fourier transform.
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  • 4.4 ECE301Fall2008mboutin
    Apply the inverse fourier transform integral:
    1 KB (172 words) - 12:10, 12 December 2008
  • 4.5 ECE301Fall2008mboutin
    Find the inverse Fourier transform of:
    1 KB (242 words) - 12:11, 12 December 2008
  • Mathematician Cracks Mystery Beatles Chord MA453Fall2008walther
    ...y and see if he could apply a mathematical calculation known as '''Fourier transform''' to solve the Beatles’ riddle. The process allowed him to decompose the
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  • Comb Function Old Kiwi
    = Fourier Properties = The fourier transform of the comb function is the [[rep function_Old Kiwi]].
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  • ECE662:Glossary Old Kiwi
    ...aussian noise on both x and y. In some cases, PCA corresponds to a Fourier transform, such as the DCT used in JPEG image compression.
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  • Chapter 4 Old Kiwi
    [[Convergence of Fourier Transforms_Old Kiwi]] [[Fourier Transform table_Old Kiwi]]
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  • Duality property Old Kiwi
    I found something interesting when you use duality on the same transform pair over and over... Note: I can not find a way to display a proper fourier symbol, so I went with the <math>\quad\displaystyle{\bf{F}} </math> as seen
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  • References Old Kiwi
    * [[Fourier, Laplace and Z-Transform Equation Reference Sheet_Old Kiwi]]
    607 B (80 words) - 14:27, 30 March 2008
  • Frequency Response Example Old Kiwi
    1: Take the Fourier transform ([Meaning of Fourier Transform]) of the equation, ...uide to Partial Fraction Expansion]) to facilitate use of inverse Fourier transform,
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  • Homework Problem 5.31 Old Kiwi
    ...0 </math>is actually <math>\omega</math> when you want to take the inverse transform and therefore it is a variable and not a constant. So when you write the in ...division by zero. I also don't understand why the integral for the inverse transform is taken of -pi to pi when the solution key previously restricted it from 0
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  • Principal Component Analysis Old Kiwi
    ...aussian noise on both x and y. In some cases, PCA corresponds to a Fourier transform, such as the DCT used in JPEG image compression.
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  • ECE301:SanSummer08 Old Kiwi
    ##[[Fourier Series representation of continuous-time periodic signals_Old Kiwi]] ##[[Fourier Series Representation of CT periodic signals_Old Kiwi]]
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  • Guide to Partial Fraction Expansion Old Kiwi
    ...on allows us to fit functions to the known ones given by the known Fourier Transform pairs table. ...obtaining the capital letters quickly are from learning to do the Laplace Transform in ECE 202.
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  • ECE301:SanSummer08:Exam II Old Kiwi
    1)a)If a discrete time singal x[n] is periodic with period N, then the Fourier series coefficients <math>a_k</math> of the signal x[n] is also periodic wi ...er a continuous-time periodic signal x(t) with period T = 5 whose non-zero Fourier series coefficients <math>a_k</math> are given by
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  • Course Summary ECE438Fall09mboutin
    *Fourier Series ** PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
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  • Hw3ECE438F09boutin
    [[Important properties of Z-Transform]] --[[User:kakyel|kakyel]] [[Convergence of Z Transform|Convergence of Z Transform, ECE 438 Notes Sept. 2, 2009]] --[[User:kmhacker|kmhacker]]
    4 KB (543 words) - 07:02, 25 August 2010
  • Student summary Discrete Fourier transform ECE438F09
    [[Category:discrete Fourier transform]] == DFT ( Discrete Fourier Transform ) ==
    4 KB (695 words) - 06:46, 23 September 2011
  • Exams/Quizzes
    ...ill cover all material covered ''since'' the Midterm (including CT Fourier Transform). A list of topics include * CT Fourier Transform
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  • Homework 5
    ...scriptive to their content while still including your name, e.g. [[Fourier Transform - Landis Huffman]]
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  • HW 3.3 - Ryne Rayburn ECE301 Summer2009
    '''''Linearity'' - Property of Continuous Time Fourier Transform'''
    2 KB (327 words) - 08:33, 8 July 2009
  • HW 3.3 - Adam Frey ECE301 Summer2009
    Proof of ''Parseval's Relation'' in Continuous-Time Transform 4.3.7 If x(t) and X(jt) are a Fourier transform pair, then :
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  • HW 3.3 - Walter Mulflur ECE301 Summer2009
    (The right hand side of this equation is the Fourier transform analysis equation for x*(t))
    832 B (147 words) - 04:37, 9 July 2009
  • HW 3.3 - Howard Ho ECE301 Summer2009
    Aperiodic signal <===> Fourier transform
    521 B (90 words) - 12:57, 8 July 2009
  • HW 3.3 - Muhammad Aizuddin Zulkifli ECE301 Summer2009
    Time Shifting property of the Fourier Transform
    179 B (24 words) - 16:37, 8 July 2009
  • HW 3.3 - Takashi Nakachi ECE301 Summer2009
    Proving the property of Linearity in Fourier Transform: Summing the two prior to transform we derive
    663 B (121 words) - 15:17, 8 July 2009
  • HW 3.3 - Xiaodian Xie ECE301 Summer2009
    Suppose z(t) = {ax(t)+by(t)}, then the fourier transform of z is z(w)=d^(-1)/dt((ax(t)+by(t))*exp(-jwt))
    249 B (58 words) - 18:03, 8 July 2009
  • HW 3.3 - Tylor Thompson ECE301 Summer2009
    By definition of Fourier Transform:
    384 B (82 words) - 18:49, 8 July 2009
  • HW 3.3 - Lu Zhang ECE301 Summer2009
    Property: Linearity in Fourier Transform: The fourier transform of ax(t) is the integration of 1/T * (ax(t)*exp(-jwt))
    378 B (68 words) - 21:45, 8 July 2009
  • HW 3.3 - Evan Witkoske ECE301 Summer2009
    Define a function x(t) with its Fourier transform being X(jw) so '''Fourier transform'''(x(t)') = jwX(jw)
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  • HW 3.3 - Tyler Mattmuller ECE301 Summer2009
    ...with a multiplication operation in the frequecy domain for easier Fourier transform enalysis
    530 B (101 words) - 04:45, 9 July 2009
  • HW 3.3 - Stuart Pulliam ECE301 Summer2009
    Proving that the Continuous-Time Fourier Transform demonstrates linearity
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  • Midterm Cheat Sheet
    == Fourier Series == * [[CT Fourier series expansion]]
    1 KB (152 words) - 04:06, 23 July 2009
  • CT Fourier transform
    [[CT Fourier Transform - Xiaodian Xie]]
    39 B (6 words) - 11:53, 19 July 2009
  • CT inverse Fourier transform
    [[CT Inverse Fourier Transform -- Alex Gaul]]
    45 B (7 words) - 14:31, 22 July 2009
  • CT Fourier transform properties
    [[Continuous Time Fourier Transform (CTFT) - Muhammad Aizuddin Zulkifli]]
    73 B (9 words) - 16:54, 22 July 2009
  • DT Fourier series properties
    [[Discrete Time Fourier Transform Properties (DTFT) - Evan Witkoske]] [[Discrete Time Fourier Transform Properties (DTFT) - Mohammed Almathami]]
    145 B (18 words) - 04:36, 23 July 2009
  • CTFS Property: - Ali Alyoussef
    CT Fourier Transform Properties
    1 KB (178 words) - 04:40, 23 July 2009
  • Discrete Time Fourier Transform Properties (DTFT) - Mohammed Almathami
    [[Category:discrete time Fourier transform]] =DT Fourier Transform Properties=
    537 B (85 words) - 07:16, 14 November 2011
  • Final Cheat Sheet
    == CT Fourier Transform (Book chapter 4)== * [[CT Fourier transform]]
    1 KB (118 words) - 01:11, 30 July 2009
  • Homework 6
    ...scriptive to their content while still including your name, e.g. [[Fourier Transform - Landis Huffman]]
    288 B (42 words) - 09:50, 23 July 2009
  • ECE301 (BoumanFall2009)
    *Continuous Time Fourier Series (CTFS) **[https://engineering.purdue.edu/~bouman/ece301/notes/pdf2/FourierSeries.pdf Fourier Series Expansion]
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  • Peer Legacy ECE202
    ...438, ECE440), bode plots (ECE382), and Laplace transforms (these roll into Fourier Transforms). The second year courses are the ones that count the MOST in yo ...minute by [[ECE202]. This course was a good introduction into the Fourier Transform and the frequency domain with the Laplace Transforms. The knowledge in this
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  • DT Fourier transform
    [[DT Fourier Transform - William Owens]]
    40 B (6 words) - 07:29, 26 July 2009
  • The Pirate's Booty
    b) As noted, the inverse fourier transform is only equal a.e. to f. Needs more work.
    3 KB (404 words) - 05:58, 11 June 2013
  • Number two, ye scallywags!
    Definition of Fourier Transform:
    1 KB (264 words) - 05:57, 11 June 2013
  • Number five, me hearties!
    Define the Fourier Transform to be:
    2 KB (315 words) - 05:55, 11 June 2013
  • Number thirteen is walkin' the plank
    b) From the reverse Fourier Transform we know that <math>f(t)=\int\hat{f}(x)e^{2\pi ixt}dx</math>
    1 KB (207 words) - 05:57, 11 June 2013
  • Laplace Transform Definition - Vishal Ramani
    == Laplace Transform == The Laplace Transform of any signal '''<math>x(t)</math>''' is....
    388 B (72 words) - 06:39, 29 July 2009
  • DT inverse Fourier transform
    [[Ryne Rayburn - ECE 301 - DT Inverse Fourier Transform]]
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  • Ryne Rayburn - ECE 301 - DT Inverse Fourier Transform
    == DT Inverse Fourier Transform ==
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  • MA598R 7.2
    Define the Fourier transform of <math>f \in L^1(\mathbb{R})</math> by Applying the definitions of Fourier transform and convolution, followed by Fubini (since <math>f, g \in L(\mathbb{R})</ma
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  • Number six, thar she blows!
    From the Inverse Fourier Transform we clearly see that <math>f\equiv 0</math> a.e.
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  • Number 11, Pirates Team
    [[Category:Fourier transform]] 11.) Compute the Fourier transform of <math>H(x) = (4\pi)^{-\frac{n}{2}}e^{-\frac{|x|^2}{4}}, x \in {\mathbb R
    4 KB (797 words) - 05:54, 11 June 2013
  • Relationship between DTFT & Z-Transform - Howard Ho
    [[Category:discrete-time Fourier transform]] [[Category:z-transform]]
    1 KB (216 words) - 14:49, 1 May 2015
  • ROCs in Laplace transform
    ...tence of Laplace transform $X(s)$ of a given $x(t)$ depends on whether the transform integral converges ...le and of finite duration, then the ROC is the entire s-plane (the Laplace transform integral is finite, i.e., $X(s)$ exists, for any $s$).
    3 KB (494 words) - 04:22, 30 July 2009
  • DTFT periodicity - Mark Scherschel (mschersc)
    [[Category:discrete time Fourier transform]]
    201 B (31 words) - 07:18, 14 November 2011
  • Laplace/Fourier transform comparison
    [[Laplace/Fourier Transform Comparison -- Yicheng Guo]]
    55 B (7 words) - 04:54, 30 July 2009
  • Laplace/Fourier Transform Comparison -- Yicheng Guo
    Laplace Transform is an extension of Fourier Transform.
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  • ECE 438 Fall 2009 mboutin Definitions
    the properties of the Fourier Transform and other stuff. Plus it has proofs! http://fourier.eng.hmc.edu/e101/lectures/handout3/handout3.html
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  • Student summary CT DT Fourier transform ECE438F09
    CTFT ( Continuous Time Fourier Transform ) DTFT ( Discrete Time Fourier Transform )
    2 KB (375 words) - 04:11, 3 September 2009
  • Hw2 discussion (ECE438BoutinFall09)
    *for Question 1, I obtained the Fourier transform in terms of the general zeros and poles, and then replaced, say z1 by r1.ex ...etc. But at any rate, are we supposed to be plotting magnitude of Fourier Transform over 0 to 2*pi radians? I think the directions are very unclear. -- rscheid
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  • Essay contest discussion
    ...d one math related. I was thinking of "Why you should cherish the Fourier transform" for EE. Somebody suggested "The future of operating systems" for Compe/CS.
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  • Student summary sampling part1 ECE438F09
    ...on is conveniently packaged within the complex coefficients of the Fourier Transform. So if it is understood that a sinsuoid must be sampled twice within a sing ...f x(t) with the frequency domain representation of p(t). Since the Fourier Transform of the comb is also an impulse train in the frequency domain, the convoluti
    8 KB (1,452 words) - 06:49, 16 September 2013
  • EssayContestFall2009
    ** Examples: the Fourier Transform for Engineering, or perhaps the theory of NP-Completeness for Computer Scie
    1 KB (204 words) - 10:04, 16 September 2009
  • GPS Signal Processing
    ...d to improved signal processing and has led to the use of the Fast Fourier Transform. The Fast Fourier Transform (FFT) can be seen below as the correlation between the incoming and referen
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  • HW3 Abish
    Taking the Fourier transform of Eq. 3 gives:
    3 KB (527 words) - 11:50, 22 September 2009
  • Speech Spectrogram
    ==Fourier Analysis and the Speech Spectrogram== ...ency component's contribution to the original signal. Finally, the Fourier Transform is calculated to express these coefficients as a function of frequency. Fo
    8 KB (1,268 words) - 07:16, 23 September 2009
  • Notes on Discrete Fourier Transform
    [[Category:discrete Fourier transform]] =Notes on Discrete Fourier Transform=
    3 KB (640 words) - 13:17, 2 December 2011
  • HW3 Signal Reconstruction Interpolation
    :1) It is band-limited. This means that the Fourier transform of the original signal, also known as the spectrum, is 0 for |f| > B, where
    2 KB (436 words) - 19:51, 22 September 2009
  • 9-21 lecture note
    == Discrete Fourier Transform == same formula as for discrete fourier series.
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  • Rep and Comb functions : Lecture on 26/08/09
    '''Note''': The Fourier Transform of a <math> rep_T </math> x(t) gives the comb function of x(t) but in the f ...rep operator surfaces when we take the operator's Continuous Time Fourier Transform :
    2 KB (365 words) - 07:38, 25 August 2010
  • DSP in Guitar Effects
    ...ify different frequency components of the signal. Once we have the fourier transform, we can start applying some effects to the sound. ...n has been done to the signal in the frequency domain, the inverse fourier transform is taken and the signal is coverted back to analog to be played through an
    1 KB (206 words) - 09:10, 23 September 2009
  • Fourier Transforms and its Properties
    ==Fourier Transform and its basic Properties:== ===Fourier Transform:===
    1 KB (218 words) - 07:34, 25 August 2010
  • Fourier Optics
    ...m. In this article I will go over a simple example of how to use a Fourier transform to describe the diffraction pattern encountered when light passes through a where 2a is the width of the slit. Now, taking the Fourier transform of the aperture shape we get:
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  • Collective Table of Formulas
    **[[Laplace Transforms Table|(bidirectional) Laplace Transform Pairs and Properties]] (used in [[ECE301]], [[ECE438]]) **[[unidirectional_Laplace_Transform_Table|(unidirectional) Laplace Transform Pairs and Properties]]
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  • Male vs. Female Voice characterestics
    ...is under the threshold level.Spectrograms are based on Short Time Fourier Transform(STFT),where the input signal is broken down into blocks and then DFT of eac
    2 KB (356 words) - 06:07, 23 September 2014
  • DTFourierTransformCollectedfromECE301
    ..."2" style="background: #e4bc7e; font-size: 110%;" | Discrete-time Fourier Transform Pairs and Properties ! colspan="2" style="background: #eee;" | DT Fourier transform and its Inverse
    2 KB (351 words) - 12:52, 22 October 2010
  • CT Fourier Transform (frequency in radians per time unit)
    [[Category:Fourier transform]] Table of Continuous-time (CT) Fourier Transform Pairs and Properties
    8 KB (1,130 words) - 11:45, 24 August 2016
  • More on CT Fourier transform
    =About the Continuous-time Fourier Transform= *[[Examples_ECE301Fall2008mboutin|Example of computation of a Fourier transform]] (from [[ECE301]], Fall 2008)
    2 KB (262 words) - 12:14, 21 February 2011
  • Introduction to Wavelets
    '''Taking Fourier's torch forward...''' ...e first person that comes to mind when someone says "SIGNAL PROCESSING" is Fourier.
    10 KB (1,646 words) - 11:26, 18 March 2013
  • 2D Signals-Rect(x,y)
    [[Category:continuous-space Fourier transform]] ...ct|rect function]] lies in the origin of the image plot and on the fourier transform plot, those DC components should coincide with the center of the plot. But
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  • Student summary spectral analysis 2D signalsb
    [[Category:continuous-space Fourier transform]] ...not much different from the one-dimensional (1D) FFT <small>(Fast Fourier Transform - see [http://en.wikipedia.org/wiki/Fast_Fourier_transform])</small> that w
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  • Student summary spectral analysis 2D signals
    ...om the Continuous-Space Fourier Transform(CSFT) definitons and its inverse transform. *Forward transform- <math>F(u,v) = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}{f(x,y)e^{-j2
    5 KB (950 words) - 15:17, 30 November 2010
  • ECE 438 Fall 2009 mboutin plotCSFTofbasicfilters
    [[Category:discrete-space Fourier transform]]
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  • Peer Legacy ECE301
    ...to take any courses related to signal processing. Also, your concepts of Fourier and Z transforms should be absolutely clear for signal processing (DSP ECE ...s. ECE301 course introduces some transforms such as laplace, furiere and z-transform and signals and systems of continuous-time and discrete-time. However, it c
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  • Peer Legacy ECE438
    ...8 is pretty similar to ECE301. You will learn about furier transfrom and z-transform again, which you learned from ECE301. By taking ECE438, I understand better ...t is much more interesting than the endless [[More_on_CT_Fourier_transform|Fourier transforms]] of ECE301. To attain success: '''go to class!''' Missing a sin
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  • Image Processing Recitation
    If we Fourier Transform the filter, we discover that the filter is linear:
    5 KB (811 words) - 16:19, 19 December 2009
  • Discrete Fourier Transform table
    Discrete Fourier transforms (DFT) Pairs and Properties ...="2" | Discrete Fourier Transform Pairs and Properties [[Discrete Fourier Transform|(info)]]
    4 KB (633 words) - 15:28, 23 April 2013
  • Snikitha ListECE301
    ...ystems: difference equations, Discrete-Time Fourier Transform, bilateral z-Transform. Sampling, quantization, and discrete-time processing of continuous-time si ...transforms, bilateral Laplace transforms, Z transforms, and discrete time Fourier transforms and an ability to compute the transforms and inverse transforms
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  • My use for the DFT!
    [[Category:discrete Fourier transform]] In [[ECE301|ECE 301]] students were introduced to the concept of Fourier Transforms. No matter whom you had been taught by it seemed intimidating an
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  • 2010 Fall ECE 438 Boutin
    **[[Practice_Question_2_ECE439F10|Practice Question 2 (on z-transform computation)]] **[[Practice_Question_3_ECE439F10|Practice Question 3 (on inverse z-transform computation)]]
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  • Lecture Schedule ECE438Fall10 Boutin
    *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
    9 KB (1,331 words) - 07:15, 29 December 2010
  • 2010 Fall ECE 301 Pollak
    ...xercise_Fourier_series_computation|A collective page to practice computing Fourier series of a CT signal]] ...cise_Fourier_series_computation_DT|A collective page to practice computing Fourier series of a DT signal]]
    2 KB (211 words) - 05:39, 26 September 2011
  • Lecture2ECE438F10
    ...n terms of frequency "f" and discussed its relationship with the frequency transform in terms of <math>\omega</math>. The "rep" and "comb" functions were introd *[[Student_summary_CT_DT_Fourier_transform_ECE438F09|Summary of CT and DT Fourier transforms]]
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  • Hw1ECE38F10
    ...of CT Fourier transform pairs and properties]], which used the CT Fourier transform in terms of <math>\omega</math> in radians. (You should have seen and used to obtain a corresponding pair/property for the CT Fourier transform in terms of frequency f (in hertz). In each case, simplify your answer as m
    803 B (115 words) - 08:50, 25 August 2010
  • Lecture3ECE438F10
    ...ransform of the "comb" and "rep" functions. We also defined the DT Fourier transform and computed the DTFT of a complex exponential.
    660 B (96 words) - 04:26, 29 August 2011
  • Lecture5ECE438F10
    ...urier transform does not exist. The first student who creates a table of z-transform on Rhea with at least 15 signals will get a 0.5% bonus. (You must use the s *[[Student_summary_z_transform_ECE438F09|A student summary of the z-transform and its properties]]
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  • ECE438 HW1 Solution
    ...th>\omega</math>. Also, I would not use the "mathcal" (curly) font for the transform variable, just a capital letter instead. </span> --[[User:Mboutin|Mboutin]] ...span class="texhtml">f</span> in hertz per time unit) [[More on CT Fourier transform|(info)]]
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  • CT Fourier Transform (frequency in hertz)
    [[Category:Fourier transform]] Continuous-time Fourier Transform Pairs and Properties
    5 KB (687 words) - 21:01, 4 March 2015
  • Explain CTFT
    =How to obtain the CT Fourier transform formula in terms of f in hertz (from the formula in terms of <math>\omega</
    491 B (88 words) - 10:57, 15 September 2010
  • Explain InverseCTFT
    =How to obtain the Inverse DT Fourier Transform formula in terms of f in hertz (from the formula in terms of <math>\omega</
    732 B (127 words) - 10:58, 15 September 2010
  • Lecture9ECE438F10
    ...een the poles/zeros of the z-transform and the magnitude of the DT Fourier transform. We also began talking about sampling. It was announced that the deadline f Several students asked me after class how to obtain the ROC of a z-transform. There is a really good example on
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  • Partial Fraction Expansion
    ...on allows us to fit functions to the known ones given by the known Fourier Transform pairs table. ...obtaining the capital letters quickly are from learning to do the Laplace Transform in [[ECE202|ECE 202]].
    4 KB (602 words) - 13:49, 3 March 2015
  • Lecture11ECE438F10
    ...der hold. We then begin talking about the relationship between the Fourier transform of a signal x(t) and the sampling
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  • ECE438 Week5 Quiz
    <math>\text{1. Find inverse Z-transform of } \frac{1}{1-az^{-1}} \text{ where } |z|<|a|. \,\!</math> <math>\text{2. Find inverse Z-transform of } \frac{3z^{-3}}{1-az^{-1}} \text{ where } |z|<|a|. \,\!</math>
    2 KB (315 words) - 10:39, 11 November 2011
  • Lecture12ECE438F10
    ...elationship between the Fourier transform of a signal x(t) and the Fourier transform of its sampling y[n]=x(nT). We then talked about resampling. More specifica
    811 B (114 words) - 04:34, 27 October 2010
  • Hw5ECE438F10
    a) What is the relationship between the DT Fourier transform of x[n] and that of y[n]=x[3n]? (Give the mathematical relation and sketch b) What is the relationship between the DT Fourier transform of x[n] and that of
    2 KB (327 words) - 03:55, 24 September 2010
  • Lecture13ECE438F10
    ...r you, trust me!) We then obtained the relationship between the DT Fourier transform of <math>x_1[n]</math> and that of an upsampling of x[n] by a factor D. Fr
    1 KB (220 words) - 16:07, 22 September 2010
  • DTFT Window Function
    [[Category:discrete-time Fourier transform]] =Discrete-time Fourier transform of a window function=
    1 KB (243 words) - 09:25, 29 December 2010
  • 2010 Fall ECE 438 Boutin/ECE438Mid1FormulaSheet Work
    *Fourier series of a continuous-time signal x(t) periodic with period T *Fourier series coefficients of a continuous-time signal x(t) periodic with period T
    2 KB (292 words) - 17:13, 30 September 2010
  • ECE438 Week7 Quiz
    Let <math>X_N[k],k=0,...,N-1</math> denote the N point Discrete Fourier Transform (DFT) of the signal x[n],n=0,...,N-1. a. Compute <math>X(e^{j\omega})</math> the Fourier Transform of x[n].
    2 KB (439 words) - 10:41, 11 November 2011
  • ECE637
    ...Space_Fourier_Transform_%28frequences_in_hertz%29|Continuous-space Fourier transform]]
    2 KB (190 words) - 11:23, 29 May 2013
  • Discrete Fourier Transform Definition
    = Discrete Fourier Transform = ...et x[n] be a discrete-time signal with Period N. Then the Discrete Fourier Transform X[k] of x[n] is the discrete-time signal defined by
    521 B (90 words) - 15:35, 8 October 2010
  • Discrete Fourier Transform
    [[Category:discrete Fourier transform]] = Discrete Fourier Transform =
    1 KB (219 words) - 13:25, 2 December 2011
  • Lecture15ECE438F10
    ...strate the leakage effect, we [[DTFT_Window_Function|looked at the Fourier transform of a window function]].
    985 B (141 words) - 15:57, 8 October 2010
  • Lecture16ECE438F10
    ...structing the DTFT of a finite duration signal from the [[Discrete Fourier Transform|DFT]] of its periodic repetition. The formula was observed to hold whenever ...ute Fourier series, as computing DFTs is essentially the same as computing Fourier series coefficients.
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  • Lecture18ECE438F10
    Recovering from the first midterm exam, we attacked the Fast Fourier Transform (FFT). More specifically, we illustrated how "decimating by a factor two" y
    632 B (85 words) - 04:36, 27 October 2010
  • Practice question 1 eECE439F10
    [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
    5 KB (766 words) - 14:22, 21 April 2013
  • Hw7ECE438F10
    Compute the discrete Fourier transform of the following discrete-time signals: How do your answers relate to the Fourier series coefficients of x[n]?
    4 KB (661 words) - 11:22, 30 October 2011
  • CT DT Fourier transform ECE438F10
    [[Category:Fourier transform]] == The Continuous Time Fourier Transform (CTFT) ==
    4 KB (746 words) - 08:47, 11 November 2013
  • Practice Question 4 ECE438F10
    ...m of x(t) and sketch it. Obtain a mathematical expression for the Fourier transform of y[n] and sketch it. Fourier Transform of x(t) = 1
    7 KB (1,273 words) - 12:42, 26 November 2013
  • Lecture25ECE438F10
    *[[DTFT_Window_Function|Fourier transform of a DT window function]]
    2 KB (260 words) - 12:42, 22 October 2010
  • Table DT Fourier Transforms
    [[Category:Fourier transform]] [[Discrete-time_Fourier_transform_info|Discrete-time (DT) Fourier Transforms]] Pairs and Properties
    7 KB (1,037 words) - 21:05, 4 March 2015
  • Decision Theory Glossary ECE662Spring2008
    ...aussian noise on both x and y. In some cases, PCA corresponds to a Fourier transform, such as the DCT used in JPEG image compression.
    31 KB (4,787 words) - 18:21, 22 October 2010
  • Discrete Fourier transform ECE438F10
    [[Category:discrete Fourier transform]] [[Category:Fourier transform]]
    1 KB (166 words) - 08:50, 11 November 2013
  • ECE438 Week10 Quiz Q3sol
    Taking Z transform, <br/> Taking the Fourier transform, <br/>
    4 KB (643 words) - 04:31, 1 November 2010
  • ECE438 HW7 Solution
    Recall, the Discrete Fourier Transform is defined as follows - ...The DFT of the N samples comprising one period of x[n] equals N times the Fourier series coefficients.
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  • Continuous Space Fourier Transform (frequences in hertz)
    [[Category:Fourier transform]] Table of Continuous-space (CS) Fourier Transform Pairs and Properties
    8 KB (1,167 words) - 15:32, 23 April 2013
  • Lecture33ECE438F10
    ...second part of the lecture was spent talking about the short-time Fourier transform and sound spectograms. The issue of window function length and shapes were
    2 KB (234 words) - 08:49, 11 November 2010
  • Lecture34ECE438F10
    ...finished the lecture by giving a filtering view of the short-time Fourier transform, the proof of which will be given in the next lecture.
    2 KB (347 words) - 13:13, 12 November 2010
  • 2D rect
    *2D Rect function and its Fourier transform *View the Fourier transform of the 2D rect function on [[Student_summary_spectral_analysis_2D_signalsb|
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  • Lecture35ECE438F10
    ...e "[[:Category:continuous-space Fourier transform|continuous-space Fourier transform]]". [[Category:continuous-space Fourier transform]]
    933 B (122 words) - 09:32, 11 November 2011
  • Lecture36ECE438F10
    ...s put on understanding how to extent these to the 2D versions of the other Fourier transforms we say (e.g., DTFT and DFT). We also defined some basic 2D signa [[Category:continuous-space Fourier transform]]
    977 B (131 words) - 09:30, 11 November 2011
  • ECE 600 Prerequisites Joint Characteristic Function
    ...}\mathbf{Y}\right)}f_{\mathbf{XY}}\left(x,y\right)dxdy=\text{2-dim Fourier transform}.</math> Inverse Fourier transform relation:
    4 KB (711 words) - 11:32, 30 November 2010
  • ECE438 Week13 Quiz Q4sol
    Taking Fourier Transform on both sides, <br/>
    3 KB (504 words) - 19:54, 17 November 2010
  • ECE 600 General Concepts of Stochastic Processes The Power Spectrum
    ..."inline">\mathbf{X}\left(t\right)</math> , real or complex, is the Fourier transform of the autocorrelation function: ...{\infty}S_{\mathbf{XX}}\left(\omega\right)e^{i\omega\tau}d\omega</math> . (Fourier inversion formula)
    3 KB (492 words) - 11:53, 30 November 2010
  • 2010 Fall ECE 438 Boutin/ECE438Mid2FormulaSheet Work
    | align="right" style="padding-right: 1em;" | Z-Transform | align="right" style="padding-right: 1em;" | Time Shift Property of Z-Transform
    3 KB (518 words) - 16:06, 2 December 2010
  • Info multiplication property FT w
    =About the Multiplication Property of the continuous-time Fourier transform= The multiplication property of the continuous-time Fourier transform can be stated as follows:
    751 B (105 words) - 16:17, 30 November 2010
  • Lecture37ECE438F10
    [[Category:continuous-space Fourier transform]]
    1 KB (174 words) - 09:31, 11 November 2011
  • More on CTFTs
    Well, we know that <math>e^{j2\pi f_0 t}</math> is an impulse function in the Fourier domain. Can we guess that this would be a shifted delta? ...pace_Fourier_Transform_%28frequences_in_hertz%29| Continuous-Space Fourier Transform.]]
    1 KB (210 words) - 11:17, 22 November 2010
  • Summary spectral analysis 2D signals Chen Fall 2010
    == Continuous Space Fourier Transform of 2D Signals == ...-size: 110%;" colspan="2" | Continuous Space Fourier Transform (2D Fourier Transform)
    8 KB (1,206 words) - 22:08, 30 November 2010
  • Vuvuzelas ECE438F10
    ...periodic. Which is very convenient to implement DSP methods using Fourier transform.
    3 KB (409 words) - 08:53, 11 November 2013
  • PracFMA527Fall2010
    L=pi in this problem. The given Fourier series for f(x) tells When you square the coefficients of the Fourier series, you get
    7 KB (1,359 words) - 02:59, 14 December 2010
  • 2011 Spring ECE 301 Boutin
    ...ract of a talk by Prof. Joe Havlicek explaining the meaning of the Fourier transform very clearly using music. *Computing the Fourier series coefficients of a CT signal
    18 KB (2,485 words) - 10:36, 11 November 2011
  • Lecture 10 online ECE301S11 Prof Boutin
    ...uickly now, but we will get back to it later once we have seen the Fourier transform.
    10 KB (1,922 words) - 13:46, 2 February 2011
  • ECE301 signals systems learning material
    ...mboutin_Common_Questions_on_FS/FT_Answered_By_Mimi|Questions about Fourier transform of periodic signals, answered by Prof. Mimi]] *[[ECE_301_Fall_2007_mboutin_DT_Fourier_Series_in_Matlab|DT Fourier series with a single command in MATLAB]]
    6 KB (818 words) - 06:12, 16 September 2013
  • ECE301 signals systems formulas
    *[[LaplaceTransformPairsCollectedfromECE301|Laplace Transform Pairs and Properties]] ...ier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</span> in radi
    890 B (101 words) - 17:30, 21 April 2013
  • Signals and systems practice problems list
    *[[CT_Fourier_series_practice_problems_list|Problems on continuous-time Fourier series]] ...urier_transform_practice_problems_list|Problems on continuous-time Fourier transform]]
    12 KB (1,768 words) - 10:25, 22 January 2018
  • Lecture17ECE301S11
    ...compute; this was exemplified when we tried to compute the inverse Fourier transform of the constant function 1. *Solve the following practice problem on CT Fourier transform.
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  • Fourier transform etu CT ECE301S11
    = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    1 KB (197 words) - 10:25, 11 November 2011
  • Lecture18ECE301S11
    ...ransform of a periodic signal. We found that we cannot compute the Fourier transform of such signals using the integral formula. However, we were able to guess ...the lecture by discussing a few properties of the continuous-time Fourier transform.
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  • Fourier transform cosine CT ECE301S11
    = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    2 KB (276 words) - 10:25, 11 November 2011
  • Fourier transform cosine no2 CT ECE301S11
    = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    2 KB (355 words) - 10:26, 11 November 2011
  • Fourier transform periodic triangular pulse train CT ECE301S11
    = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    853 B (122 words) - 10:26, 11 November 2011
  • Fourier transform periodic rectangular pulse train CT ECE301S11
    = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
    1 KB (196 words) - 10:26, 11 November 2011
  • Lecture19ECE301S11
    Today we discussed some important properties of the continuous-time Fourier transform (CTFT). I particular, we saw the duality property and the convolution prope ...form_(frequency_in_radians_per_time_unit)|Table of continuous-time Fourier transform pairs and properties]]
    1 KB (144 words) - 14:12, 28 February 2011
  • Lecture20ECE301S11
    ...t ready for the next lecture where we will begin talking about the Fourier transform for discrete-time signals!
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  • HW5 ECE301 Spring2011 Prof Boutin
    ...urier_Transform_%28frequency_in_radians_per_time_unit%29| table of Fourier transform pairs and properties]]. (Explain how you checked your answer.) Compute the Fourier transform of the signal
    4 KB (633 words) - 12:31, 2 March 2011
  • Lecture21ECE301S11
    ...ture, we finished discussing the properties of the continuous-time Fourier transform. We then used these properties to obtain a simple expression for the freque ...of a discrete-time complex exponential. We then "guessed" what the Fourier transform of a discrete-time complex exponential should be. Our guess was somewhat wr
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  • Fourier transform 3numinusn DT ECE301S11
    = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Discrete-time Signal = Compute the Fourier transform of the signal
    1 KB (198 words) - 10:27, 11 November 2011
  • Fourier transform cosine DT ECE301S11
    = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Discrete-time Signal = Compute the Fourier transform of the signal
    1 KB (161 words) - 10:27, 11 November 2011
  • Fourier transform window DT ECE301S11
    = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Discrete-time Signal = Compute the Fourier transform of the signal
    1 KB (203 words) - 10:28, 11 November 2011
  • Problem on time shifting and time scaling property of Fourier transform ECE301S11Boutin
    ...lving|Practice Question]] on the Properties of the Continuous-time Fourier Transform = Let x(t) be a continuous time signal with Fourier transform <math class="inline">{\mathcal X} (\omega) </math>.
    2 KB (401 words) - 10:27, 11 November 2011
  • Lecture22ECE301S11
    ...both be able to use the Fourier transform properties and prove the Fourier transform properties".
    1 KB (162 words) - 12:46, 2 March 2011
  • HW5 ECE301 Spring2011 Prof Boutin Solutions
    ...anging the value of a signal at a single point does not change its Fourier transform. -pm </span> Now, since the Fourier transform (FT) is linear, we have that:
    10 KB (1,817 words) - 11:34, 7 March 2011
  • Lecture23ECE301S11
    Today we finished the material on the discrete-time Fourier transform so we have now covered all the material for the second test. We also discus
    1,022 B (140 words) - 18:58, 4 March 2011
  • HW6 ECE301 Spring2011 Prof Boutin
    *<span style="color:red"> 15 pts </span> for the computation of the Fourier transform of the continuous-time signal. Check every step of the computation and remo ...f the Fourier transform (i.e., the integral formula) to obtain the Fourier transform of either the constant function 1 or of the complex exponential functions,
    7 KB (1,161 words) - 18:50, 4 March 2011
  • HW7 ECE301 Spring2011 Prof Boutin
    ...your answer using this [[Table_DT_Fourier_Transforms| table of DT Fourier transform pairs and properties]]. (Explain how you checked your answer.) ...(i.e., the integral formula) to compute the inverse Discrete-time Fourier transform of the signal
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  • Causal LTI System Difference Equation no1 ECE301S11
    ...constant. But I don't know how to compute that constant from the fourier transform.
    5 KB (793 words) - 10:28, 11 November 2011
  • Lecture25ECE301S11
    ...of the sampling of a band-limited signal consists of copies of the Fourier transform of the original signal. Satisfying Nyquist's condition insures that there i
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  • Discussion HW7 ECE301 Spring2011
    I think the table of DT Fourier Transform pairs has a mistake. where it says <math>(n-1)a^nu[n]</math> it should be <
    1 KB (258 words) - 06:25, 11 March 2011
  • HW8 ECE301 Spring2011 Prof Boutin
    *<span style="color:red"> 15 pts </span> for the computation of the Fourier transform of the discrete-time signal. If an integral was used in place of a summatio ...yle="color:red"> 15 pts </span> for the computation of the inverse Fourier transform. If a summation was used in place of the integral, give zero points. Check
    6 KB (1,090 words) - 07:36, 22 March 2011
  • HW7 ECE301 Spring2011 Prof Boutin Solutions
    ...nds to the part of the spectrum for k=0) to compute the inverse DT Fourier transform of the given signal:
    10 KB (1,783 words) - 08:23, 21 March 2011
  • ECE301inBME
    ...stems (maybe even [[Fourier_Transform_Video |Fourier]]/Laplace/[[Compute z-transform u n ECE301S11|Z transforms]] from [[2011 Spring ECE 301 Boutin|ECE301]]!) a ...nications, and networking. Imaging techniques involving diffraction and/or Fourier analysis with application to tomography, magnetic resonance imaging, synthe
    17 KB (2,368 words) - 10:53, 6 May 2012
  • HW9 ECE301 Spring2011 Prof Boutin
    ...="inline"> T</math>. For each of the values of T below, sketch the Fourier transform of the sampling and indicate whether or not one can recover <math class="i
    3 KB (451 words) - 06:40, 1 April 2011
  • Nyquist rate for a sinc function
    Yes, this signal is band limited. It is a sinc function, and its Fourier transform can be found using the table of formulas in the textbook on page 329. ...orrect max frequency of the signal. It would be ok to say that the Fourier transform is a non-zero constant multiple of a low-pass filter with gain 1 and cutoff
    3 KB (431 words) - 10:28, 11 November 2011
  • Nyquist rate for a signal ECE301S11
    ...or:red">Instructor's comment: Reality check: the only signal whose Fourier transform is a constant is an impulse. So your answer cannot possibly be correct. -pm
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  • HW10 ECE301 Spring2011 Prof Boutin
    a) Sketch the spectrum (i.e., the Fourier transform) of y(t). Compute the Laplace transform of the following signals. (Do not forget to indicate the ROC.)
    5 KB (797 words) - 09:19, 7 April 2011
  • Signal modulation with exponential ECE301S11
    Let x(t) be a signal whose Fourier transform <math>{\mathcal X} (\omega) </math> satisfies
    2 KB (393 words) - 10:31, 11 November 2011
  • Signal modulation with cosine ECE301S11
    Let x(t) be a signal whose Fourier transform <math>{\mathcal X} (\omega) </math> satisfies
    2 KB (400 words) - 10:31, 11 November 2011
  • HW9 ECE301 Spring2011 Prof Boutin Solutions
    ...& \text{else.}\end{array} \right. \ </math>, <br><br> then why does the F.Transform not account for the factor of "2" in front in the answers above and below? ...er transform of the CT signal representing the sampling in CT. The Fourier transform of the DT signal obtained by storing the values of the samples in an array,
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  • Hw1 ECE438F11
    ...of CT Fourier transform pairs and properties]], which uses the CT Fourier transform in terms of frequency <math>f</math> in hertz. Note that we will use the la In [[ECE301]], you learned that the Fourier transform of a step function <math>x(t)=u(t)</math> is the following:
    2 KB (400 words) - 03:53, 31 August 2013
  • HW10 ECE301 Spring2011 Prof Boutin Solutions
    a) The Fourier series coefficients of <span class="texhtml">''c''(''t'')</span> are: and using the synthesis equation of the Fourier series we get:
    12 KB (2,109 words) - 05:58, 22 April 2011
  • Nyquist rate after multiplicating sinc signals ECE301S11
    ...rm of the product of two functions is (1/2pi) times the convolution of the Fourier transforms of the individual functions.
    2 KB (336 words) - 10:31, 11 November 2011
  • Review of an alternative book by M.J. Roberts
    In this chapter author explains Fourier Series and Fourier Transforms of CT signals. The explanation is very good and clear. It is ver ...are well designed so that students can practice all aspects of the Laplace Transform and get more examples how to apply it. Proporties are explained very well t
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  • Book Review: Signals & Systems MJR
    In this chapter author explains Fourier Series and Fourier Transforms of CT signals. The explanation is very good and clear. It is ver ...are well designed so that students can practice all aspects of the Laplace Transform and get more examples how to apply it. Proporties are explained very well t
    6 KB (955 words) - 10:54, 6 May 2012
  • Linearity Spring 2011
    Linearity can be used to simplify the Fourier transform. &nbsp;Integration and differentiation are also linear. &nbsp;Once a non-li
    2 KB (255 words) - 10:50, 6 May 2012
  • Fourier Transform Video
    =Video on the Fourier Transform= <player>ECE 301 Credit_0.avi|The Fourier Transform</player>
    234 B (31 words) - 10:52, 6 May 2012
  • Book Review/Bhakti
    ...dedicated to LTI systems, Laplace Transfer of CT LTI systems, Z Transform, Fourier Analysis. Which means this book explains material covered over Midterms 1 a ...ctually refers to the ninth chapter in the Oppenheim called “The Laplace Transform.” This chapter has 62 solved problems. <br>
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  • 2011 Fall ECE 438 Boutin
    **[[Practice_Question_2_ECE439F10|Practice Question 2 (on z-transform computation)]] **[[Practice_Question_3_ECE439F10|Practice Question 3 (on inverse z-transform computation)]]
    10 KB (1,359 words) - 03:50, 31 August 2013
  • Lecture Schedule ECE438Fall11 Boutin
    *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
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  • Lecture1ECE438F11
    We finished the lecture with a discussion about the meaning of the Fourier transform and a video where Prof. Joe Havlicek illustrates this meaning using music.
    2 KB (231 words) - 12:48, 21 September 2011
  • Practice CTFT computation rect and sinc ECE438F11
    [[Category:Fourier transform]] Topic: Continuous-time Fourier transform computation (in terms of frequency f in hertz)
    7 KB (1,302 words) - 09:45, 11 November 2013
  • Lecture2ECE438F11
    ...ced, and in the [[Lecture3ECE438F11|next lecture]], we shall compute their Fourier transforms. **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]]
    2 KB (285 words) - 12:48, 21 September 2011
  • Lecture3ECE438F11
    ...ition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. **[[Practice DTFT computation cosine ECE438F11|What is the Fourier transform of this DT cosine?]]
    2 KB (252 words) - 12:48, 21 September 2011
  • Practice DTFT computation cosine ECE438F11
    [[Category:discrete-time Fourier transform]] Topic: Discrete-time Fourier transform computation
    6 KB (1,000 words) - 12:33, 26 November 2013
  • Practice DTFT computation rect ECE438F11
    [[Category:discrete time Fourier transform]] Topic: Discrete-time Fourier transform computation
    6 KB (1,090 words) - 12:35, 26 November 2013
  • Practice CTFT from omega to f step function
    [[Category:Fourier transform]] Topic: Continuous-time Fourier transform: from omega to f
    7 KB (1,143 words) - 09:44, 11 November 2013
  • Practice CTFT complex exponential ECE438F11
    [[Category:Fourier transform]] Topic: Continuous-time Fourier transform of a complex exponential
    3 KB (610 words) - 09:47, 11 November 2013
  • Lecture5ECE438F11
    ...We introduced the notion of "region of absolute converge" (ROC) for the z-transform and observed the fact that it consists of circles around the origin of the *[[practice_CTFT_from_omega_to_f_step_function|Obtain the Fourier transform in terms of f of a step function (from FT in terms of omega)]]
    2 KB (294 words) - 06:19, 11 September 2013
  • Hw1 ECE438F11sln
    In [[ECE301]], you learned that the Fourier transform of a step function <math>x(t)=u(t)</math> is the following: Use this fact to obtain an expression for the Fourier transform <math>X(f)</math> (in terms of frequency in hertz) of the step function. (Y
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  • Lecture10ECE438F11
    ...een the poles/zeros of the z-transform and the magnitude of the DT Fourier transform. We also began talking about sampling. [[Category:z-transform]]
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  • Lecture11ECE438F11
    ...xpansion. We then begin talking about the relationship between the Fourier transform of a signal x(t) and that of the sampling
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  • Lecture12ECE438F11
    ...elationship between the Fourier transform of a signal x(t) and the Fourier transform of its sampling y[n]=x(nT). (Note that it is VERY IMPORTANT that you unders
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  • Lecture13ECE438F11
    ...D. In the next lecture, we will use this relationship to figure out how to transform this signal into the (higher resolution) signal
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  • Hw3 ECE438F11
    ...e Fourier transform from a table; either use the definition of the Fourier transform or use some other way to fully justify your answer.) Write a mathematical expression for the Fourier transform <math>X_s(f) </math> of
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  • Lecture14ECE438F11
    Having obtained the relationship between the DT Fourier transform of <math>x_1[n]</math> and that of an upsampling of x[n] by a factor D in We then began discussing the [[Discrete_Fourier_Transform|Discrete Fourier Transform]] (DFT).
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  • Compute DFT practice no1 ECE438F11
    [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
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  • Compute DFT practice no2 ECE438F11
    [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
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  • 2011 Fall ECE 301 Pollak
    ...xercise_Fourier_series_computation|A collective page to practice computing Fourier series of a CT signal]] ...cise_Fourier_series_computation_DT|A collective page to practice computing Fourier series of a DT signal]]
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  • Lecture15ECE438F11
    ...nite duration signal and the [[Discrete_Fourier_Transform|Discrete Fourier Transform]] of its periodic repetition. ...exercises of Fourier series computations for DT signals]] (to brush up on Fourier series))
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  • Practice problem finding band limited signals ECE438F11
    ...t a transformation that would simply shift the frequencies of the Fourier transform? Another way to obtain new band-limited signal is to combine band-limited s By nature of the Fourier Transform, band limited signals
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  • Lecture16ECE438F11
    [[Category:discrete Fourier transform]]
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  • Lecture17ECE438F11
    ...structing the DTFT of a finite duration signal from the [[Discrete Fourier Transform|DFT]] of its periodic repetition. The formula was observed to hold whenever [[Category:discrete Fourier transform]]
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  • Lecture18ECE438F11
    Today's lecture was about the Fast Fourier Transform (FFT). As a first step, we covered the "decimation by two" FFT algorithm. [[Category:discrete Fourier transform]]
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  • Lecture19ECE438F11
    [[Category:discrete Fourier transform]]
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  • Lecture21ECE438F11
    [[Category:discrete Fourier transform]] [[Category:Fast Fourier transform]]
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  • MathWorksTest
    ...lp! We need a [[Discrete_Fourier_Transform_table|table of Discrete Fourier transform pairs and properties]]! **[[Practice_Question_2_ECE439F10|Practice Question 2 (on z-transform computation)]]
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  • Exercise effect of zero padding on DFT ECE438F11
    [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
    4 KB (759 words) - 14:18, 21 April 2013
  • Lecture27ECE438F11
    [[Category:discrete Fourier transform]]
    1 KB (158 words) - 06:30, 11 September 2013
  • Continuous-space Fourier transform
    [[Category:continuous-space Fourier transform]] =More on the Continuous-space (2D) Fourier transform (CSFT)=
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  • Lecture31ECE438F11
    ...voiced phonemes in a speech signal. We also defined the short time Fourier transform (STFT) of a signal and the "spectogram" of a speech signal. We distinguishe
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  • Lecture32ECE438F11
    ...obtained a formula for reconstructing a signal from its short time Fourier transform. We then moved on to the topic of "Spectral Analysis of 2D Signals" with an
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  • Lecture33ECE438F11
    ...he [[:Category:continuous-space Fourier transform|Continuous-space Fourier transform]] (CSFT). [[Category:continuous-space Fourier transform]]
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  • Obtain CSFT complex exponential
    [[Category:continuous-space Fourier transform]] Topic: Continuous-space Fourier transform of a complex exponential
    3 KB (576 words) - 12:57, 26 November 2013
  • Compute CSFT of 2D rect function ECE438F11
    [[Category:continuous-space Fourier transform]] Topic: Continuous-space Fourier transform of a 2D "rect" function
    3 KB (487 words) - 12:57, 26 November 2013
  • Compute CSFT of 2D sinc function ECE438F11
    [[Category:continuous-space Fourier transform]] Topic: Continuous-space Fourier transform of a 2D sinc function
    4 KB (678 words) - 12:58, 26 November 2013
  • Lecture34ECE438F11
    ...Fourier transform|CSFT]] and inverse [[:Category:continuous-space Fourier transform|CSFT]] in polar coordinates. **[[Obtain_CSFT_complex_exponential|Obtain the continuous-space Fourier transform of a complex exponential]]
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  • Discrete-time Fourier transform info
    [[Category:discrete-time Fourier transform]] =About the Discrete-time Fourier transform (DTFT)=
    2 KB (290 words) - 14:47, 1 May 2015
  • Obtain DSFT rectangle
    [[Category:discrete-space Fourier transform]] Topic: Discrete-space Fourier transform computation
    2 KB (355 words) - 12:58, 26 November 2013
  • Compute DSFT product two step functions ECE438F11
    [[Category:discrete-space Fourier transform]] Topic: Discrete-space Fourier transform computation
    3 KB (473 words) - 12:59, 26 November 2013
  • Compute DSFT cosine ECE438F11
    [[Category:discrete-space Fourier transform]] Topic: Discrete-space Fourier transform computation
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  • Digital signal processing practice problems list
    **[[Practice CTFT from omega to f step function|Obtain the Fourier transform in terms of f of a step function (from FT in terms of omega)]] **[[Practice CTFT computation rect and sinc ECE438F11|Compute the Fourier transform of a rect and a sinc]]
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  • Lecture35ECE438F11
    ...mmetric space signals and separable space signals can be analyzed using 1D transform formulas. **[[Obtain_DSFT_rectangle|Obtain the discrete-space Fourier transform of a rectangle]]
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  • Lecture36ECE438F11
    ...arability of the filter greatly facilitated the computation of its Fourier transform. We discussed different ways to determine whether a filter is separable and **[[Obtain_DSFT_rectangle|Obtain the discrete-space Fourier transform of a rectangle]]
    2 KB (213 words) - 06:32, 11 September 2013
  • Lecture37ECE438F11
    **[[Obtain_DSFT_rectangle|Obtain the discrete-space Fourier transform of a rectangle]] ...FT_product_two_step_functions_ECE438F11|Compute the discrete-space Fourier transform of this function]]
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  • Implementation of the Divide and Conquer DFT via Matrices
    [[Category:Fourier transform]] [[Category:discrete Fourier transform]]
    10 KB (1,717 words) - 12:02, 6 June 2014
  • Lecture38ECE438F11
    ...uting and plotting the frequency response (i.e. the discrete-space Fourier transform) of the corresponding filter. We then studied another type of filter introd [[Category:discrete-space Fourier transform]]
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  • ECE538
    *[[Laplace_Transforms_Table|Laplace Transform Pairs and Properties]] ...ier_Transform_(frequency_in_radians_per_time_unit)|Continuous-time Fourier Transform Pairs and Properties]]
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  • ECE301 signals systems videos
    *'''How the Fourier Transform Works, by Prof. Joseph Havlicek'''
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  • Lecture4ECE438F13
    ...ition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]
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  • Collective problem solving why and how to
    *[[Practice_Question_2_ECE439F10|Computing a z-transform]] *[[Practice_Question_4_ECE438F10|Fourier transform of a sampling]]
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  • 2018 Fall ECE 301 Boutin
    | [[FourierSeriesConvergenceBonusProject | Convergence of Parametric Fourier Series]] | [[The_2-D_Fourier_Transform_and_Images|The 2-D Fourier Transform and Images]]
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  • ECE-QE CS1-2011
    ...ime-invariant system with impulse response <math>h(t)</math> whose Fourier transform <math>H(\omega)</math> has the ideal low-pass characteristic
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  • ECE-QE CS5-2011
    \text{Let } F(\mu,\nu) \text{ be the continuous-time Fourier transform of } f(x,y) \text{ given by} \text{and let } P_{\theta}(\rho) \text{ be the continuous-time Fourier transform of } p_{\theta}(r) \text{ given by}
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  • ECE-QE CS5-2011 solusion-2
    \text{Let } F(\mu,\nu) \text{ be the continuous-time Fourier transform of } f(x,y) \text{ given by} \text{and let } P_{\theta}(\rho) \text{ be the continuous-time Fourier transform of } p_{\theta}(r) \text{ given by}
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  • 2012 Fall ECE 438 Ersoy
    | [[Application Fourier transform ECE438F12Ersoy|Application of the Fourier transform]] | [[Application Z transform ECE438F12Ersoy|Application of the Z-transform]]
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  • 2012 ECE 301 Dr. Love
    *[[LaplaceTransformPairsCollectedfromECE301|Laplace Transform Pairs and Properties]] ...ier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</span> in radi
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  • 2013 Spring ECE 301 Krogmeier
    *'''Bonus opportunity 4!!!''' Post and solve problems related to z-transform [[Bonus_opportunity_4_ECE301_sp13|here]]. We will post the solution of fina **[[LaplaceTransformPairsCollectedfromECE301|Laplace Transform Pairs and Properties]]
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  • Lab 2 Additional Information ECE637 Spring2013 Bouman
    ...Section 2 - For calculationg Sx anlyitically, is this just doing a Fourier transform of and multiplying by its complex conjugate and 1/(N^2)? Not exactly sure
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  • DYL Tuesday 1
    <br> '''''On Mimi's Fourier Transform Skills''''' ...my way out of a paper bag. Not sure what that means.<br>D: You can Fourier transform your way out of... a paper bag?<br>M: Yea, a paper bag.<br>D: Sounds like a
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  • Practice Question joint from marginals independent variables ECE302S13Boutin
    ...just as the Fourier transform X(jw) is the envelope function of the set of Fourier coefficients {a_k}, where <math>prob(x) = \int_{x^-}^{x^+}f_X(x) dx</math>?
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  • ECE301bonus2
    2. Use Matlab to demonstrate summing of a finite number of terms of a Fourier Series ... pick a fun time function with a discontinuity to illustrate Gibb c) Plot Fourier Transform of filter’s impulse response in 3D.
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  • ECE 301 Spring 2013 mtgyure Bonus2 Question2
    [[Category:Fourier series]] ''2. Use Matlab to demonstrate summing of a finite number of terms of a Fourier Series ... pick a fun time function with a discontinuity to illustrate Gibb
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  • Practice Question characteristic function ECE302S13Boutin
    I tried taking the inverse fourier transform since PX(x) = F^-1 { Mx(jw)}, however my resultant pmf has j (sqrt(-1)) in
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  • ECE637 Bouman lectures Image Processing sLecture mhossain
    **[[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transform]] ** [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
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  • ECE637 optical imaging systems space domain models S13 mhossain
    ...the PSF because the star is like a delta function. If you take its Fourier transform, you will get the frequency response of the system. Given that your system
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  • ECE301 signals systems lecture notes
    **[[Lecture19 ECE301Fall2008mboutin|Lecture 19]]: TA Example Session w/ DT Fourier Transforms and inverses **[[Image:ECE 301 Fall 2007 Lecture12 04.pdf|Dec. 4 Lecture, Fall 2007 (on x-Transform)]]
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  • 4th Bonus Point - Ryan Miller
    Since ROC is |z|>1/2 (i.e. includes the unit circle), the Fourier Transform exists.
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  • ECE637 tomographic reconstruction intro S13 mhossain
    ::↳ [[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transform]] ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
    8 KB (1,168 words) - 07:24, 26 February 2014
  • ECE637 tomographic reconstruction S13 mhossain
    ::↳ [[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transform]] ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
    4 KB (443 words) - 07:24, 26 February 2014
  • ECE637 tomographic reconstruction CT S13 mhossain
    ::↳ [[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transform]] ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
    9 KB (1,390 words) - 07:24, 26 February 2014
  • ECE637 tomographic reconstruction PET S13 mhossain
    ::↳ [[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transform]] ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
    6 KB (913 words) - 07:24, 26 February 2014
  • ECE637 tomographic reconstruction coordinate rotation S13 mhossain
    ::↳ [[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transform]] ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
    6 KB (834 words) - 07:25, 26 February 2014
  • Linear algebra tutorials
    ..._Divide_and_Conquer_DFT_via_Matrices|"divide and conquer" Discrete Fourier Transform (DFT)]]
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  • ECE637 tomographic reconstruction convolution back projection S13 mhossain
    ::↳ [[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transform]] ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
    9 KB (1,486 words) - 07:25, 26 February 2014
  • ECE637 tomographic reconstruction radon transform S13 mhossain
    ::↳ [[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transform]] ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
    6 KB (942 words) - 07:25, 26 February 2014
  • ECE637 tomographic reconstruction fourier slice theorem S13 mhossain
    ::↳ [[ECE637_tomographic_reconstruction_radon_transform_S13_mhossain|Radon Transform]] ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
    9 KB (1,485 words) - 12:30, 17 April 2014
  • Lemma boutin mhossain 05 2013
    * the Fourier transforms of their pdfs exist Taking the inverse Fourier transform, we get<br/>
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  • ECE637 MRI S13 mhossain
    ** Reconstruction computed with inverse Fourier transform If the RF pulse is a sinc function modulated at 63.8 MHz, its Fourier transform would be a shifted rect. This would essentially be a slice in the frequency
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  • ECE637 discrete parameter signals and systems discrete transforms S13 mhossain
    ==Discrete Time Fourier Transform (DTFT)== The DTFT is the analogous transform for discrete time signals as the CTFT is for continuous time signals. Let <
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  • 2013 Fall ECE 438 Boutin
    **[[Z_Transform_table|z-transform]] **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]]
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  • Lecture Schedule ECE438Fall13 Boutin
    *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
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  • 2013 Fall ECE 544 Krogmeier
    **[[LaplaceTransformPairsCollectedfromECE301|Laplace Transform Pairs and Properties]] ...ier_Transform_(frequency_in_radians_per_time_unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</span> in radi
    4 KB (480 words) - 18:57, 10 December 2013
  • Lecture2ECE438F13
    ...ely, duality, multiplication, and convolution) and we computed the Fourier transform of some basic signals (namely, Dirac delta, rect, sinc, and complex exponen **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]]
    3 KB (505 words) - 06:56, 2 September 2013
  • HW1ECE38F13
    [[Category:fourier transform]] ...of CT Fourier transform pairs and properties]], which used the CT Fourier transform in terms of <math>\omega</math> in radians. (You should have seen and used
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  • Lecture3ECE438F13
    ...ier transform of the "comb" and "rep" operators in terms of the CT Fourier transform of the signal they are applied to.
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  • HW4ECE438F13
    [[Category:inverse z-transform]] [[Category:z-transform]]
    1 KB (180 words) - 05:37, 20 September 2013
  • HW2ECE438F13
    [[Category:fourier transform]]
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  • Lecture7ECE438F13
    [[Category:z-transform]] ...omparing the expression for the given z-transform to the formula for the z-transform. As we will see later, this trick will be very handy for inverting z-transf
    3 KB (386 words) - 06:09, 11 September 2013
  • Practice DTFT computation rect ECE438F13
    [[Category:discrete time Fourier transform]] Topic: Discrete-time Fourier transform computation
    4 KB (673 words) - 12:36, 26 November 2013
  • Practice DTFT computation sine ECE438F13
    [[Category:discrete time Fourier transform]] Topic: Discrete-time Fourier transform computation
    5 KB (740 words) - 12:36, 26 November 2013
  • HW1 Solution ECE438F13
    [[Category:fourier transform]] ...[CT_Fourier_Transform_%28frequency_in_radians_per_time_unit%29|table of CT Fourier transforms]] in terms of <math>\omega</math> in radians and to obtain the c
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  • HW3ECE438F13
    [[Category:fourier transform]] [[Category:z-transform]]
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  • Practice z transform computation 3 ECE438F13
    [[Category:z-transform]] Topic: Computing a z-transform
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  • Lecture10ECE438F13
    [[Category:z-transform]] [[Category:inverse z-transform]]
    3 KB (334 words) - 06:00, 11 September 2013
  • Lecture12ECE438F13
    [[Category:z-transform]] [[Category:inverse z-transform]]
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  • Student projects
    *[[InverseZtransform|Summary of inverse z-transform, with examples]] **[[HonorsContractECE438CoordinateAndRadon|Coordinate Rotation and the Radon Transform]]
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  • CT Fourier transform practice problems list
    [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    7 KB (966 words) - 18:17, 23 February 2015
  • HW5ECE438F13
    [[Category:inverse z-transform]] [[Category:z-transform]]
    2 KB (362 words) - 13:59, 26 September 2013
  • Lecture15ECE438F13
    **Review the relationship between the z-transform and the Fourier transform **Review how to invert a z-transform
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  • ECE440 Lab1 Typed
    by digitizing the signal and using a digital Fast-Fourier Transform.
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  • HW6ECE$38F13
    [[Category:discrete Fourier transform]] a) What is the relationship between the DT Fourier transform of x[n] and that of y[n]=x[5n]? (Give the mathematical relation and sketch
    3 KB (480 words) - 09:13, 27 September 2013
  • HW7ECE438F13
    [[Category:discrete Fourier transform]]
    2 KB (388 words) - 11:43, 11 October 2013
  • Lecture23ECE438F13
    [[Category:discrete Fourier transform]]
    2 KB (294 words) - 05:58, 14 October 2013
  • Lecture24ECE438F13
    [[Category:discrete Fourier transform]]
    2 KB (300 words) - 05:47, 16 October 2013
  • HWK8MA527Fall2013
    If you hit the system of differential equations by the Laplace transform, you'll get If you take the Laplace transform with respect to t you'll have
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  • Lecture25ECE438F13
    [[Category:discrete Fourier transform]]
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  • ECE600 F13 Characteristic Functions mhossain
    '''Note:''' The characteristic function looks like the Fourier Transform of f<math>_X</math>, with opposite sign in the exponent. We can show that <
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  • HW9ECE438F13
    ...trum.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?
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  • HWK9MA527Fall2013
    ...e a question about the even extension in problem 29. I am getting that the fourier series is 2/pi-4/pi(1/3 cos(2x) + 1/(3*5) cos (4x) + 1/(5*7) *cos(6x)... Th ...rier Sine Function did you guys get bn=0 for all n? Which implies that the Fourier Sine Function is equal to zero for all x.
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  • Comparison of DFT and FFT via Matrices
    ...on assumes the user understands the basic concepts of the Discrete Fourier Transform. ...k = 0, 1, 2, ... N-1. Referring to our definition of the Discrete Fourier Transform above, to compute an N point DFT, all we need to do is simply repeat Eq. 1,
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  • ECE438 digital signal processing textbooks
    ...438/lecturehandouts/ztexample.pdf partial fractial expansion for inverse z-transform] ...ue.edu/~bouman/ece438/lecture/module_1/1.3_fourier_analysis/1.3.3_dtft.pdf Fourier analysis]
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  • ECE438 digital signal processing formulas
    *[[Laplace Transforms Table|Laplace Transform Pairs and Properties]] *[[CT Fourier Transform (frequency in hertz)|Continuous-time Fourier Transform Pairs and Properties]]
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  • ECE438 digital signal processing learning material
    *[[CT_DT_Fourier_transform_ECE438F10|Summary of CT and DT Fourier transform]] *[[Z_transform_ECE438F10|Z-transform]]
    4 KB (471 words) - 19:34, 9 February 2015
  • HWK10MA527Fall2013
    ...ecognize that this integral is an instance of formulas (4) and (5) for the Fourier Integral formulas. Your problem is to figure out what the f(x) is. Table 1 in 11.10 on Page 534 is a table of Fourier Cosine Transforms.
    6 KB (1,130 words) - 18:15, 5 November 2013
  • Review2MA527Fall2013
    The Laplace Transform of the convolution in 1a would be the > Laplace transform on each function and then
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  • Lecture31ECE438F13
    ...hen talked about spectrograms of speech signals and the short-time Fourier transform. We discussed the difference between using a large window and a small wind
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  • Lecture32ECE438F13
    [[Category:discrete Fourier transform]] ...lly we derived a linear filtering interpretation of the short time Fourier transform. We then used this interpretation to obtain a formula for reconstructing a
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  • Lecture33ECE438F13
    [[Category:Fourier transform]] ...e 2D rect, 2D sinc, circ, and 2D delta) ) and the continuous-space Fourier transform. As correctly pointed out by a student, "2D signals" is a misnomer. Instead
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  • Lecture34ECE438F13
    [[Category:Fourier transform]] ...ctions of 2 variables. We call this transform the continuous-space Fourier transform, or CSFT for short. We stated the definition of the CSFT and gave the formu
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  • Lecture35ECE438F13
    [[Category:Fourier transform]] ...eparable functions can be obtained from using the formulas for the Fourier transform of contuous-time signals (i.e., functions of 1 variable).
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  • Lecture37ECE438F13
    [[Category:Fourier transform]] ...arability of the filter greatly facilitated the computation of its Fourier transform. We discussed different ways to determine whether a filter is separable and
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  • Lecture36ECE438F13
    [[Category:Fourier transform]]
    2 KB (315 words) - 06:46, 15 November 2013
  • Moon Landing Speech Analysis
    X=fft(x((m+1):(m+L)),N); %take the fourier transform
    4 KB (753 words) - 09:46, 13 February 2014
  • Lecture38ECE438F13
    [[Category:Fourier transform]]
    2 KB (215 words) - 06:49, 20 November 2013
  • Lecture39ECE438F13
    [[Category:Fourier transform]]
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  • ReviewFinalMA527Fall2013
    about complex Fourier Series on the Final Exam. There might, however, be questions about the complex Fourier TRANSFORM.
    2 KB (444 words) - 17:30, 10 December 2013
  • ECE600 F13 Linear Systems with Random Inputs mhossain
    ...ectral density''' or '''PSD''' of a WSS random process X(t) is the Fourier transform of its autocorrelation function: <br/>
    8 KB (1,476 words) - 12:13, 21 May 2014
  • Lecture44ECE438F13
    ...ll 2011. We also did a short yoga sequence to better visualize the Fourier transform of some important signals. It's a good exercise to repeat at home!
    2 KB (238 words) - 07:40, 6 December 2013
  • Prove of the CSFT of the signals
    ...f signals. The general way we solve CSFT questions is to guess its Fourier Transform, then prove it by taking the inverse F.T. of the signals.
    1 KB (225 words) - 05:39, 14 December 2013
  • 2016 Summer ECE 301 Shenk
    ...ble to calculate the Fourier series coefficients of a period CT signal (DT Fourier series will NOT be on the exam). (3.28a(subparts abc), 3.22, 3.31, 3.28d, 3 * Tables for [[Media:ECE301Summer2016_table3p1.png| Fourier series]], [[Media:ECE301Summer2016_table4p1.png| CTFT properties]], and [[M
    6 KB (765 words) - 13:35, 4 August 2016
  • 2014 Fall ECE 438 Boutin
    **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
    13 KB (1,944 words) - 16:51, 13 March 2015
  • Lecture Schedule ECE438Fall14 Boutin
    *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
    9 KB (1,320 words) - 04:46, 11 September 2014
  • Lecture2ECE438F14
    ...ely, duality, multiplication, and convolution) and we computed the Fourier transform of some basic signals (namely, Dirac delta, rect, sinc, and complex exponen **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]]
    3 KB (393 words) - 06:37, 27 August 2014
  • HW1ECE38F14
    [[Category:fourier transform]] ...of CT Fourier transform pairs and properties]], which lists the CT Fourier transform in terms of <math>\omega</math> in radians. (You should have seen and used
    1 KB (198 words) - 06:08, 29 August 2014
  • Lecture3ECE438F14
    ...ep" and "comb" operators. We finished the lecture by computing the Fourier transform of a rep, but we did not quite finish the computation.
    2 KB (272 words) - 06:01, 3 September 2014
  • Lecture4ECE438F14
    ...ition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]
    2 KB (339 words) - 05:39, 8 September 2014
  • HW2ECE438F14
    [[Category:fourier transform]]
    1 KB (241 words) - 05:28, 8 September 2014
  • HW1ECE38F14 Solution
    [[Category:fourier transform]] ...p/CTFourierTransformPairsCollectedfromECE301withomega table], we have the transform pair:<br>
    4 KB (563 words) - 05:31, 22 September 2014
  • Fourier Transform rep com Youqin Liu ECE438 slecture
    Topic 3:Fourier transform of "rep" and "comb" ...Rep function. In my selecture, I am going to introduce the definition, the Fourier Transformation and the relationship of Comb function and Rep function.
    4 KB (610 words) - 18:55, 16 March 2015
  • HW3ECE438F14
    [[Category:fourier transform]] ...he Fourier transform of the interpolation you wrote in 2a) and the Fourier transform of x(t). (Do not simply write down the formula; show how to derive it.)
    3 KB (462 words) - 09:43, 18 September 2014
  • Slecture Fourier transform w f ECE438
    Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f ...ill explain Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f (in hertz).
    4 KB (613 words) - 18:51, 16 March 2015
  • Fourier Transform as a FUnction of Frequency w versus Frequency f (in Hertz)
    '''Fourier Transform as a Function of Frequency ''w'' Versus Frequency f (in Hertz)''' To show the relationship between the Fourier Transform of frequency <math>\omega</math> versus frequency <math>f</math> (in hertz)
    3 KB (512 words) - 09:50, 14 March 2015
  • Lecture11ECE438F14
    ...ationship between the Fourier transform of a sampling x[n] and the Fourier transform of a downsample of this sampling y[n]=x[Dn], where D is a positive integer.
    2 KB (261 words) - 07:08, 19 September 2014
  • HW4ECE438F14
    [[Category:fourier transform]] a) What is the relationship between the DT Fourier transform of x[n] and that of y[n]=x[4n]? (Give the mathematical relation and sketch
    3 KB (486 words) - 06:19, 22 September 2014
  • Lecture13ECE438F14
    We finished the lecture by stating the definition of the Discrete Fourier transform.
    2 KB (315 words) - 05:54, 24 September 2014
  • Slecture Fourier transform w f ECE438 review
    ...w f ECE438|Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f]] </font> I liked that you compared the formulas for the Fourier Transforms in both the w and f forms. Showing a few more steps in the secon
    5 KB (843 words) - 05:30, 15 October 2014
  • Discrete-time Fourier transform Xian Zhang ECE438 slecture
    Discrete-time Fourier Transform (DTFT) ...periodic function of a frequency as the variable, <math>\omega</math>. The Fourier series is:
    3 KB (515 words) - 20:02, 16 March 2015
  • Fourier Transform as a FUnction of Frequency w versus Frequency f in Hertz review
    ...ansform as a FUnction of Frequency w versus Frequency f (in Hertz)|Fourier Transform as a Function of Frequency w Versus Frequency f (in Hertz)]] </font> The steps you take to find each Fourier transform are well explained, and I really like your use of color to track the import
    5 KB (907 words) - 05:30, 15 October 2014
  • DTFT of a sampled cosine Yijun ECE438 slecture
    Discrete-time Fourier transform (DTFT) of a sampled cosine slecture, I will talk about how does the discrete-time Fourier transform of the sampling of this signal look like. Suppose
    4 KB (598 words) - 20:05, 16 March 2015
  • HW3ECE438F14 Soln
    [[Category:fourier transform]] ...he Fourier transform of the interpolation you wrote in 2a) and the Fourier transform of x(t). (Do not simply write down the formula; show how to derive it.)
    7 KB (1,178 words) - 20:16, 18 December 2014

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Prof. Dan Fleetwood