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  • *[[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
  • [[Category: Fourier]] [[Category: Fourier Transform]]
    2 KB (268 words) - 12:14, 10 December 2008
  • ...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
  • 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 Fourier Series|Fourier Series]]== {{:ECE 301 Fall 2007 mboutin Fourier Series}}
    3 KB (297 words) - 16:56, 23 April 2013
  • ...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
  • [[Category: Fourier]] [[Category: Fourier Transform]]
    2 KB (321 words) - 11:28, 10 December 2008
  • [[Category: Fourier]] [[Category: Fourier Series]]
    1 KB (186 words) - 17:25, 23 April 2013
  • ...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
  • [[Category: Fourier]] Jean Baptiste Joseph Fourier (1768 - 1830)
    3 KB (390 words) - 12:10, 11 December 2008
  • [[Category: Fourier]] [[Category: Fourier Transforms]]
    2 KB (263 words) - 12:19, 11 December 2008
  • ...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
  • [[Category: Fourier]] [[Category: Fourier Transform]]
    3 KB (431 words) - 17:29, 23 April 2013
  • [[Category: Fourier]] [[Category: Fourier Transform]]
    2 KB (303 words) - 10:13, 12 December 2008
  • 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
  • [[Category: Fourier]] [[Category: Fourier Transforms]]
    2 KB (379 words) - 08:35, 9 March 2011
  • ...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
  • ...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
  • ...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
  • ...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
  • - 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
  • ...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
  • == 1.6.4 FFT "Fast Fourier transform" ==
    2 KB (376 words) - 06:44, 16 September 2013
  • * 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
  • | [[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
  • === Fourier series === ===CT Fourier transform ===
    2 KB (243 words) - 08:04, 21 November 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (384 words) - 10:55, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    863 B (144 words) - 10:54, 16 September 2013
  • == 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
  • 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
  • ==Fourier Transform== ==Inverse Fourier Transform==
    6 KB (711 words) - 11:28, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (270 words) - 12:24, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (252 words) - 12:41, 16 September 2013
  • 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
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    913 B (139 words) - 12:24, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (279 words) - 12:25, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    2 KB (384 words) - 12:42, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (215 words) - 12:26, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    966 B (151 words) - 12:42, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (213 words) - 12:26, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (167 words) - 12:42, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    905 B (142 words) - 12:45, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    759 B (126 words) - 12:27, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (206 words) - 12:44, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (171 words) - 12:28, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (260 words) - 12:28, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (191 words) - 12:29, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (281 words) - 12:29, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (263 words) - 12:30, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1,011 B (164 words) - 12:46, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (156 words) - 12:46, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    2 KB (379 words) - 12:47, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (292 words) - 12:27, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (199 words) - 12:31, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (183 words) - 12:31, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (187 words) - 12:43, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    881 B (135 words) - 12:31, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    847 B (132 words) - 12:46, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (240 words) - 12:45, 16 September 2013
  • I feel that computing Fourier Transform of summation problem.
    108 B (16 words) - 17:25, 7 October 2008
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (188 words) - 12:33, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (309 words) - 12:33, 16 September 2013
  • It was too hard to get fourier transform of summation term.
    97 B (16 words) - 18:19, 7 October 2008
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (176 words) - 12:32, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    848 B (136 words) - 12:49, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    2 KB (368 words) - 12:49, 16 September 2013
  • ...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
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (233 words) - 12:34, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1,015 B (175 words) - 12:34, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    943 B (144 words) - 12:50, 16 September 2013
  • ...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
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (266 words) - 12:35, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    921 B (156 words) - 12:50, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (177 words) - 12:35, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (168 words) - 12:51, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    846 B (122 words) - 12:51, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    845 B (149 words) - 12:36, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    981 B (144 words) - 12:47, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    842 B (140 words) - 12:30, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    906 B (151 words) - 12:51, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (192 words) - 12:35, 16 September 2013
  • ...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
  • 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
  • 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
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    929 B (140 words) - 12:48, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (179 words) - 12:32, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (353 words) - 12:23, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (181 words) - 12:36, 16 September 2013
  • Fourier Series Transformation - I had problems in determining which frequency is th Fourier Transform -
    402 B (70 words) - 16:57, 8 October 2008
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (218 words) - 12:25, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (218 words) - 12:22, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    919 B (145 words) - 12:52, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (280 words) - 12:37, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    757 B (115 words) - 12:48, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (184 words) - 12:47, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (177 words) - 12:24, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (239 words) - 12:39, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    917 B (138 words) - 12:52, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    965 B (145 words) - 12:37, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (160 words) - 12:40, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (201 words) - 12:44, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
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  • I still have difficulty calculating Fourier Transform coefficients.
    67 B (8 words) - 18:37, 8 October 2008
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (203 words) - 12:53, 16 September 2013
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    1 KB (206 words) - 12:36, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (161 words) - 12:52, 16 September 2013
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    803 B (124 words) - 12:49, 16 September 2013
  • '''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
  • '''Question:''' Compute the Fourier transform of the signal
    882 B (162 words) - 13:42, 24 October 2008
  • * [[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
  • [[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
  • ...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
  • ...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
  • == 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
  • ...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
  • == 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
  • We can solve by the definition of a Fourier Transform
    1 KB (256 words) - 09:42, 23 October 2008
  • ...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
  • ...ut thinking, you rush into the problem using the definition of the Fourier Transform...
    3 KB (665 words) - 19:39, 23 October 2008
  • ...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
  • 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
  • ...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
  • First, we do the Fourier transform on both sides, which yields:
    1 KB (197 words) - 10:50, 24 October 2008
  • ...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
  • ==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
  • '''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
  • == CT Fourier Transform == *[[CT Fourier Transform_ECE301Fall2008mboutin]] {{:CT Fourier Transform}}
    2 KB (255 words) - 16:12, 24 October 2008
  • Fourier Transform of delta functions
    860 B (156 words) - 18:26, 24 October 2008
  • Then the Fourier Transform: Then the Fourier Transform:
    822 B (164 words) - 18:11, 24 October 2008
  • 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)
    2 KB (367 words) - 11:27, 7 November 2008
  • This answer can be found simply by using the Fourier Transform of the <math>X_p(\omega) </math>.
    3 KB (582 words) - 06:11, 16 September 2013
  • ...inuous-time signal and X(j<math>\omega\,</math>) be the continuous Fourier transform of that signal. Then,
    1 KB (214 words) - 08:00, 10 November 2008
  • ...a continuous-time signal and <math>X(W)\,</math> be the continuous Fourier transform of that signal
    2 KB (303 words) - 10:24, 10 November 2008
  • ...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)
    2 KB (303 words) - 12:15, 10 November 2008
  • Taking the Fourier Transform of this function yields,
    1 KB (274 words) - 06:49, 16 September 2013
  • 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
    2 KB (356 words) - 08:49, 17 November 2008
  • ...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===
    927 B (170 words) - 09:59, 17 November 2008
  • then the fourier transform of the wave would look as follows
    971 B (172 words) - 17:48, 17 November 2008
  • ...>|{\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.
    2 KB (279 words) - 12:53, 17 November 2008
  • taking the fourier transform
    1 KB (183 words) - 14:05, 17 November 2008
  • 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.
    648 B (110 words) - 17:16, 17 November 2008
  • == '''Fundamentals of Laplace Transform''' == Here is how to compute the Laplace Transform of <math>x(t)</math>:
    4 KB (499 words) - 11:29, 16 September 2013
  • ...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.
    2 KB (427 words) - 10:25, 21 November 2008
  • == Laplace Transform == The laplace transform of a general signal <math> x(t) </math> is defined as
    1 KB (198 words) - 09:15, 23 November 2008
  • ==Laplace Transform== The Laplace transform of a function ''f''(''t''), defined for all real numbers, is the function '
    2 KB (292 words) - 21:24, 23 November 2008
  • == 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
    3 KB (553 words) - 17:12, 24 November 2008
  • == definition of laplace transform == The Laplace transform of a function ''f''(''t''), defined for all real numbers ''t'' ≥ 0, is th
    3 KB (438 words) - 16:26, 24 November 2008
  • == The relationship between Fourier and Laplace transform == The continuous-time Fourier transform provides us with a representation for signals as linear combinations of com
    1 KB (183 words) - 17:02, 24 November 2008
  • [[Category:Fourier transform]] [[Category:Laplace transform]]
    2 KB (283 words) - 07:33, 18 January 2013
  • 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
    2 KB (291 words) - 19:18, 24 November 2008
  • [[Category:z transform]] == The Z-Transform ==
    3 KB (452 words) - 10:28, 4 February 2013
  • == 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^
    3 KB (537 words) - 17:27, 3 December 2008
  • CT Fourier Transform Pair DT Fourier Transform Pair
    21 KB (3,312 words) - 11:58, 5 December 2008
  • 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.
    6 KB (938 words) - 06:59, 8 December 2008
  • ...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===
    7 KB (1,017 words) - 10:05, 11 December 2008
  • 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
    5 KB (911 words) - 07:54, 8 December 2008
  • ...if x(t) is band-limited, one must exam <math>X(\omega)</math> the Fourier transform of x(t).
    2 KB (254 words) - 07:05, 8 December 2008
  • ...operties of integrating an absolute value and the linearity of the Fourier transform.
    2 KB (356 words) - 12:08, 12 December 2008
  • Apply the inverse fourier transform integral:
    1 KB (172 words) - 12:10, 12 December 2008
  • Find the inverse Fourier transform of:
    1 KB (242 words) - 12:11, 12 December 2008
  • ...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
    3 KB (541 words) - 17:40, 14 November 2008
  • = Fourier Properties = The fourier transform of the comb function is the [[rep function_Old Kiwi]].
    354 B (58 words) - 22:31, 7 February 2008
  • ...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 (4,832 words) - 18:13, 22 October 2010
  • [[Convergence of Fourier Transforms_Old Kiwi]] [[Fourier Transform table_Old Kiwi]]
    332 B (47 words) - 22:23, 23 March 2008
  • 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
    1 KB (218 words) - 11:10, 24 March 2008
  • * [[Fourier, Laplace and Z-Transform Equation Reference Sheet_Old Kiwi]]
    607 B (80 words) - 14:27, 30 March 2008
  • 1: Take the Fourier transform ([Meaning of Fourier Transform]) of the equation, ...uide to Partial Fraction Expansion]) to facilitate use of inverse Fourier transform,
    1 KB (198 words) - 19:08, 4 April 2008
  • ...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
    4 KB (683 words) - 21:46, 6 April 2008
  • ...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.
    657 B (104 words) - 01:45, 17 April 2008
  • ##[[Fourier Series representation of continuous-time periodic signals_Old Kiwi]] ##[[Fourier Series Representation of CT periodic signals_Old Kiwi]]
    4 KB (531 words) - 11:32, 25 July 2008
  • ...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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  • 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 (803 words) - 11:10, 22 July 2008
  • *Fourier Series ** PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
    9 KB (1,237 words) - 09:29, 5 October 2009
  • [[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]]
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  • [[Category:discrete Fourier transform]] == DFT ( Discrete Fourier Transform ) ==
    4 KB (695 words) - 06:46, 23 September 2011
  • ...ill cover all material covered ''since'' the Midterm (including CT Fourier Transform). A list of topics include * CT Fourier Transform
    5 KB (643 words) - 11:55, 6 August 2009
  • ...scriptive to their content while still including your name, e.g. [[Fourier Transform - Landis Huffman]]
    983 B (157 words) - 08:02, 21 July 2009
  • '''''Linearity'' - Property of Continuous Time Fourier Transform'''
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  • 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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  • (The right hand side of this equation is the Fourier transform analysis equation for x*(t))
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  • Aperiodic signal <===> Fourier transform
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  • Time Shifting property of the Fourier Transform
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  • 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
  • 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))
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  • By definition of Fourier Transform:
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  • Property: Linearity in Fourier Transform: The fourier transform of ax(t) is the integration of 1/T * (ax(t)*exp(-jwt))
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  • Define a function x(t) with its Fourier transform being X(jw) so '''Fourier transform'''(x(t)') = jwX(jw)
    667 B (109 words) - 01:07, 9 July 2009
  • ...with a multiplication operation in the frequecy domain for easier Fourier transform enalysis
    530 B (101 words) - 04:45, 9 July 2009
  • Proving that the Continuous-Time Fourier Transform demonstrates linearity
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  • == Fourier Series == * [[CT Fourier series expansion]]
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  • [[CT Fourier Transform - Xiaodian Xie]]
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  • [[CT Inverse Fourier Transform -- Alex Gaul]]
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  • [[Continuous Time Fourier Transform (CTFT) - Muhammad Aizuddin Zulkifli]]
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  • [[Discrete Time Fourier Transform Properties (DTFT) - Evan Witkoske]] [[Discrete Time Fourier Transform Properties (DTFT) - Mohammed Almathami]]
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  • CT Fourier Transform Properties
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  • [[Category:discrete time Fourier transform]] =DT Fourier Transform Properties=
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  • == CT Fourier Transform (Book chapter 4)== * [[CT Fourier transform]]
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  • ...scriptive to their content while still including your name, e.g. [[Fourier Transform - Landis Huffman]]
    288 B (42 words) - 09:50, 23 July 2009
  • *Continuous Time Fourier Series (CTFS) **[https://engineering.purdue.edu/~bouman/ece301/notes/pdf2/FourierSeries.pdf Fourier Series Expansion]
    6 KB (785 words) - 06:02, 1 March 2010
  • ...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
    7 KB (1,297 words) - 11:41, 10 December 2011
  • [[DT Fourier Transform - William Owens]]
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  • 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
  • Definition of Fourier Transform:
    1 KB (264 words) - 05:57, 11 June 2013
  • Define the Fourier Transform to be:
    2 KB (315 words) - 05:55, 11 June 2013
  • 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 == The Laplace Transform of any signal '''<math>x(t)</math>''' is....
    388 B (72 words) - 06:39, 29 July 2009
  • [[Ryne Rayburn - ECE 301 - DT Inverse Fourier Transform]]
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  • == DT Inverse Fourier Transform ==
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  • 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
    1 KB (206 words) - 05:52, 11 June 2013
  • From the Inverse Fourier Transform we clearly see that <math>f\equiv 0</math> a.e.
    994 B (157 words) - 05:56, 11 June 2013
  • [[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
  • [[Category:discrete-time Fourier transform]] [[Category:z-transform]]
    1 KB (216 words) - 14:49, 1 May 2015
  • ...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
  • [[Category:discrete time Fourier transform]]
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  • [[Laplace/Fourier Transform Comparison -- Yicheng Guo]]
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  • Laplace Transform is an extension of Fourier Transform.
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  • 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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  • CTFT ( Continuous Time Fourier Transform ) DTFT ( Discrete Time Fourier Transform )
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  • *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
    4 KB (628 words) - 15:47, 30 November 2010
  • ...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.
    992 B (171 words) - 05:45, 11 September 2009
  • ...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
  • ** 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
  • ...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
    1 KB (248 words) - 11:07, 22 September 2009
  • Taking the Fourier transform of Eq. 3 gives:
    3 KB (527 words) - 11:50, 22 September 2009
  • ==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
  • [[Category:discrete Fourier transform]] =Notes on Discrete Fourier Transform=
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  • :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
  • == Discrete Fourier Transform == same formula as for discrete fourier series.
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  • '''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
  • ...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 Transform and its basic Properties:== ===Fourier Transform:===
    1 KB (218 words) - 07:34, 25 August 2010
  • ...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:
    2 KB (286 words) - 10:19, 23 September 2009
  • **[[Laplace Transforms Table|(bidirectional) Laplace Transform Pairs and Properties]] (used in [[ECE301]], [[ECE438]]) **[[unidirectional_Laplace_Transform_Table|(unidirectional) Laplace Transform Pairs and Properties]]
    3 KB (294 words) - 15:44, 12 March 2015
  • ...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
  • ..."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
  • [[Category:Fourier transform]] Table of Continuous-time (CT) Fourier Transform Pairs and Properties
    8 KB (1,130 words) - 11:45, 24 August 2016
  • =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
  • '''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
  • [[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
    3 KB (495 words) - 10:13, 11 November 2011
  • [[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
    8 KB (1,397 words) - 11:23, 18 March 2013
  • ...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
  • [[Category:discrete-space Fourier transform]]
    1 KB (163 words) - 12:50, 26 November 2014
  • ...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
    14 KB (2,366 words) - 17:32, 21 April 2013
  • ...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
    17 KB (3,004 words) - 08:11, 15 December 2011
  • If we Fourier Transform the filter, we discover that the filter is linear:
    5 KB (811 words) - 16:19, 19 December 2009
  • 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
  • ...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
    3 KB (394 words) - 07:08, 4 May 2010
  • [[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
    13 KB (2,348 words) - 13:25, 2 December 2011
  • **[[Practice_Question_2_ECE439F10|Practice Question 2 (on z-transform computation)]] **[[Practice_Question_3_ECE439F10|Practice Question 3 (on inverse z-transform computation)]]
    9 KB (1,221 words) - 11:00, 22 December 2014
  • *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

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