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  • ...ntation of continuous-time periodic signals_(ECE301Summer2008asan)|Fourier Series representation of continuous-time periodic signals]] ...eries Representation of CT periodic signals_(ECE301Summer2008asan)|Fourier Series Representation of CT periodic signals]]
    7 KB (921 words) - 06:08, 21 October 2011
  • Determine the Fourier Series co-efficient for the following continuous time periodic signals.Show the de
    1 KB (182 words) - 11:05, 21 November 2008
  • ...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 with peri ...tinuous-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
  • #REDIRECT [[Fourier Series representation of continuous-time periodic signals (ECE301Summer2008asan)]]
    102 B (11 words) - 11:16, 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
  • [[Category: Fourier]] [[Category: Fourier Series]]
    842 B (120 words) - 12:21, 9 December 2008
  • [[Category: Fourier]] [[Category: Fourier Series]]
    5 KB (834 words) - 17:26, 23 April 2013
  • ==[[ECE 301 Fall 2007 mboutin DT Fourier Series in Matlab|DT Fourier Series in Matlab with ONE Command]]== {{:ECE 301 Fall 2007 mboutin DT Fourier Series in Matlab}}
    1,000 B (121 words) - 12:50, 18 December 2008
  • [[Category: Fourier]] [[Category: Fourier Series]]
    1 KB (186 words) - 17:25, 23 April 2013
  • [[Category: Fourier]] [[Category: Fourier Transform]]
    3 KB (431 words) - 17:29, 23 April 2013
  • [[Category: Fourier]] [[Category: Fourier Series]]
    936 B (157 words) - 12:11, 12 December 2008
  • [[Category: Fourier]] [[Category: Fourier Series]]
    808 B (131 words) - 13:04, 18 December 2008
  • [[Fourier Series Homework_MA181Fall2008bell]]
    3 KB (390 words) - 06:35, 10 August 2010
  • *[[Lecture19_ECE301Fall2008mboutin|Lecture 19]]: TA Example Session w/ DT Fourier Transforms and inverses ...ll2008mboutin|Session 1: 9/2/2008]]: Phasors, Energy, Power, and Geometric Series '''Updated'''
    5 KB (720 words) - 06:10, 16 September 2013
  • (Look at the syntax of the geometric series below for an example.) This will allow other people to refer to your formul ! colspan="2" style="background: #eee;" | Series
    8 KB (989 words) - 07:20, 5 February 2009
  • * PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409, ...38/FALL01/Fourier_notes1.pdf Prof. Pollak's supplementary notes on Fourier series]
    8 KB (1,226 words) - 11:40, 1 May 2009
  • Find the Fourier Sine Series for:
    408 B (71 words) - 12:35, 6 December 2008
  • ...ine are common periodic functions, with period 2π. The subject of Fourier series investigates the idea that an 'arbitrary' periodic function is a sum of tri
    1 KB (253 words) - 07:04, 14 April 2010
  • ==Periodic CT Signal, Fourier Series Coefficients== ==Periodic DT Signal, Fourier Series Coefficients==
    12 KB (1,544 words) - 11:27, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (217 words) - 11:04, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1,021 B (156 words) - 10:58, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (197 words) - 10:59, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (192 words) - 10:58, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (242 words) - 10:58, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (186 words) - 10:58, 16 September 2013
  • Find the Fourier Series coefficients of x[n] ...do not have to use the formula for this problem. x[n] looks like a Fourier series. wo=pi/2, so
    2 KB (415 words) - 11:46, 23 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    671 B (107 words) - 10:57, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    778 B (122 words) - 10:57, 16 September 2013
  • ...system to the signal you defined in Question 1 using H(s) and the Fourier series coefficients of your signal.
    1 KB (223 words) - 07:30, 25 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (306 words) - 10:57, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (384 words) - 10:56, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    783 B (123 words) - 10:59, 16 September 2013
  • '''Fourier series:'''
    229 B (44 words) - 10:40, 24 September 2008
  • ==Fourier Series Coefficients==
    1 KB (162 words) - 13:40, 24 September 2008
  • The Fourier series coefficients can be calculated with: Let us look for the Fourier series coefficients for the DT signal <big><math>x[n] = cos(3\pi n)</math></big>
    1 KB (230 words) - 14:22, 26 September 2008
  • ==DT Signal Fourier Coefficients== Now to find the fourier series coefficients:
    2 KB (271 words) - 17:36, 25 September 2008
  • The Fourier series coefficients for <math>x[n]</math> are:
    1 KB (222 words) - 13:55, 24 September 2008
  • ==CT Signal & its Fourier coefficients== Knowing that its Fourier series is
    369 B (68 words) - 21:38, 23 September 2008
  • == Fourier Series Coefficients for a DT signal ==
    650 B (95 words) - 07:26, 24 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    3 KB (464 words) - 10:58, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    834 B (129 words) - 10:56, 16 September 2013
  • === Fourier series === ===CT Fourier transform ===
    2 KB (243 words) - 08:04, 21 November 2008
  • <font size="3">Let <math>x(t)=cos(4 \pi t) + sin(6 \pi t)</math> with Fourier series coefficients are as follows: ...to the system <math>y(t)</math> based on <math>H(s)</math> and the Fouries series coefficients is:
    904 B (165 words) - 12:58, 24 September 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 ==
    2 KB (360 words) - 10:55, 16 September 2013
  • Fourier Series Coefficients:
    1 KB (175 words) - 17:18, 24 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (429 words) - 10:55, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (250 words) - 10:54, 16 September 2013
  • == Fourier Series for DT signals ==
    907 B (155 words) - 06:49, 25 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    837 B (141 words) - 10:56, 16 September 2013
  • ==Define a periodic DT signal and compute its Fourier series coefficients. ==
    480 B (88 words) - 18:22, 26 September 2008
  • ...system to the signal you defined in Question 1 using H(s) and the Fourier series coefficients of your signal.
    1 KB (241 words) - 18:42, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    863 B (144 words) - 10:54, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (363 words) - 10:56, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    966 B (160 words) - 10:53, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (410 words) - 10:53, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (216 words) - 11:02, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (279 words) - 10:54, 16 September 2013
  • == Define a Periodic DT Signal and Compute the Fourier Series Coefficients ==
    3 KB (405 words) - 12:42, 25 September 2008
  • == Computing the Fourier series coefficients for a Discrete Time signal x[n] ==
    900 B (178 words) - 12:47, 25 September 2008
  • ...e of y[n] to the signal I defined in Question 2 using H[z] and the Fourier series coefficients ==
    1 KB (242 words) - 13:11, 25 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (283 words) - 10:55, 16 September 2013
  • ...finite sum of shifted copies of a non-periodic signal, compute its Fourier series coefficients. The equation for determining the Fourier coefficients of a DT signal is
    2 KB (375 words) - 15:10, 25 September 2008
  • '''Problem:''' Find the Fourier series coefficients of x[n], where x[n] is a square wave with fundamental period N '''Solution:''' A periodic DT signal can be expressed as a Fourier series in the following manner:
    2 KB (313 words) - 14:17, 25 September 2008
  • ....2_Brian_Thomas_ECE301Fall2008mboutin|here]] by using H(z) and the Fourier series coefficients of x[n]. '''b)''' Given the Fourier coefficients, x[n] can be expressed as follows:
    2 KB (355 words) - 16:48, 25 September 2008
  • Computing the Fourier series coefficients...<br><br>
    770 B (140 words) - 15:12, 25 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (205 words) - 10:56, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (210 words) - 11:03, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    911 B (165 words) - 11:03, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (215 words) - 10:59, 16 September 2013
  • == CT Fourier Series ==
    662 B (136 words) - 09:55, 26 September 2008
  • == DT Fourier Series ==
    1 KB (280 words) - 15:40, 26 September 2008
  • Discrete time Fourier series
    499 B (77 words) - 19:03, 25 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (182 words) - 11:03, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    984 B (159 words) - 11:04, 16 September 2013
  • == Fourier Series == == Fourier Series Coefficients ==
    967 B (170 words) - 14:35, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    891 B (142 words) - 11:01, 16 September 2013
  • The Fourier Series coefficients are:
    876 B (173 words) - 04:45, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    777 B (123 words) - 11:05, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    885 B (159 words) - 11:01, 16 September 2013
  • ...system to the signal you defined in Question 1 using H(s) and the Fourier series coefficients of your signal==
    2 KB (349 words) - 08:25, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (163 words) - 11:05, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    938 B (158 words) - 11:02, 16 September 2013
  • ...system to the signal you defined in Question 2 using H(z) and the Fourier series coefficients of your signal=
    1 KB (241 words) - 09:04, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    989 B (173 words) - 11:06, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    806 B (120 words) - 11:06, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (195 words) - 11:07, 16 September 2013
  • Recall the Fourier Series formulae for the continuous time signal case: ==Finding the Series==
    1 KB (261 words) - 13:32, 26 September 2008
  • x[n] with Fourier series representation (pg. 230):<br>
    637 B (101 words) - 13:22, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (201 words) - 11:06, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (228 words) - 11:07, 16 September 2013
  • == DT signal & its Fourier Coefficients == Knowing its Fourier series is:
    1 KB (200 words) - 17:10, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (188 words) - 11:08, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (215 words) - 11:04, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    923 B (155 words) - 11:07, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    877 B (147 words) - 10:53, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (311 words) - 10:57, 16 September 2013
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    931 B (147 words) - 10:59, 16 September 2013
  • == Fourier Series Coefficients ==
    462 B (89 words) - 16:43, 26 September 2008
  • The Fourier series coefficients in <math>x(t)=cos(3 \pi t) + sin(8 \pi t)</math> are:
    986 B (178 words) - 16:31, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    2 KB (291 words) - 10:54, 16 September 2013
  • ==Response of the Signal and Fourier Series Coefficients==
    1 KB (214 words) - 17:41, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    863 B (140 words) - 11:08, 16 September 2013
  • = Fourier series coefficients for DT signal = ==Fourier series coefficients==
    818 B (140 words) - 17:14, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    822 B (139 words) - 10:57, 16 September 2013
  • 2. x(t) is periodic with period T = 4 and Fourier coefficients <math> \ a_k </math>. as cos(t) is an even function with a Fourier Series representation that has coefficients of 0 for absolute values of k greater
    992 B (159 words) - 18:33, 26 September 2008
  • [[Category:Fourier series]] == Example of Computation of Fourier series of a CT SIGNAL ==
    1 KB (169 words) - 11:09, 16 September 2013
  • Compute the response of the system to the signal using H(s) and the Fourier series coefficients of the signal.<br><br>
    905 B (182 words) - 19:11, 26 September 2008
  • [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
    1 KB (187 words) - 12:43, 16 September 2013
  • Also, I am confused about what is needed to define a Fourier series in DT as opposed to CT.
    242 B (50 words) - 16:13, 7 October 2008
  • ...ncept that I seem to struggle with is how to correctly compute the Fourier Series.
    88 B (16 words) - 17:25, 7 October 2008
  • ...analogy that a vector is to its components as a function is to its fourier series, but I don't know what these transforms are showing.
    365 B (65 words) - 14:45, 8 October 2008
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (353 words) - 12:23, 16 September 2013
  • Fourier Series Transformation - I had problems in determining which frequency is the funde Fourier Transform -
    402 B (70 words) - 16:57, 8 October 2008
  • [[Category:Fourier transform]] == Example of Computation of Fourier transform of a CT SIGNAL ==
    2 KB (280 words) - 12:37, 16 September 2013
  • 4. Compute the coefficients <math>a_{k}</math> of the Fourier series of the signal x(t) with period T = 4 defined by
    2 KB (303 words) - 19:47, 8 October 2008
  • '''4.''' Compute the coefficients <math>a_k</math> of the Fourier series of the signal <math>x(t)</math> periodic with period <math>T=4</math> defin
    1 KB (195 words) - 16:16, 13 October 2008
  • Compute the coefficients <math>a_k</math> of the Fourier series of the signal <math>x(t)</math> periodic with period <math>T=4</math> defin Next, we procede to calculate <math>a_k\,</math> Notice that the fourier transformation of a square signal is made up from sin waves with infinite n
    2 KB (300 words) - 07:39, 14 October 2008
  • 4. Compute the coefficients <math>a_{k} \!</math> of the Fourier series signal <math>x(t) \!</math> periodic with period <math>T = 4 \!</math> defi
    1 KB (210 words) - 16:19, 14 October 2008
  • '''4.''' Compute the coefficients '''<math>a\ _k</math>''' of the Fourier series of the signal '''<math>x\ (t)</math>''' periodic with period '''<math>T\ =
    851 B (138 words) - 18:23, 14 October 2008
  • Compute the coefficients <math>a_k</math> of the Fourier series of the signal <math>x(t)</math> periodic with period <math>T=4</math> defin
    1 KB (193 words) - 09:12, 15 October 2008
  • Compute the coefficients <math>a_k</math> of the Fourier series of the signal x(t) periodic with period T = 4 defined by
    1 KB (217 words) - 11:05, 15 October 2008
  • 4. Compute the coefficients <math>a_k</math> of the Fourier series of the signal x(t) periodic with period T=4 defined by
    764 B (143 words) - 17:52, 15 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
  • ==Continuous Time Fourier Transform Pair for Aperiodic and Periodic Signals== The Fourier transform exists if the signal is absolutely integrable or if the signal ha
    3 KB (465 words) - 14:38, 24 October 2008
  • ...ling involves a function known as an impulse train. An impulse train is a series of impulses that are spaced out by a period T, known as the Sampling Period Taking the Fourier Transform of this function yields,
    1 KB (274 words) - 06:49, 16 September 2013
  • We have a series of impulses in the time domain, but we want them to extend across, so we mu This is most easiest performed in the frequency domain with Fourier transforms. To most easily find <math>h_2(t)</math>, make sure that :
    2 KB (411 words) - 17:16, 17 November 2008
  • [[Category:geometric series]] ...omega}\!</math> with <math>\omega\!</math> real, this summation equals the Fourier Transform of <math>h[n]\!</math>. When <math>z\!</math> is not restricted
    3 KB (452 words) - 10:28, 4 February 2013
  • In order to get further insight into the relationship between the Fourier Transform and the Z-Transform it is useful to look at the complex plane or ...ourier transform as the z-transform on the unit circle, the periodicity of Fourier transform is easily seen.
    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
  • ...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
  • ...se-Hulman. It was called Boundary Value Problems. We worked with Fourier Series and all that fun stuff. It was actually pretty fun. We used maple a lot s
    1 KB (210 words) - 15:01, 18 December 2008
  • ...nce of Gaussian noise on both x and y. In some cases, PCA corresponds to a Fourier transform, such as the DCT used in JPEG image compression. Imagine an organism or machine which experiences a series of inputs from different sensors: x1, x2, x3, x4, . . . The machine is also
    31 KB (4,832 words) - 18:13, 22 October 2010
  • ==Fourier Series== [[Fourier Series(3.6)_Old Kiwi]]
    456 B (75 words) - 22:17, 23 March 2008
  • DT Fourier Series
    780 B (131 words) - 20:10, 22 March 2008
  • Even odd Fourrier Series Coefficients ...a real periodic sequence with fundamental period <math>{N}_{0}</math> and Fourier coefficients <math>{c}_{k}={a}_{k}+j{b}_{k}</math> where ak and bk are both
    868 B (154 words) - 17:36, 30 March 2008
  • 1: Take the Fourier transform ([Meaning of Fourier Transform]) of the equation, ...sion ([Guide to Partial Fraction Expansion]) to facilitate use of inverse Fourier transform,
    1 KB (198 words) - 19:08, 4 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
  • Determine the Fourier Series co-efficient for the following continuous time periodic signals.Show the de
    988 B (163 words) - 16:25, 3 July 2008
  • ...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 with peri ...tinuous-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
  • ...e exam will 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
  • ==Multiplication Property of Continuous - Time Fourier Series== ...dic with period '''T''', we can expand it in a Fourier series with Fourier series coefficients '''<math>h_k</math>''' expressed in terms of those for x(t) an
    583 B (107 words) - 09:20, 8 July 2009
  • ..._0</math> to created the shifted signal <math>x(t-t_0)</math>, the Fourier series coefficients of the shifted will be <math>a_k e^{-jkw_0t_0}</math>, where < Let <math>a_k</math> be the Fourier series coefficients of <math>x(t)</math>, so
    1 KB (240 words) - 16:58, 8 July 2009
  • == Continous - Time Fourier Series: Time Reversal == Right-hand side of the equation has the form of a Fourier series synthesis equation for x(-t)
    539 B (102 words) - 18:39, 8 July 2009
  • '''== Time Shifting Property of Continuous-Time Fourier Series ==''' <br> The Fourier series coefficients <math>b_{k}</math> of the resulting signal y(t)=x(t-<math>t_{0
    1 KB (200 words) - 03:44, 9 July 2009
  • * [[Geometric Series]] == Fourier Series ==
    1 KB (152 words) - 04:06, 23 July 2009
  • Fourier Series for discrete time signals.
    116 B (22 words) - 13:45, 22 July 2009
  • Discrete Time Fourier Series Coefficients
    117 B (21 words) - 18:02, 22 July 2009
  • CT Fourier Series Expansion - Walter Mulflur
    119 B (23 words) - 18:26, 22 July 2009
  • then the Fourier series coefficients <math>b_k</math> of the resulting signal y(t) = x(t - <math>t_ where <math>a_k</math> is the <math>k^{th}</math> Fourier series coefficient of x(t). That is, if
    1 KB (266 words) - 03:10, 23 July 2009
  • *Continuous Time Fourier Series (CTFS) ...engineering.purdue.edu/~bouman/ece301/notes/pdf2/FourierSeries.pdf Fourier Series Expansion]
    6 KB (785 words) - 06:02, 1 March 2010
  • Fourier series. It turns out that ALL of the Fourier coefficients are equal to 1.
    1 KB (196 words) - 04:17, 30 July 2009
  • * A knowledge of Fourier series and periodic signals. * An understanding of Fourier transforms for linear time invariant systems and the basics of sampling and
    7 KB (1,153 words) - 14:06, 24 August 2009
  • |Homework 6 due – Fourier Series |Exam 2 – LTI system properties; orthonormal transforms; Fourier series
    1 KB (190 words) - 15:00, 24 August 2009
  • ...nformation is conveniently packaged within the complex coefficients of the Fourier Transform. So if it is understood that a sinsuoid must be sampled twice wit ...tation of 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
    8 KB (1,452 words) - 06:49, 16 September 2013
  • This, in Fourier Domain becomes The Fourier Series of this function can be represented as
    4 KB (655 words) - 07:13, 23 September 2009
  • ==Fourier Analysis and the Speech Spectrogram== ...ch frequency component's contribution to the original signal. Finally, the Fourier Transform is calculated to express these coefficients as a function of freq
    8 KB (1,268 words) - 07:16, 23 September 2009
  • == Discrete Fourier Transform == same formula as for discrete fourier series.
    2 KB (491 words) - 23:03, 22 September 2009
  • *[[PowerSeriesFormulas|Power Series]] (used in [[ECE301]], [[ECE438]]) **[[CT Fourier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of radial frequency- in radians
    3 KB (294 words) - 15:44, 12 March 2015
  • '''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
  • ...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 ...concepts,things will be easier.Complex analysis,functions,limits,geometric series lies in the heart of signals.Plotting various signals seemed so abstruse in
    14 KB (2,366 words) - 17:32, 21 April 2013
  • ...ansform. Discrete-time linear systems: difference equations, Discrete-Time Fourier Transform, bilateral z-Transform. Sampling, quantization, and discrete-time ...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
  • ...ises of Fourier series computations for CT signals]], especially [[Fourier series coefficients student 1|this one]]. ...ed exercise Fourier series computation DT|Recommended exercises of Fourier series computations for DT signals]]
    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
  • ...Fourier_series_computation|A collective page to practice computing Fourier series of a CT signal]] ...rier_series_computation_DT|A collective page to practice computing Fourier series of a DT signal]]
    2 KB (211 words) - 05:39, 26 September 2011
  • .../www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier series expansion example] <br/>
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  • [[Category:Fourier series continuous-time]] = This pages contains exercises to practice computing the Fourier series of a CT signal =
    5 KB (797 words) - 09:43, 29 December 2010
  • [[Category:Fourier series discrete-time]] =This pages contains exercises to practice computing the Fourier series of a DT signal =
    2 KB (355 words) - 09:44, 29 December 2010
  • For those of you wishing to brush up on Fourier series, here are two collective study pages: ...ended_exercise_Fourier_series_computation|Recommended exercises of Fourier series computations for CT signals]]
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  • =Exercise: Compute the Fourier series coefficients of the following signal:= After you have obtained the coefficients, write the Fourier series of x(t).
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  • =Exercise: Compute the DT Fourier series coefficients of the following discrete-time signal:= After you have obtained the coefficients, write the Fourier series of x[n].
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  • <math>\text{3. Compute the Fourier series coefficients of the following signal:} \,\!</math>
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  • [[Category:Fourier series]] =Exercise: Compute the Fourier series coefficients of the following periodic signal:=
    6 KB (999 words) - 13:00, 16 September 2013
  • *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
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  • *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
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  • ...or reconstructing the DTFT of a finite duration signal from the [[Discrete Fourier Transform|DFT]] of its periodic repetition. The formula was observed to hol ...ier series, as computing DFTs is essentially the same as computing Fourier series coefficients.
    1 KB (158 words) - 15:59, 8 October 2010
  • [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
    5 KB (766 words) - 14:22, 21 April 2013
  • 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
  • ...nce of Gaussian noise on both x and y. In some cases, PCA corresponds to a Fourier transform, such as the DCT used in JPEG image compression. Imagine an organism or machine which experiences a series of inputs from different sensors: x1, x2, x3, x4, . . . The machine is also
    31 KB (4,787 words) - 18:21, 22 October 2010
  • Answer: You will need to note that the Fourier Series converges to the function. After that, you'll need to plug in x=0 and x=1 and notice that the Fourier Series pops out the sum you are after. Page 482 is helpful.
    2 KB (402 words) - 18:48, 2 November 2010
  • Recall, the Discrete Fourier Transform is defined as follows - ...of the N samples comprising one period of x[n] equals N times the Fourier series coefficients.
    19 KB (3,208 words) - 11:23, 30 October 2011
  • ...ng that there is still both a complex part and a real part for the Fourier series. Am I just supposed to write the real part, or am I doing this problem inco ...lit the series into two parts since it is not defined for n=0. The Fourier series in problem 9 is:
    8 KB (1,441 words) - 15:52, 10 November 2010
  • that just puts the same k in front of the series for the solution.) ...s cancel and it leaves you with 3 sine terms that then go into the fourier series.
    6 KB (1,054 words) - 09:24, 1 December 2010
  • ...t it is periodic. Which is very convenient to implement DSP methods using Fourier transform. The audio signal will go through the filters connected in series and the output will be a much better audio signal with Vuvuzelas noise grea
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  • 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
  • *Video Extract 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
  • .../www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier series expansion example] <br/>
    2 KB (352 words) - 07:06, 31 January 2011
  • ...I think that it's always 1, and therefore not periodic, so it doesn't have fourier coefficients. What am I doing wrong? ...hoping you can resolve this. For 2g the function is already in its Fourier series. So to find the a_k values you need to manipulate the exponential terms. I
    2 KB (404 words) - 04:50, 14 February 2011
  • Obtain the Fourier series coefficients of the following signals. What is the Fourier series for each of the signals in Question 2?
    4 KB (663 words) - 15:15, 12 February 2011
  • ...ll_2007_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
  • *[[PowerSeriesFormulas|Power Series]] *[[CT Fourier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</spa
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  • ...ine/sine as a Fourier series, we are effectively writing out their Fourier series.
    1 KB (212 words) - 14:11, 28 February 2011
  • ...of terms. Next lecture, I will give examples of computations of DT Fourier series coefficients. It still not be a bad thing if you tried the corresponding p *Solve the Practice problems on the Fourier series computation
    2 KB (287 words) - 14:11, 28 February 2011
  • [[Category:Fourier series]] = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Series coefficients of a sine wave=
    3 KB (502 words) - 12:59, 16 September 2013
  • = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Series coefficients of a discrete-time (sampled) cosine wave = Obtain the Fourier series coefficients of the DT signal
    3 KB (548 words) - 10:24, 11 November 2011
  • [[Category:Fourier series]] = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Series continuous-time signal=
    4 KB (594 words) - 12:59, 16 September 2013
  • = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Series discrete-time signal = Obtain the Fourier series the DT signal
    2 KB (264 words) - 10:25, 11 November 2011
  • ...remember that there are two different methods for computing the DT Fourier series coefficients. One is very quick but only applies when you can figure out a *Practice computing DT Fourier series: Two practice problems are posted already. Let me know if you need more.
    2 KB (275 words) - 14:11, 28 February 2011
  • = Table of CT Fourier Series Coefficients and Properties = == Some Fourier series ==
    2 KB (419 words) - 10:52, 6 May 2012
  • ..._Fourier_series_practice_problems_list|Problems on continuous-time Fourier series]] *[[CT_Fourier_transform_practice_problems_list|Problems on continuous-time Fourier transform]]
    12 KB (1,768 words) - 10:25, 22 January 2018
  • = [[: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
  • 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
  • In this chapter author explains Fourier Series and Fourier Transforms of CT signals. The explanation is very good and clear. It is ver In this chapter author introduces Laplace Transform and generalizes Fourier Transforms. Explanations and justifications are very good and useful, it do
    6 KB (972 words) - 06:29, 1 November 2011
  • In this chapter author explains Fourier Series and Fourier Transforms of CT signals. The explanation is very good and clear. It is ver In this chapter author introduces Laplace Transform and generalizes Fourier Transforms. Explanations and justifications are very good and useful, it do
    6 KB (955 words) - 10:54, 6 May 2012
  • **[[Problem Generalized Geometric Series Formula ECE438F11|When is this summation formula valid?]] **[[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)]]
    10 KB (1,359 words) - 03:50, 31 August 2013
  • .../www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier Series Example]<br/>
    3 KB (456 words) - 10:20, 12 October 2011
  • *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
    9 KB (1,341 words) - 03:52, 31 August 2013
  • 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 fa We then began discussing the [[Discrete_Fourier_Transform|Discrete Fourier Transform]] (DFT).
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  • [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
    4 KB (735 words) - 14:19, 21 April 2013
  • [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
    3 KB (513 words) - 14:20, 21 April 2013
  • ...Fourier_series_computation|A collective page to practice computing Fourier series of a CT signal]] ...rier_series_computation_DT|A collective page to practice computing Fourier series of a DT signal]]
    2 KB (212 words) - 05:44, 26 September 2011
  • ...of a finite duration signal and the [[Discrete_Fourier_Transform|Discrete Fourier Transform]] of its periodic repetition. ...es of Fourier series computations for DT signals]] (to brush up on Fourier series))
    1 KB (181 words) - 06:24, 11 September 2013
  • *Please help! We need a [[Discrete_Fourier_Transform_table|table of Discrete Fourier transform pairs and properties]]! **[[Problem Generalized Geometric Series Formula ECE438F11|When is this summation formula valid?]]
    9 KB (1,273 words) - 20:52, 15 October 2011
  • **[[Problem Generalized Geometric Series Formula ECE438F11|When is this summation formula valid?]] **[[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)]]
    6 KB (801 words) - 22:04, 19 April 2015
  • ...2! Professor Palais noted that "... Cauchy's integral formula and Fourier series formulas all begin with 1/2<math>\pi</math>, Stirling's approximation and t
    5 KB (820 words) - 08:33, 11 December 2011
  • ==Fourier Series==
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  • [[Category:Fourier series]]
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  • | [[FourierSeriesConvergenceBonusProject | Convergence of Parametric Fourier Series]] ...Computations: [[Computation_of_Energy_and_Power_of_a_DT_signal|DTGeometric Series]] [[Computation_of_Energy_and_Power_of_a_CT_sinusoidal_signal|CT Cosine wav
    4 KB (534 words) - 19:10, 4 December 2018
  • *[[PowerSeriesFormulas|Power Series]] *[[CT Fourier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</spa
    2 KB (236 words) - 11:24, 21 September 2012
  • **[[PowerSeriesFormulas|Power Series]] **[[CT_Fourier_Transform_(frequency_in_radians_per_time_unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</spa
    6 KB (799 words) - 10:10, 15 May 2013
  • 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 Gibbs pheno c) Plot Fourier Transform of filter’s impulse response in 3D.
    4 KB (573 words) - 10:15, 15 May 2013
  • *[[Fourier_analysis_in_Music| Fourier Analysis in Music]] by [[user:mbell|Maria Bell]] *[[Geometric_Series_Explanation|Geometric Series Explanation]] by [[user:amcgail|Alec McGail]]
    2 KB (287 words) - 13:01, 12 January 2018
  • [[Category:Fourier series]]
    2 KB (322 words) - 23:38, 10 March 2013
  • [[Category:Fourier series]] ...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 Gibbs pheno
    2 KB (348 words) - 10:50, 11 March 2013
  • Joseph Fourier first represented Fourier integral theorem in the following DOE: [[Category:Fourier series]]
    1 KB (174 words) - 11:34, 11 March 2013
  • ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]] This set of notes is on Lectures 5, 6 and 7 of the series and covers Tomographic Reconstruction. You can watch the unedited videos fo
    4 KB (443 words) - 07:24, 26 February 2014
  • == Fourier Analysis in Music == <pre> keyword: tutorial, Fourier, Fourier analysis, harmonics </pre>
    5 KB (883 words) - 13:06, 25 November 2013
  • *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
    9 KB (1,353 words) - 09:04, 11 November 2013
  • .../www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier Series Example]<br/>
    2 KB (341 words) - 15:54, 14 August 2013
  • .../www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier Series Example]<br/>
    2 KB (351 words) - 17:43, 16 August 2013
  • **[[PowerSeriesFormulas|Power Series]] **[[CT_Fourier_Transform_(frequency_in_radians_per_time_unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</spa
    4 KB (480 words) - 18:57, 10 December 2013
  • ...component is equal to the corresponding coefficient of the complex Fourier series. To show this, plug in the spectral component from the complex Fourier series into the formula for RMS
    2 KB (392 words) - 10:08, 15 January 2014
  • *[[Geometric_Series_Explanation|Tutorial on the geometric series]], by [[user:amcgail | Alec McGail]], member of [[Math_squad | Rhea's Math **[[practice_DTFT_computation_sine_ECE438F13|Compute the DT Fourier transform of a sinc]]
    3 KB (386 words) - 06:09, 11 September 2013
  • Then use your answer to obtain the Fourier transform of the signal. (Write enough intermediate steps to fully justify By geometric series formula,
    7 KB (1,100 words) - 12:53, 26 November 2013
  • [[Category:Fourier series]] on continuous-time Fourier series
    7 KB (992 words) - 18:16, 23 February 2015
  • From here I solved for Bn. The fourier series I calculated is F(x) = 2/pi sinx - 2/4pi sin2x + 2/9pi sin3x ... When graph Fourier series up to the n=5 terms. By the way, to
    7 KB (1,302 words) - 04:58, 23 October 2013
  • ...tion 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)... The answe ...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.
    8 KB (1,388 words) - 14:51, 29 October 2013
  • ...ue.edu/~bouman/ece438/lecture/module_1/1.3_fourier_analysis/1.3.3_dtft.pdf Fourier analysis] ...p://dynamo.ecn.purdue.edu/~ipollak/ee438/FALL01/Fourier_notes1.pdf Fourier series]
    6 KB (759 words) - 08:10, 11 November 2013
  • *[[CT_DT_Fourier_transform_ECE438F10|Summary of CT and DT Fourier transform]] *[[Discrete_Fourier_transform_ECE438F10|Discrete Fourier transform]]
    4 KB (471 words) - 19:34, 9 February 2015
  • > For #4-b we are asked to find the real Fourier > series from the complex one, is there a way to
    11 KB (1,959 words) - 17:57, 10 November 2013
  • ...st step of finding a solution to a wave or heat equation, why do we take a SERIES of the eigen functions, and then incorporate the initial condition to get t Farhan, I think the series of the eigenfunctions is needed to satisfy both the boundary conditions and
    5 KB (978 words) - 17:36, 3 December 2013
  • 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
  • ...alculate 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, 3.47) * Tables for [[Media:ECE301Summer2016_table3p1.png| Fourier series]], [[Media:ECE301Summer2016_table4p1.png| CTFT properties]], and [[Media:EC
    6 KB (765 words) - 13:35, 4 August 2016
  • *[[Fourier_analysis_in_Music| Fourier Analysis in Music]] by [[user:mbell|Maria Bell]] *[[Geometric_Series_Explanation|Geometric Series Explanation]] by [[user:amcgail|Alec McGail]]
    3 KB (359 words) - 04:26, 16 May 2014
  • .../www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier Series Example]
    2 KB (380 words) - 08:18, 2 December 2014
  • *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
  • 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
  • Discrete-time Fourier Transform (DTFT) ...function of a frequency as the variable, <math>\omega</math>. The Fourier series is:
    3 KB (515 words) - 20:02, 16 March 2015

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