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- [[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 greater992 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 by2 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> defin1 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 n2 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> defi1 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> defin1 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 by1 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 by764 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 ha3 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 restricted3 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 Pair21 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 s1 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 also31 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 Series780 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 both868 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 de988 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 by4 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 Transform5 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) an583 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>, so1 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_{01 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 Coefficients117 B (21 words) - 18:02, 22 July 2009
- CT Fourier Series Expansion - Walter Mulflur119 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, if1 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 and7 KB (1,153 words) - 14:06, 24 August 2009
- |Homework 6 due – Fourier Series |Exam 2 – LTI system properties; orthonormal transforms; Fourier series1 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, the8 KB (1,452 words) - 06:49, 16 September 2013
- This, in Fourier Domain becomes The Fourier Series of this function can be represented as4 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 freq8 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 radians3 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 in14 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 transforms3 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 an13 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/>3 KB (431 words) - 07:07, 31 January 2011
- [[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]]875 B (123 words) - 12:42, 10 September 2010
- =Exercise: Compute the Fourier series coefficients of the following signal:= After you have obtained the coefficients, write the Fourier series of x(t).2 KB (324 words) - 08:08, 15 February 2011
- =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].982 B (156 words) - 16:41, 30 November 2010
- <math>\text{3. Compute the Fourier series coefficients of the following signal:} \,\!</math>2 KB (315 words) - 10:39, 11 November 2011
- [[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 T2 KB (292 words) - 17:13, 30 September 2010
- *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 T1 KB (241 words) - 06:50, 30 September 2010
- ...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 Transform5 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 also31 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 grea3 KB (409 words) - 08:53, 11 November 2013
- L=pi in this problem. The given Fourier series for f(x) tells When you square the coefficients of the Fourier series, you get7 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 signal18 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. I2 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</spa890 B (101 words) - 17:30, 21 April 2013
- ...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 computation2 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 signal3 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 signal2 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
