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  • CTFS Property: Time Shift - Jamis Martin
    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
  • ECE301 (BoumanFall2009)
    *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
  • Reconstruction
    Fourier series. It turns out that ALL of the Fourier coefficients are equal to 1.
    1 KB (196 words) - 04:17, 30 July 2009
  • Detailed Course Description
    * 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
  • Course Syllabus with Homework Due Dates
    |Homework 6 due – Fourier Series |Exam 2 – LTI system properties; orthonormal transforms; Fourier series
    1 KB (190 words) - 15:00, 24 August 2009
  • Student summary sampling part1 ECE438F09
    ...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
  • Sampling Rate Conversion - Downsampling
    This, in Fourier Domain becomes The Fourier Series of this function can be represented as
    4 KB (655 words) - 07:13, 23 September 2009
  • Speech Spectrogram
    ==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
  • 9-21 lecture note
    == Discrete Fourier Transform == same formula as for discrete fourier series.
    2 KB (491 words) - 23:03, 22 September 2009
  • Collective Table of Formulas
    *[[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
  • Introduction to Wavelets
    '''Taking Fourier's torch forward...''' ...e first person that comes to mind when someone says "SIGNAL PROCESSING" is Fourier.
    10 KB (1,646 words) - 11:26, 18 March 2013
  • Peer Legacy ECE301
    ...to take any courses related to signal processing. Also, your concepts of Fourier and Z transforms should be absolutely clear for signal processing (DSP ECE ...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
  • Snikitha ListECE301
    ...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
  • My use for the DFT!
    [[Category:discrete Fourier transform]] In [[ECE301|ECE 301]] students were introduced to the concept of Fourier Transforms. No matter whom you had been taught by it seemed intimidating an
    13 KB (2,348 words) - 13:25, 2 December 2011
  • 2010 Fall ECE 438 Boutin
    ...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
  • Lecture Schedule ECE438Fall10 Boutin
    *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
    9 KB (1,331 words) - 07:15, 29 December 2010
  • 2010 Fall ECE 301 Pollak
    ...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
  • ECE438 Lab Fall 2010
    .../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
  • Recommended exercise Fourier series computation
    [[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
  • Recommended exercise Fourier series computation DT
    [[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
  • Lecture8ECE438F10
    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
  • Fourier series coefficients of a periodic square wave period two
    =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
  • DT Fourier Coefficients Periodic Square wave
    =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
  • ECE438 Week5 Quiz
    <math>\text{3. Compute the Fourier series coefficients of the following signal:} \,\!</math>
    2 KB (315 words) - 10:39, 11 November 2011
  • Fourier series coefficients student 1
    [[Category:Fourier series]] =Exercise: Compute the Fourier series coefficients of the following periodic signal:=
    6 KB (999 words) - 13:00, 16 September 2013
  • 2010 Fall ECE 438 Boutin/ECE438Mid1FormulaSheet Work
    *Fourier series of a continuous-time signal x(t) periodic with period T *Fourier series coefficients of a continuous-time signal x(t) periodic with period T
    2 KB (292 words) - 17:13, 30 September 2010
  • 2010 Fall ECE 438 Boutin/ECE438Mid1FormulaSheet Work wrk
    *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
    1 KB (241 words) - 06:50, 30 September 2010
  • Lecture16ECE438F10
    ...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
  • Practice question 1 eECE439F10
    [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
    5 KB (766 words) - 14:22, 21 April 2013
  • Hw7ECE438F10
    Compute the discrete Fourier transform of the following discrete-time signals: How do your answers relate to the Fourier series coefficients of x[n]?
    4 KB (661 words) - 11:22, 30 October 2011
  • Decision Theory Glossary ECE662Spring2008
    ...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
  • HWK10MA527Fall2010
    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
  • ECE438 HW7 Solution
    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
  • HWK11MA527Fall2010
    ...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
  • HWK13MA527Fall2010
    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
  • Vuvuzelas ECE438F10
    ...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
    3 KB (409 words) - 08:53, 11 November 2013
  • PracFMA527Fall2010
    L=pi in this problem. The given Fourier series for f(x) tells When you square the coefficients of the Fourier series, you get
    7 KB (1,359 words) - 02:59, 14 December 2010
  • 2011 Spring ECE 301 Boutin
    *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
  • ECE438 Lab Spring 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
  • Discussion HW4 ECE301 Spring2011
    ...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
  • HW4 ECE301 Spring2011 Prof Boutin
    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
  • ECE301 signals systems learning material
    ...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
  • ECE301 signals systems formulas
    *[[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
    890 B (101 words) - 17:30, 21 April 2013
  • Lecture11ECE301S11
    ...ine/sine as a Fourier series, we are effectively writing out their Fourier series.
    1 KB (212 words) - 14:11, 28 February 2011
  • Lecture12ECE301S11
    ...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
  • Fourier series coefficients sinusoidal CT ECE301S11
    [[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
  • Fourier series coefficients sinusoidal DT ECE301S11
    = [[: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
  • Fourier series coefficients pulse train CT ECE301S11
    [[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
  • Fourier series coefficients pulse train DT ECE301S11
    = [[: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
  • Lecture13ECE301S11
    ...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

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