Search results for "Fourier" - Rhea

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• Lecture18ECE301S11
  ...ourier transform of a periodic signal. We found that we cannot compute the Fourier transform of such signals using the integral formula. However, we were abl We finished the lecture by discussing a few properties of the continuous-time Fourier transform.
  2 KB (215 words) - 14:12, 28 February 2011
• Fourier transform cosine CT ECE301S11
  = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
  2 KB (276 words) - 10:25, 11 November 2011
• Fourier transform cosine no2 CT ECE301S11
  = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
  2 KB (355 words) - 10:26, 11 November 2011
• Fourier transform periodic triangular pulse train CT ECE301S11
  = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
  853 B (122 words) - 10:26, 11 November 2011
• Fourier transform periodic rectangular pulse train CT ECE301S11
  = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Continuous-time Signal = Compute the Fourier transform of the signal
  1 KB (196 words) - 10:26, 11 November 2011
• Lecture19ECE301S11
  Today we discussed some important properties of the continuous-time Fourier transform (CTFT). I particular, we saw the duality property and the convolu ...er_Transform_(frequency_in_radians_per_time_unit)|Table of continuous-time Fourier transform pairs and properties]]
  1 KB (144 words) - 14:12, 28 February 2011
• Lecture20ECE301S11
  ...test. Get ready for the next lecture where we will begin talking about the Fourier transform for discrete-time signals!
  928 B (123 words) - 14:12, 28 February 2011
• HW5 ECE301 Spring2011 Prof Boutin
  ...[[CT_Fourier_Transform_%28frequency_in_radians_per_time_unit%29| table of Fourier transform pairs and properties]]. (Explain how you checked your answer.) Compute the Fourier transform of the signal
  4 KB (633 words) - 12:31, 2 March 2011
• Lecture21ECE301S11
  ...ay's lecture, we finished discussing the properties of the continuous-time Fourier transform. We then used these properties to obtain a simple expression for ...ansform of a discrete-time complex exponential. We then "guessed" what the Fourier transform of a discrete-time complex exponential should be. Our guess was s
  2 KB (346 words) - 14:13, 28 February 2011
• Fourier transform 3numinusn DT ECE301S11
  = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Discrete-time Signal = Compute the Fourier transform of the signal
  1 KB (198 words) - 10:27, 11 November 2011
• Fourier transform cosine DT ECE301S11
  = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Discrete-time Signal = Compute the Fourier transform of the signal
  1 KB (161 words) - 10:27, 11 November 2011
• Fourier transform window DT ECE301S11
  = [[:Category:Problem_solving|Practice Question]] on Computing the Fourier Transform of a Discrete-time Signal = Compute the Fourier transform of the signal
  1 KB (203 words) - 10:28, 11 November 2011
• Problem on time shifting and time scaling property of Fourier transform ECE301S11Boutin
  ...oblem_solving|Practice Question]] on the Properties of the Continuous-time Fourier Transform = Let x(t) be a continuous time signal with Fourier transform <math class="inline">{\mathcal X} (\omega) </math>.
  2 KB (401 words) - 10:27, 11 November 2011
• Lecture22ECE301S11
  ...tant to both be able to use the Fourier transform properties and prove the Fourier transform properties".
  1 KB (162 words) - 12:46, 2 March 2011
• HW5 ECE301 Spring2011 Prof Boutin Solutions
  ...ever, changing the value of a signal at a single point does not change its Fourier transform. -pm </span> Now, since the Fourier transform (FT) is linear, we have that:
  10 KB (1,817 words) - 11:34, 7 March 2011
• Lecture23ECE301S11
  Today we finished the material on the discrete-time Fourier transform so we have now covered all the material for the second test. We a
  1,022 B (140 words) - 18:58, 4 March 2011
• HW6 ECE301 Spring2011 Prof Boutin
  *<span style="color:red"> 15 pts </span> for the computation of the Fourier transform of the continuous-time signal. Check every step of the computatio ...nition of the Fourier transform (i.e., the integral formula) to obtain the Fourier transform of either the constant function 1 or of the complex exponential f
  7 KB (1,161 words) - 18:50, 4 March 2011
• HW7 ECE301 Spring2011 Prof Boutin
  ...en check your answer using this [[Table_DT_Fourier_Transforms| table of DT Fourier transform pairs and properties]]. (Explain how you checked your answer.) ...ransform (i.e., the integral formula) to compute the inverse Discrete-time Fourier transform of the signal
  4 KB (695 words) - 18:23, 7 March 2011
• Causal LTI System Difference Equation no1 ECE301S11
  ...complex constant. But I don't know how to compute that constant from the fourier transform.
  5 KB (793 words) - 10:28, 11 November 2011
• Lecture25ECE301S11
  ...ansform of the sampling of a band-limited signal consists of copies of the Fourier transform of the original signal. Satisfying Nyquist's condition insures th
  1 KB (182 words) - 08:37, 30 March 2011
• Discussion HW7 ECE301 Spring2011
  I think the table of DT Fourier Transform pairs has a mistake. where it says <math>(n-1)a^nu[n]</math> it s
  1 KB (258 words) - 06:25, 11 March 2011
• HW8 ECE301 Spring2011 Prof Boutin
  *<span style="color:red"> 15 pts </span> for the computation of the Fourier transform of the discrete-time signal. If an integral was used in place of *<span style="color:red"> 15 pts </span> for the computation of the inverse Fourier transform. If a summation was used in place of the integral, give zero poin
  6 KB (1,090 words) - 07:36, 22 March 2011
• HW7 ECE301 Spring2011 Prof Boutin Solutions
  ...corresponds to the part of the spectrum for k=0) to compute the inverse DT Fourier transform of the given signal:
  10 KB (1,783 words) - 08:23, 21 March 2011
• ECE301inBME
  ...discrete computer signals. Systems (maybe even [[Fourier_Transform_Video |Fourier]]/Laplace/[[Compute z-transform u n ECE301S11|Z transforms]] from [[2011 Sp ...nications, and networking. Imaging techniques involving diffraction and/or Fourier analysis with application to tomography, magnetic resonance imaging, synthe
  17 KB (2,368 words) - 10:53, 6 May 2012
• HW9 ECE301 Spring2011 Prof Boutin
  ...th class="inline"> T</math>. For each of the values of T below, sketch the Fourier transform of the sampling and indicate whether or not one can recover <mat
  3 KB (451 words) - 06:40, 1 April 2011
• Nyquist rate for a sinc function
  Yes, this signal is band limited. It is a sinc function, and its Fourier transform can be found using the table of formulas in the textbook on page ...in the correct max frequency of the signal. It would be ok to say that the Fourier transform is a non-zero constant multiple of a low-pass filter with gain 1
  3 KB (431 words) - 10:28, 11 November 2011
• Nyquist rate for a signal ECE301S11
  ...yle="color:red">Instructor's comment: Reality check: the only signal whose Fourier transform is a constant is an impulse. So your answer cannot possibly be co
  4 KB (666 words) - 10:29, 11 November 2011
• HW10 ECE301 Spring2011 Prof Boutin
  a) Sketch the spectrum (i.e., the Fourier transform) of y(t). ...form has exactly two poles located at s=-1 and s=-3, respectively. If the Fourier transform of <math class="inline"> g(t)=e^{2t}x(t)</math> converges, could
  5 KB (797 words) - 09:19, 7 April 2011
• Signal modulation with exponential ECE301S11
  Let x(t) be a signal whose Fourier transform <math>{\mathcal X} (\omega) </math> satisfies
  2 KB (393 words) - 10:31, 11 November 2011
• Signal modulation with cosine ECE301S11
  Let x(t) be a signal whose Fourier transform <math>{\mathcal X} (\omega) </math> satisfies
  2 KB (400 words) - 10:31, 11 November 2011
• HW9 ECE301 Spring2011 Prof Boutin Solutions
  ...he Fourier transform of the CT signal representing the sampling in CT. The Fourier transform of the DT signal obtained by storing the values of the samples in
  9 KB (1,462 words) - 07:01, 22 April 2011
• Hw1 ECE438F11
  ...9|table of CT Fourier transform pairs and properties]], which uses the CT Fourier transform in terms of frequency <math>f</math> in hertz. Note that we will In [[ECE301]], you learned that the Fourier transform of a step function <math>x(t)=u(t)</math> is the following:
  2 KB (400 words) - 03:53, 31 August 2013
• HW10 ECE301 Spring2011 Prof Boutin Solutions
  a) The Fourier series coefficients of <span class="texhtml">''c''(''t'')</span> are: and using the synthesis equation of the Fourier series we get:
  12 KB (2,109 words) - 05:58, 22 April 2011
• Nyquist rate after multiplicating sinc signals ECE301S11
  ...rm of the product of two functions is (1/2pi) times the convolution of the Fourier transforms of the individual functions.
  2 KB (336 words) - 10:31, 11 November 2011
• Review of an alternative book by M.J. Roberts
  In this chapter author explains Fourier Series and Fourier Transforms of CT signals. The explanation is very good and clear. It is ver 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
• Book Review: Signals & Systems MJR
  In this chapter author explains Fourier Series and Fourier Transforms of CT signals. The explanation is very good and clear. It is ver 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
• Linearity Spring 2011
  Linearity can be used to simplify the Fourier transform. &nbsp;Integration and differentiation are also linear. &nbsp;Onc
  2 KB (255 words) - 10:50, 6 May 2012
• Fourier Transform Video
  =Video on the Fourier Transform= <player>ECE 301 Credit_0.avi|The Fourier Transform</player>
  234 B (31 words) - 10:52, 6 May 2012
• Book Review/Bhakti
  ...dedicated to LTI systems, Laplace Transfer of CT LTI systems, Z Transform, Fourier Analysis. Which means this book explains material covered over Midterms 1 a Fourier Analysis of CT Signals and Systems: This chapter corresponds to the fourth
  5 KB (802 words) - 16:44, 23 April 2013
• 2011 Fall ECE 438 Boutin
  **[[Practice CTFT from omega to f step function|Obtain the Fourier transform in terms of f of a step function (from FT in terms of omega)]] **[[Practice CTFT computation rect and sinc ECE438F11|Compute the Fourier transform of a rect and a sinc]]
  10 KB (1,359 words) - 03:50, 31 August 2013
• ECE438 Lab Fall 2011
  ...[https://www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier Series Example]<br/>
  3 KB (456 words) - 10:20, 12 October 2011
• Lecture Schedule ECE438Fall11 Boutin
  *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
• Lecture1ECE438F11
  We finished the lecture with a discussion about the meaning of the Fourier transform and a video where Prof. Joe Havlicek illustrates this meaning usi
  2 KB (231 words) - 12:48, 21 September 2011
• Practice CTFT computation rect and sinc ECE438F11
  [[Category:Fourier transform]] Topic: Continuous-time Fourier transform computation (in terms of frequency f in hertz)
  7 KB (1,302 words) - 09:45, 11 November 2013
• Lecture2ECE438F11
  ...ced, and in the [[Lecture3ECE438F11|next lecture]], we shall compute their Fourier transforms. **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]]
  2 KB (285 words) - 12:48, 21 September 2011
• Lecture3ECE438F11
  ...he definition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. **[[Practice DTFT computation cosine ECE438F11|What is the Fourier transform of this DT cosine?]]
  2 KB (252 words) - 12:48, 21 September 2011
• Practice DTFT computation cosine ECE438F11
  [[Category:discrete-time Fourier transform]] Topic: Discrete-time Fourier transform computation
  6 KB (1,000 words) - 12:33, 26 November 2013
• Practice DTFT computation rect ECE438F11
  [[Category:discrete time Fourier transform]] Topic: Discrete-time Fourier transform computation
  6 KB (1,090 words) - 12:35, 26 November 2013
• Practice CTFT from omega to f step function
  [[Category:Fourier transform]] Topic: Continuous-time Fourier transform: from omega to f
  7 KB (1,143 words) - 09:44, 11 November 2013
• Practice CTFT complex exponential ECE438F11
  [[Category:Fourier transform]] Topic: Continuous-time Fourier transform of a complex exponential
  3 KB (610 words) - 09:47, 11 November 2013
• Lecture5ECE438F11
  .... We noted that there are signals for which the z-transform exists but the Fourier transform does not. We introduced the notion of "region of absolute converg *[[practice_CTFT_from_omega_to_f_step_function|Obtain the Fourier transform in terms of f of a step function (from FT in terms of omega)]]
  2 KB (294 words) - 06:19, 11 September 2013
• Hw1 ECE438F11sln
  In [[ECE301]], you learned that the Fourier transform of a step function <math>x(t)=u(t)</math> is the following: Use this fact to obtain an expression for the Fourier transform <math>X(f)</math> (in terms of frequency in hertz) of the step fu
  2 KB (397 words) - 05:15, 7 September 2011
• Microprocessor Architecture
  <br> [[Image:Fourier xkcd.jpg|300px]]
  2 KB (244 words) - 09:48, 21 September 2011
• Lecture10ECE438F11
  ...hip between the poles/zeros of the z-transform and the magnitude of the DT Fourier transform. We also began talking about sampling.
  660 B (84 words) - 06:23, 11 September 2013
• Lecture11ECE438F11
  ...hannon expansion. We then begin talking about the relationship between the Fourier transform of a signal x(t) and that of the sampling
  872 B (116 words) - 06:23, 11 September 2013
• Lecture12ECE438F11
  ...ng the relationship between the Fourier transform of a signal x(t) and the Fourier transform of its sampling y[n]=x(nT). (Note that it is VERY IMPORTANT that
  776 B (106 words) - 06:23, 11 September 2013
• Lecture13ECE438F11
  ...>, for some integer D>1. We then obtained the relationship between the DT Fourier transform of <math>x_1[n]</math> and that of an upsampling of x[n] by a fa
  2 KB (243 words) - 06:23, 11 September 2013
• Hw3 ECE438F11
  ...btain the Fourier transform from a table; either use the definition of the Fourier transform or use some other way to fully justify your answer.) Write a mathematical expression for the Fourier transform <math>X_s(f) </math> of
  2 KB (320 words) - 03:54, 31 August 2013
• Lecture14ECE438F11
  Having obtained the relationship between the DT Fourier transform of <math>x_1[n]</math> and that of an upsampling of x[n] by a fa We then began discussing the [[Discrete_Fourier_Transform|Discrete Fourier Transform]] (DFT).
  1 KB (213 words) - 06:24, 11 September 2013
• Compute DFT practice no1 ECE438F11
  [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
  4 KB (735 words) - 14:19, 21 April 2013
• Compute DFT practice no2 ECE438F11
  [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
  3 KB (513 words) - 14:20, 21 April 2013
• 2011 Fall ECE 301 Pollak
  ...xercise_Fourier_series_computation|A collective page to practice computing Fourier series of a CT signal]] ...cise_Fourier_series_computation_DT|A collective page to practice computing Fourier series of a DT signal]]
  2 KB (212 words) - 05:44, 26 September 2011
• Lecture15ECE438F11
  ...of a finite duration signal and the [[Discrete_Fourier_Transform|Discrete Fourier Transform]] of its periodic repetition. ...exercises of Fourier series computations for DT signals]] (to brush up on Fourier series))
  1 KB (181 words) - 06:24, 11 September 2013
• Practice problem finding band limited signals ECE438F11
  ...how about a transformation that would simply shift the frequencies of the Fourier transform? Another way to obtain new band-limited signal is to combine band By nature of the Fourier Transform, band limited signals
  2 KB (326 words) - 12:38, 26 November 2013
• Lecture16ECE438F11
  [[Category:discrete Fourier transform]]
  1 KB (199 words) - 06:25, 11 September 2013
• Lecture17ECE438F11
  ...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 [[Category:discrete Fourier transform]]
  1 KB (192 words) - 06:18, 29 September 2014
• Lecture18ECE438F11
  Today's lecture was about the Fast Fourier Transform (FFT). As a first step, we covered the "decimation by two" FFT al [[Category:discrete Fourier transform]]
  614 B (78 words) - 06:25, 11 September 2013
• Lecture19ECE438F11
  [[Category:discrete Fourier transform]]
  574 B (73 words) - 06:26, 11 September 2013
• Lecture21ECE438F11
  [[Category:discrete Fourier transform]] [[Category:Fast Fourier transform]]
  902 B (122 words) - 06:26, 11 September 2013
• MathWorksTest
  *Please help! We need a [[Discrete_Fourier_Transform_table|table of Discrete Fourier transform pairs and properties]]! **[[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)]]
  9 KB (1,273 words) - 20:52, 15 October 2011
• Exercise effect of zero padding on DFT ECE438F11
  [[Category:discrete Fourier transform]] Topic: Discrete Fourier Transform
  4 KB (759 words) - 14:18, 21 April 2013
• Lecture27ECE438F11
  [[Category:discrete Fourier transform]]
  1 KB (158 words) - 06:30, 11 September 2013
• Continuous-space Fourier transform
  [[Category:continuous-space Fourier transform]] =More on the Continuous-space (2D) Fourier transform (CSFT)=
  848 B (125 words) - 09:52, 11 November 2011
• Lecture31ECE438F11
  ...cognize voiced phonemes in a speech signal. We also defined the short time Fourier transform (STFT) of a signal and the "spectogram" of a speech signal. We di
  937 B (128 words) - 06:31, 11 September 2013
• Lecture32ECE438F11
  ...We also obtained a formula for reconstructing a signal from its short time Fourier transform. We then moved on to the topic of "Spectral Analysis of 2D Signal
  1 KB (149 words) - 06:31, 11 September 2013
• Lecture33ECE438F11
  ...ion of the [[:Category:continuous-space Fourier transform|Continuous-space Fourier transform]] (CSFT). [[Category:continuous-space Fourier transform]]
  872 B (107 words) - 06:31, 11 September 2013
• Obtain CSFT complex exponential
  [[Category:continuous-space Fourier transform]] Topic: Continuous-space Fourier transform of a complex exponential
  3 KB (576 words) - 12:57, 26 November 2013
• Compute CSFT of 2D rect function ECE438F11
  [[Category:continuous-space Fourier transform]] Topic: Continuous-space Fourier transform of a 2D "rect" function
  3 KB (487 words) - 12:57, 26 November 2013
• Compute CSFT of 2D sinc function ECE438F11
  [[Category:continuous-space Fourier transform]] Topic: Continuous-space Fourier transform of a 2D sinc function
  4 KB (678 words) - 12:58, 26 November 2013
• Lecture34ECE438F11
  ...s-space Fourier transform|CSFT]] and inverse [[:Category:continuous-space Fourier transform|CSFT]] in polar coordinates. **[[Obtain_CSFT_complex_exponential|Obtain the continuous-space Fourier transform of a complex exponential]]
  2 KB (196 words) - 06:32, 11 September 2013
• Discrete-time Fourier transform info
  [[Category:discrete-time Fourier transform]] =About the Discrete-time Fourier transform (DTFT)=
  2 KB (290 words) - 14:47, 1 May 2015
• Obtain DSFT rectangle
  [[Category:discrete-space Fourier transform]] Topic: Discrete-space Fourier transform computation
  2 KB (355 words) - 12:58, 26 November 2013
• Compute DSFT product two step functions ECE438F11
  [[Category:discrete-space Fourier transform]] Topic: Discrete-space Fourier transform computation
  3 KB (473 words) - 12:59, 26 November 2013
• Compute DSFT cosine ECE438F11
  [[Category:discrete-space Fourier transform]] Topic: Discrete-space Fourier transform computation
  4 KB (703 words) - 12:59, 26 November 2013
• Digital signal processing practice problems list
  **[[Practice CTFT from omega to f step function|Obtain the Fourier transform in terms of f of a step function (from FT in terms of omega)]] **[[Practice CTFT computation rect and sinc ECE438F11|Compute the Fourier transform of a rect and a sinc]]
  6 KB (801 words) - 22:04, 19 April 2015
• Lecture35ECE438F11
  **[[Obtain_DSFT_rectangle|Obtain the discrete-space Fourier transform of a rectangle]] ...mpute_DSFT_product_two_step_functions_ECE438F11|Compute the discrete-space Fourier transform of this function]]
  2 KB (301 words) - 06:32, 11 September 2013
• Audio Signal Generating and Processing Project, Previous method
  First, by looking at the Fourier domain, one can and measure the amplitude of each harmonics. The intention
  6 KB (931 words) - 20:33, 15 November 2011
• Lecture36ECE438F11
  ...the separability of the filter greatly facilitated the computation of its Fourier transform. We discussed different ways to determine whether a filter is sep **[[Obtain_DSFT_rectangle|Obtain the discrete-space Fourier transform of a rectangle]]
  2 KB (213 words) - 06:32, 11 September 2013
• Lecture37ECE438F11
  **[[Obtain_DSFT_rectangle|Obtain the discrete-space Fourier transform of a rectangle]] ...mpute_DSFT_product_two_step_functions_ECE438F11|Compute the discrete-space Fourier transform of this function]]
  1 KB (163 words) - 06:32, 11 September 2013
• Implementation of the Divide and Conquer DFT via Matrices
  [[Category:Fourier transform]] [[Category:discrete Fourier transform]]
  10 KB (1,717 words) - 12:02, 6 June 2014
• Lecture38ECE438F11
  ...by computing and plotting the frequency response (i.e. the discrete-space Fourier transform) of the corresponding filter. We then studied another type of fil [[Category:discrete-space Fourier transform]]
  1 KB (157 words) - 06:33, 11 September 2013
• Lecture42ECE438F11
  ...ar, we reviewed the relationship between a signal and its sampling (in the Fourier domain), and we reviewed how to increase/decrease the resolution of a signa
  1 KB (181 words) - 06:34, 11 September 2013
• On "Pi is Wrong" and the Tau Movement
  ...ecessary 2! Professor Palais noted that "... Cauchy's integral formula and Fourier series formulas all begin with 1/2<math>\pi</math>, Stirling's approximatio
  5 KB (820 words) - 08:33, 11 December 2011
• ECE538
  *[[CT_Fourier_Transform_(frequency_in_radians_per_time_unit)|Continuous-time Fourier Transform Pairs and Properties]] *[[Table_DT_Fourier_Transforms|Discrete-time Fourier Transform Pairs and Properties]]
  1 KB (152 words) - 12:17, 24 February 2015
• ECE301 signals systems videos
  *'''How the Fourier Transform Works, by Prof. Joseph Havlicek'''
  760 B (99 words) - 17:55, 23 April 2013
• 2012 Spring ECE 433 Saeedifard
  ==Fourier Series==
  399 B (50 words) - 08:03, 17 January 2012
• Upsham Dawra - Professional Statement
  ...rchitecture and Compilers, along with classes like Signals and Systems and Fourier Transforms. This afforded me a venerable arsenal of knowledge in both Elect
  3 KB (550 words) - 12:22, 9 February 2012
• Professional statement DerekRichards ECE400S12
  ...ave taken signal analysis classes, which don’t just teach how to compute Fourier transforms, and what to do with that answer. They teach the idea that any s
  4 KB (666 words) - 12:13, 9 February 2012
• Lecture4ECE438F13
  ...he definition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]
  3 KB (398 words) - 06:10, 3 September 2014
• Eric Lewis Bonus 2
  [[Category:Fourier series]]
  1 KB (196 words) - 17:45, 21 April 2013
• Collective problem solving why and how to
  *[[Practice_Question_4_ECE438F10|Fourier transform of a sampling]]
  4 KB (658 words) - 08:25, 7 May 2012
• 2018 Fall ECE 301 Boutin
  | [[FourierSeriesConvergenceBonusProject | Convergence of Parametric Fourier Series]] | [[The_2-D_Fourier_Transform_and_Images|The 2-D Fourier Transform and Images]]
  4 KB (534 words) - 19:10, 4 December 2018
• ECE-QE CS1-2011
  ...linear time-invariant system with impulse response <math>h(t)</math> whose Fourier transform <math>H(\omega)</math> has the ideal low-pass characteristic
  4 KB (547 words) - 16:40, 30 March 2015
• ECE-QE CS5-2011
  \text{Let } F(\mu,\nu) \text{ be the continuous-time Fourier transform of } f(x,y) \text{ given by} \text{and let } P_{\theta}(\rho) \text{ be the continuous-time Fourier transform of } p_{\theta}(r) \text{ given by}
  4 KB (665 words) - 10:25, 13 September 2013
• ECE-QE CS5-2011 solusion-2
  \text{Let } F(\mu,\nu) \text{ be the continuous-time Fourier transform of } f(x,y) \text{ given by} \text{and let } P_{\theta}(\rho) \text{ be the continuous-time Fourier transform of } p_{\theta}(r) \text{ given by}
  17 KB (2,783 words) - 01:51, 31 March 2015
• 2012 Fall ECE 438 Ersoy
  | [[Application Fourier transform ECE438F12Ersoy|Application of the Fourier transform]] | [[Fast Fourier Transform ECE438F12Ersoy|The Fast Fourier transform]]
  2 KB (312 words) - 12:05, 19 November 2012
• 2012 ECE 301 Dr. Love
  *[[CT Fourier Transform (frequency in radians per time unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</spa *[[Table DT Fourier Transforms|Discrete-time Fourier Transform Pairs and Properties]]
  2 KB (236 words) - 11:24, 21 September 2012
• 2013 Spring ECE 301 Krogmeier
  **[[CT_Fourier_Transform_(frequency_in_radians_per_time_unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</spa **[[Table_DT_Fourier_Transforms|Discrete-time Fourier Transform Pairs and Properties]]
  6 KB (799 words) - 10:10, 15 May 2013
• 2013 Spring Image Processing ECE 637 Bouman
  * Fourier Slices
  3 KB (370 words) - 11:22, 29 May 2013
• Lab 2 Additional Information ECE637 Spring2013 Bouman
  ;'''Q - Section 2 - For calculationg Sx anlyitically, is this just doing a Fourier transform of and multiplying by its complex conjugate and 1/(N^2)? Not exa
  5 KB (957 words) - 08:11, 9 April 2013
• DYL Tuesday 1
  <br> '''''On Mimi's Fourier Transform Skills''''' ...ansform my way out of a paper bag. Not sure what that means.<br>D: You can Fourier transform your way out of... a paper bag?<br>M: Yea, a paper bag.<br>D: Sou
  4 KB (849 words) - 15:39, 18 February 2013
• Practice Question joint from marginals independent variables ECE302S13Boutin
  ...just as the Fourier transform X(jw) is the envelope function of the set of Fourier coefficients {a_k}, where <math>prob(x) = \int_{x^-}^{x^+}f_X(x) dx</math>?
  2 KB (394 words) - 12:03, 26 March 2013
• ECE301bonus2
  2. Use Matlab to demonstrate summing of a finite number of terms of a Fourier Series ... pick a fun time function with a discontinuity to illustrate Gibb c) Plot Fourier Transform of filter’s impulse response in 3D.
  4 KB (573 words) - 10:15, 15 May 2013
• Math squad
  *[[Fourier_analysis_in_Music| Fourier Analysis in Music]] by [[user:mbell|Maria Bell]]
  2 KB (287 words) - 13:01, 12 January 2018
• ECE301 Bonus 2 Li Pang Mo
  [[Category:Fourier series]]
  2 KB (322 words) - 23:38, 10 March 2013
• ECE 301 Spring 2013 mtgyure Bonus2 Question2
  [[Category:Fourier series]] ''2. Use Matlab to demonstrate summing of a finite number of terms of a Fourier Series ... pick a fun time function with a discontinuity to illustrate Gibb
  2 KB (348 words) - 10:50, 11 March 2013
• ECE301 Prof.KrogemeierBonus 2
  Joseph Fourier first represented Fourier integral theorem in the following DOE: [[Category:Fourier series]]
  1 KB (174 words) - 11:34, 11 March 2013
• Practice Question characteristic function ECE302S13Boutin
  I tried taking the inverse fourier transform since PX(x) = F^-1 { Mx(jw)}, however my resultant pmf has j (sqr
  1 KB (211 words) - 03:47, 27 March 2013
• ECE637 Bouman lectures Image Processing sLecture mhossain
  ** [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
  2 KB (246 words) - 07:21, 26 February 2014
• ECE637 optical imaging systems space domain models S13 mhossain
  ...obtain the PSF because the star is like a delta function. If you take its Fourier transform, you will get the frequency response of the system. Given that yo
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• ECE301 signals systems lecture notes
  **[[Lecture19 ECE301Fall2008mboutin|Lecture 19]]: TA Example Session w/ DT Fourier Transforms and inverses
  3 KB (328 words) - 17:57, 30 November 2018
• Lecture42 blog ECE302S13 Boutin
  ...YOU CAN USE A [[CT_Fourier_Transform_%28frequency_in_hertz%29|TABLE OF CT FOURIER TRANSFORMS]] TO DO THESE PROBLEMS.
  4 KB (545 words) - 07:12, 24 April 2013
• Lecture43 blog ECE302S13 Boutin
  ...YOU CAN USE A [[CT_Fourier_Transform_%28frequency_in_hertz%29|TABLE OF CT FOURIER TRANSFORMS]] TO DO THESE PROBLEMS.
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• 4th Bonus Point - Ryan Miller
  Since ROC is |z|>1/2 (i.e. includes the unit circle), the Fourier Transform exists.
  442 B (65 words) - 08:41, 28 April 2013
• ECE637 tomographic reconstruction intro S13 mhossain
  ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]] ...The [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]] is the basis of this inversion. It provides the theory to s
  8 KB (1,168 words) - 07:24, 26 February 2014
• ECE637 tomographic reconstruction S13 mhossain
  ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]] ...6: [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]] ([[ECE637_tomographic_reconstruction_fourier_slice_theorem_
  4 KB (443 words) - 07:24, 26 February 2014
• ECE637 tomographic reconstruction CT S13 mhossain
  ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
  9 KB (1,390 words) - 07:24, 26 February 2014
• ECE637 tomographic reconstruction PET S13 mhossain
  ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
  6 KB (913 words) - 07:24, 26 February 2014
• ECE637 tomographic reconstruction coordinate rotation S13 mhossain
  ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
  6 KB (834 words) - 07:25, 26 February 2014
• Fourier analysis in Music
  == Fourier Analysis in Music == <pre> keyword: tutorial, Fourier, Fourier analysis, harmonics </pre>
  5 KB (883 words) - 13:06, 25 November 2013
• Linear algebra tutorials
  ...n_of_the_Divide_and_Conquer_DFT_via_Matrices|"divide and conquer" Discrete Fourier Transform (DFT)]]
  2 KB (293 words) - 12:25, 27 March 2015
• ECE637 tomographic reconstruction convolution back projection S13 mhossain
  ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]] ...the [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]. However you do not need to perform any calculations in the
  9 KB (1,486 words) - 07:25, 26 February 2014
• ECE637 tomographic reconstruction radon transform S13 mhossain
  ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]]
  6 KB (942 words) - 07:25, 26 February 2014
• ECE637 tomographic reconstruction fourier slice theorem S13 mhossain
  ::↳ [[ECE637_tomographic_reconstruction_fourier_slice_theorem_S13_mhossain|Fourier Slice Theorem]] <font size= 3> Subtopic 6: Fourier Slice Theorem </font size>
  9 KB (1,485 words) - 12:30, 17 April 2014
• Lemma boutin mhossain 05 2013
  * the Fourier transforms of their pdfs exist Taking the inverse Fourier transform, we get<br/>
  6 KB (1,084 words) - 13:20, 13 June 2013
• ECE637 MRI S13 mhossain
  ** Reconstruction computed with inverse Fourier transform If the RF pulse is a sinc function modulated at 63.8 MHz, its Fourier transform would be a shifted rect. This would essentially be a slice in the
  27 KB (4,777 words) - 07:25, 26 February 2014
• ECE637 discrete parameter signals and systems discrete transforms S13 mhossain
  ==Discrete Time Fourier Transform (DTFT)== ...ontinuous over (-∞,∞). The DTFT must not be confused with the Discrete Fourier Transform (DFT) which is a transform on a finite length sequence whereas th
  10 KB (1,726 words) - 07:26, 26 February 2014
• 2013 Fall ECE 438 Boutin
  **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]] **[[practice_DTFT_computation_sine_ECE438F13|Compute the DT Fourier transform of a sinc]]
  8 KB (1,096 words) - 06:44, 14 December 2013
• Lecture Schedule ECE438Fall13 Boutin
  *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
• ECE 438: Digital Signal Processing With Applications, Fall 2013
  ...[https://www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier Series Example]<br/>
  2 KB (341 words) - 15:54, 14 August 2013
• ECE438 Lab Fall 2013
  ...[https://www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier Series Example]<br/>
  2 KB (351 words) - 17:43, 16 August 2013
• 2013 Fall ECE 544 Krogmeier
  **[[CT_Fourier_Transform_(frequency_in_radians_per_time_unit)|Continuous-time Fourier Transform Pairs and Properties]] (function of <span class="texhtml">ω</spa **[[Table_DT_Fourier_Transforms|Discrete-time Fourier Transform Pairs and Properties]]
  4 KB (480 words) - 18:57, 10 December 2013
• Lecture2ECE438F13
  ...FT (namely, duality, multiplication, and convolution) and we computed the Fourier transform of some basic signals (namely, Dirac delta, rect, sinc, and compl **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]]
  3 KB (505 words) - 06:56, 2 September 2013
• HW1ECE38F13
  [[Category:fourier transform]] ...ga|table of CT Fourier transform pairs and properties]], which used the CT Fourier transform in terms of <math>\omega</math> in radians. (You should have seen
  1 KB (222 words) - 07:05, 23 August 2013
• Lecture3ECE438F13
  ...CT Fourier transform of the "comb" and "rep" operators in terms of the CT Fourier transform of the signal they are applied to.
  2 KB (236 words) - 07:02, 2 September 2013
• ECE440 Lab1 discussion
  ...pectral 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
• HW4ECE438F13
  #[[practice_z_transform_computation_3_ECE438F13|Obtain the Fourier transform from the z-transform]]
  1 KB (180 words) - 05:37, 20 September 2013
• HW2ECE438F13
  [[Category:fourier transform]]
  1 KB (241 words) - 03:42, 31 August 2013
• Lecture7ECE438F13
  **[[practice_DTFT_computation_sine_ECE438F13|Compute the DT Fourier transform of a sinc]] **[[practice_DTFT_computation_rect_ECE438F13|Compute the DT Fourier transform of a rect]]
  3 KB (386 words) - 06:09, 11 September 2013
• Practice DTFT computation rect ECE438F13
  [[Category:discrete time Fourier transform]] Topic: Discrete-time Fourier transform computation
  4 KB (673 words) - 12:36, 26 November 2013
• Practice DTFT computation sine ECE438F13
  [[Category:discrete time Fourier transform]] Topic: Discrete-time Fourier transform computation
  5 KB (740 words) - 12:36, 26 November 2013
• HW1 Solution ECE438F13
  [[Category:fourier transform]] ...[CT_Fourier_Transform_%28frequency_in_radians_per_time_unit%29|table of CT Fourier transforms]] in terms of <math>\omega</math> in radians and to obtain the c
  5 KB (768 words) - 05:49, 9 September 2013
• HW3ECE438F13
  [[Category:fourier transform]] **[[practice_DTFT_computation_sine_ECE438F13|Compute the DT Fourier transform of a sinc]]
  990 B (131 words) - 05:23, 8 September 2013
• Practice z transform computation 3 ECE438F13
  Then use your answer to obtain the Fourier transform of the signal. (Write enough intermediate steps to fully justify :<span style="color:blue"> Grader's comment: Obtain the Fourier transform of the signal </span>
  7 KB (1,100 words) - 12:53, 26 November 2013
• Lecture10ECE438F13
  ...of important properties of the z-transform, emphasizing the analogy to the Fourier transform properties. We finished the lecture by stating the inverse z-tran
  3 KB (334 words) - 06:00, 11 September 2013
• Lecture12ECE438F13
  *[[CT_Fourier_Transform_%28frequency_in_hertz%29|Table of CT Fourier transform]] Can somebody please add the rep and the comb to that table?
  2 KB (310 words) - 06:47, 16 September 2013
• Student projects
  **[[ECE438HonorsContractFST|Fourier Slice Theorem (FST)]]
  3 KB (389 words) - 18:10, 23 February 2015
• CT Fourier transform practice problems list
  [[Category:Fourier transform]] [[Category:inverse Fourier transform]]
  7 KB (966 words) - 18:17, 23 February 2015
• CT Fourier series practice problems list
  [[Category:Fourier series]] on continuous-time Fourier series
  7 KB (992 words) - 18:16, 23 February 2015
• HW5ECE438F13
  ...etween the Fourier transform of the interpolation you wrote in 2a) and the Fourier transform of x(t). (Do not simply write down the formula; show how to deriv ...that you just need to low-pass-filter the ideal sampling.) Then invert the Fourier transform to get the reconstructed signal in the time-domain. -pm
  2 KB (362 words) - 13:59, 26 September 2013
• Lecture14ECE438F13
  ...th>x_d[n]=x(nT)</math> and the original signal x(t). We noted that, in the Fourier domain, the signals differ in three ways (repetition, amplitude, scale).
  2 KB (323 words) - 05:57, 27 September 2013
• Lecture15ECE438F13
  **Review the relationship between the z-transform and the Fourier transform
  2 KB (299 words) - 05:56, 27 September 2013
• ECE440 Lab1 Typed
  by digitizing the signal and using a digital Fast-Fourier Transform.
  14 KB (2,228 words) - 12:03, 15 January 2014
• HW6ECE$38F13
  [[Category:discrete Fourier transform]] a) What is the relationship between the DT Fourier transform of x[n] and that of y[n]=x[5n]? (Give the mathematical relation a
  3 KB (480 words) - 09:13, 27 September 2013
• HW7ECE438F13
  [[Category:discrete Fourier transform]]
  2 KB (388 words) - 11:43, 11 October 2013
• Lecture23ECE438F13
  [[Category:discrete Fourier transform]]
  2 KB (294 words) - 05:58, 14 October 2013
• Lecture24ECE438F13
  [[Category:discrete Fourier transform]]
  2 KB (300 words) - 05:47, 16 October 2013
• HWK8MA527Fall2013
  From here I solved for Bn. The fourier series I calculated is F(x) = 2/pi sinx - 2/4pi sin2x + 2/9pi sin3x ... Whe Fourier series up to the n=5 terms. By the way, to
  7 KB (1,302 words) - 04:58, 23 October 2013
• Lecture25ECE438F13
  [[Category:discrete Fourier transform]]
  2 KB (216 words) - 05:35, 21 October 2013
• ECE600 F13 Characteristic Functions mhossain
  '''Note:''' The characteristic function looks like the Fourier Transform of f<math>_X</math>, with opposite sign in the exponent. We can s
  5 KB (804 words) - 12:12, 21 May 2014
• HW9ECE438F13
  ...the spectrum.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?
  2 KB (353 words) - 21:19, 31 October 2013
• HWK9MA527Fall2013
  ...e a question about the even extension in problem 29. I am getting that the fourier series is 2/pi-4/pi(1/3 cos(2x) + 1/(3*5) cos (4x) + 1/(5*7) *cos(6x)... Th ...rier Sine Function did you guys get bn=0 for all n? Which implies that the Fourier Sine Function is equal to zero for all x.
  8 KB (1,388 words) - 14:51, 29 October 2013
• Comparison of DFT and FFT via Matrices
  ...xplanation assumes the user understands the basic concepts of the Discrete Fourier Transform. ...k] where k = 0, 1, 2, ... N-1. Referring to our definition of the Discrete Fourier Transform above, to compute an N point DFT, all we need to do is simply rep
  9 KB (1,539 words) - 08:25, 28 October 2013
• ECE438 digital signal processing textbooks
  ...ue.edu/~bouman/ece438/lecture/module_1/1.3_fourier_analysis/1.3.3_dtft.pdf Fourier analysis] **[http://dynamo.ecn.purdue.edu/~ipollak/ee438/FALL01/Fourier_notes1.pdf Fourier series]
  6 KB (759 words) - 08:10, 11 November 2013
• ECE438 digital signal processing formulas
  *[[CT Fourier Transform (frequency in hertz)|Continuous-time Fourier Transform Pairs and Properties]] *[[Table DT Fourier Transforms|Discrete-time Fourier Transform Pairs and Properties]]
  1,002 B (119 words) - 05:58, 28 October 2013
• ECE438 digital signal processing learning material
  *[[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
• HWK10MA527Fall2013
  ...ecognize that this integral is an instance of formulas (4) and (5) for the Fourier Integral formulas. Your problem is to figure out what the f(x) is. Table 1 in 11.10 on Page 534 is a table of Fourier Cosine Transforms.
  6 KB (1,130 words) - 18:15, 5 November 2013
• Review2MA527Fall2013
  > For #4-b we are asked to find the real Fourier about the complex Fourier SERIES on Exam 2. The
  11 KB (1,959 words) - 17:57, 10 November 2013
• Lecture31ECE438F13
  ...]]. We then talked about spectrograms of speech signals and the short-time Fourier transform. We discussed the difference between using a large window and a
  2 KB (258 words) - 06:41, 1 November 2013
• Lecture32ECE438F13
  [[Category:discrete Fourier transform]] ...pecifically we derived a linear filtering interpretation of the short time Fourier transform. We then used this interpretation to obtain a formula for reconst
  2 KB (260 words) - 06:57, 4 November 2013
• Lecture33ECE438F13
  [[Category:Fourier transform]] ...nals (the 2D rect, 2D sinc, circ, and 2D delta) ) and the continuous-space Fourier transform. As correctly pointed out by a student, "2D signals" is a misnome
  2 KB (309 words) - 12:13, 7 November 2013
• Lecture34ECE438F13
  [[Category:Fourier transform]] ...m of functions of 2 variables. We call this transform the continuous-space Fourier transform, or CSFT for short. We stated the definition of the CSFT and gave
  2 KB (274 words) - 07:11, 11 November 2013
• Lecture35ECE438F13
  [[Category:Fourier transform]] ...SFT of separable functions can be obtained from using the formulas for the Fourier transform of contuous-time signals (i.e., functions of 1 variable).
  2 KB (278 words) - 07:14, 11 November 2013
• Lecture37ECE438F13
  [[Category:Fourier transform]] ...the separability of the filter greatly facilitated the computation of its Fourier transform. We discussed different ways to determine whether a filter is sep
  3 KB (367 words) - 07:27, 15 November 2013
• Lecture36ECE438F13
  [[Category:Fourier transform]]
  2 KB (315 words) - 06:46, 15 November 2013
• Moon Landing Speech Analysis
  X=fft(x((m+1):(m+L)),N); %take the fourier transform
  4 KB (753 words) - 09:46, 13 February 2014
• Lecture38ECE438F13
  [[Category:Fourier transform]]
  2 KB (215 words) - 06:49, 20 November 2013
• Lecture39ECE438F13
  [[Category:Fourier transform]]
  2 KB (240 words) - 07:14, 22 November 2013
• HWK12MA527Fall2013
  Then, use u(x,0)=f(x) to see An is the coefficient of cosine fourier series of f(x) given by (5*) and (6*).
  5 KB (978 words) - 17:36, 3 December 2013
• ReviewFinalMA527Fall2013
  about complex Fourier Series on the Final Exam. There might, however, be questions about the complex Fourier TRANSFORM.
  2 KB (444 words) - 17:30, 10 December 2013
• ECE600 F13 Linear Systems with Random Inputs mhossain
  ...power spectral density''' or '''PSD''' of a WSS random process X(t) is the Fourier transform of its autocorrelation function: <br/>
  8 KB (1,476 words) - 12:13, 21 May 2014
• Lecture44ECE438F13
  ...from Fall 2011. We also did a short yoga sequence to better visualize the Fourier transform of some important signals. It's a good exercise to repeat at home
  2 KB (238 words) - 07:40, 6 December 2013
• Prove of the CSFT of the signals
  ...e CSFT of signals. The general way we solve CSFT questions is to guess its Fourier Transform, then prove it by taking the inverse F.T. of the signals.
  1 KB (225 words) - 05:39, 14 December 2013
• 2016 Summer ECE 301 Shenk
  ...ble to calculate the Fourier series coefficients of a period CT signal (DT Fourier series will NOT be on the exam). (3.28a(subparts abc), 3.22, 3.31, 3.28d, 3 * Tables for [[Media:ECE301Summer2016_table3p1.png| Fourier series]], [[Media:ECE301Summer2016_table4p1.png| CTFT properties]], and [[M
  6 KB (765 words) - 13:35, 4 August 2016
• Math squad 2013
  *[[Fourier_analysis_in_Music| Fourier Analysis in Music]] by [[user:mbell|Maria Bell]]
  3 KB (359 words) - 04:26, 16 May 2014
• 2014 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  13 KB (1,944 words) - 16:51, 13 March 2015
• ECE438 Lab Fall 2014
  ::[https://www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier Series Example]
  2 KB (380 words) - 08:18, 2 December 2014
• Lecture Schedule ECE438Fall14 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  9 KB (1,320 words) - 04:46, 11 September 2014
• Lecture2ECE438F14
  ...FT (namely, duality, multiplication, and convolution) and we computed the Fourier transform of some basic signals (namely, Dirac delta, rect, sinc, and compl **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]]
  3 KB (393 words) - 06:37, 27 August 2014
• HW1ECE38F14
  [[Category:fourier transform]] ...a|table of CT Fourier transform pairs and properties]], which lists the CT Fourier transform in terms of <math>\omega</math> in radians. (You should have seen
  1 KB (198 words) - 06:08, 29 August 2014
• Lecture3ECE438F14
  ...d the "rep" and "comb" operators. We finished the lecture by computing the Fourier transform of a rep, but we did not quite finish the computation.
  2 KB (272 words) - 06:01, 3 September 2014
• Lecture4ECE438F14
  ...he definition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]
  2 KB (339 words) - 05:39, 8 September 2014
• HW2ECE438F14
  [[Category:fourier transform]]
  1 KB (241 words) - 05:28, 8 September 2014
• HW1ECE38F14 Solution
  [[Category:fourier transform]]
  4 KB (563 words) - 05:31, 22 September 2014
• Fourier Transform rep com Youqin Liu ECE438 slecture
  Topic 3:Fourier transform of "rep" and "comb" ...Rep function. In my selecture, I am going to introduce the definition, the Fourier Transformation and the relationship of Comb function and Rep function.
  4 KB (610 words) - 18:55, 16 March 2015
• HW3ECE438F14
  [[Category:fourier transform]] ...etween the Fourier transform of the interpolation you wrote in 2a) and the Fourier transform of x(t). (Do not simply write down the formula; show how to deriv
  3 KB (462 words) - 09:43, 18 September 2014
• Slecture Fourier transform w f ECE438
  Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f ...ture I will explain Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f (in hertz).
  4 KB (613 words) - 18:51, 16 March 2015
• Fourier Transform as a FUnction of Frequency w versus Frequency f (in Hertz)
  '''Fourier Transform as a Function of Frequency ''w'' Versus Frequency f (in Hertz)''' To show the relationship between the Fourier Transform of frequency <math>\omega</math> versus frequency <math>f</math>
  3 KB (512 words) - 09:50, 14 March 2015
• Lecture11ECE438F14
  ...the relationship between the Fourier transform of a sampling x[n] and the Fourier transform of a downsample of this sampling y[n]=x[Dn], where D is a positiv
  2 KB (261 words) - 07:08, 19 September 2014
• HW4ECE438F14
  [[Category:fourier transform]] a) What is the relationship between the DT Fourier transform of x[n] and that of y[n]=x[4n]? (Give the mathematical relation a
  3 KB (486 words) - 06:19, 22 September 2014
• Lecture13ECE438F14
  We finished the lecture by stating the definition of the Discrete Fourier transform.
  2 KB (315 words) - 05:54, 24 September 2014
• Slecture Fourier transform w f ECE438 review
  ...ransform w f ECE438|Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f]] </font> I liked that you compared the formulas for the Fourier Transforms in both the w and f forms. Showing a few more steps in the secon
  5 KB (843 words) - 05:30, 15 October 2014
• Discrete-time Fourier transform Xian Zhang ECE438 slecture
  Discrete-time Fourier Transform (DTFT) ...periodic function of a frequency as the variable, <math>\omega</math>. The Fourier series is:
  3 KB (515 words) - 20:02, 16 March 2015
• Fourier Transform as a FUnction of Frequency w versus Frequency f in Hertz review
  ...urier Transform as a FUnction of Frequency w versus Frequency f (in Hertz)|Fourier Transform as a Function of Frequency w Versus Frequency f (in Hertz)]] </fo The steps you take to find each Fourier transform are well explained, and I really like your use of color to track
  5 KB (907 words) - 05:30, 15 October 2014
• DTFT of a sampled cosine Yijun ECE438 slecture
  Discrete-time Fourier transform (DTFT) of a sampled cosine slecture, I will talk about how does the discrete-time Fourier transform of the sampling of this signal look like. Suppose
  4 KB (598 words) - 20:05, 16 March 2015
• HW3ECE438F14 Soln
  [[Category:fourier transform]] ...etween the Fourier transform of the interpolation you wrote in 2a) and the Fourier transform of x(t). (Do not simply write down the formula; show how to deriv
  7 KB (1,178 words) - 20:16, 18 December 2014
• Discrete-time Fourier transform Zian Zhang ECE438 slecture
  Discrete-time Fourier Transform (DTFT) ...periodic function of a frequency as the variable, <math>\omega</math>. The Fourier series is:
  3 KB (535 words) - 19:30, 29 September 2014
• Discrete-time Fourier transform (DTFT) Slecture by Jacob Holtman
  <font size="4">'''Discrete-time Fourier Transform with Example''' </font> == Definition of Discrete Time Fourier Transform (DTFT) ==
  4 KB (575 words) - 20:02, 16 March 2015
• HW5ECE438F14
  [[Category:fourier transform]] ...following signals x[n] (if possible). How does your answer relate to the Fourier series coefficients of x[n]?
  2 KB (295 words) - 06:30, 29 September 2014
• HoltmanDTFTreview
  ...urier transform (DTFT) Slecture by Jacob Holtman]][[Category:Discrete-time Fourier transform (DTFT) Slecture by Jacob Holtman]] ...e Fourier transform (DTFT) Slecture by Jacob Holtman|Back to Discrete-time Fourier transform (DTFT) Slecture by Jacob Holtman]]
  584 B (68 words) - 20:37, 29 September 2014
• Holtman Slecture Review
  ...rete-time Fourier transform (DTFT) Slecture by Jacob Holtman|Discrete Time Fourier Transform with Example]] </font> ...cture clearly states the definition and periodic property of Discrete-time Fourier transform. In the exponential example, it's great to make a guess and prove
  4 KB (728 words) - 05:33, 15 October 2014
• Ftrepcomb mattmiller
  Fourier Transform of Rep and Comb Functions In this slecture, we are going to look at the fourier transforms of the <math>comb_T()</math> and <math>rep_T()</math> functions.
  4 KB (734 words) - 18:56, 16 March 2015
• Discrete Time Fourier Transform with example
  =Discrete Time Fourier Transform with example=
  131 B (18 words) - 20:59, 30 September 2014
• Discrete Time Fourier Transform with Example
  =Discrete Time Fourier Transform with Example=
  331 B (38 words) - 21:01, 30 September 2014
• Discrete-time Fourier transform Slecture by Fabian Faes
  Discrete Time Fourier Transform (DTFT) with example The discrete time fourier transform (DTFT) of a finite energy aperiodic signal x[n] can be given by t
  5 KB (862 words) - 20:02, 16 March 2015
• Fourier Transform rep com Ben ECE438 slecture
  Fourier Transform of a Rep and Comb
  921 B (136 words) - 11:44, 14 October 2014
• FTrepcomb mille507comments
  ...">Questions and Comments for </font> <font size="4">[[Ftrepcomb mattmiller|Fourier Transform of Rep and Comb Functions]] </font> ...if you explain some of the less intuitive steps, such as when you use the Fourier series representation of an impulse train. Well done, overall.
  6 KB (1,033 words) - 05:33, 15 October 2014
• DTFTCosinePawling
  Using the discrete-time Fourier transform pair for cosine: Using the discrete-time Fourier transform pair for cosine again:
  5 KB (735 words) - 20:04, 16 March 2015
• Dtft sampling slecture srh
  Discrete-time Fourier transform (DTFT) of a sampled cosine
  5 KB (801 words) - 20:04, 16 March 2015
• Nyquist Michael Hayashi ECE438 slecture
  ...cted perfectly from its sampling <math>x_s(t)</math>if the continuous-time Fourier Transform (CTFT) of <math>x(t)</math> is zero for all magnitudes of frequen The topmost plot in the figure above shows the continuous-time Fourier Transform (CTFT) of the signal of interest for this example: a 1-Hz cosine
  10 KB (1,650 words) - 19:04, 16 March 2015
• Slecture Topic 7 ECE438
  ...be sampled will be in the time domain <math> x(t) </math> and after it was Fourier transformed, the sampled signal <math> X(f) </math> will be in the frequenc ...analytical expression of sampling in the view of the frequency domain. The Fourier transform of sampling is given by:
  5 KB (852 words) - 09:58, 14 March 2015
• Slecture Topic 7
  ...ties and differences in X(f) and X_s(f). X_s(f) is the Fourier Transform of the sampling, x_s(t), of x(t). Given an arbitrary signal x(t), its Fourier Transform is X(f)
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• Slecture Topic 7 Ryan
  F = Fourier transform </math> definition of the Fourier transform of an impulse train.
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• HW6ECE438F14
  [[Category:fourier transform]]
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• Text slecture
  Below we derive Discrete-Time Fourier Transform of ''x₂ [n]'' in terms of DTFT of ''x₁ [n]'
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• HW5ECE438F14 Soln
  [[Category:fourier transform]] ...following signals x[n] (if possible). How does your answer relate to the Fourier series coefficients of x[n]?
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• Frequency-Domain-View-of-Downsampling-Slecture-David-Klouda
  Taking the Discrete Time Fourier Transform of each we get The Fourier representation
  4 KB (566 words) - 09:59, 14 March 2015
• Frequency Downsampling
  First we'll take the Discrete Time Fourier Transform of the original signal and the downsampled version of it.<br>
  4 KB (641 words) - 09:58, 14 March 2015
• Slecture DescreteTime Fourier transform ECE438 review
  <font size="4">[[DTFT of a sampled cosine Yijun ECE438 slecture|Discrete-time Fourier transform (DTFT) of a sampled cosine]] </font>
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• Questions Page
  ....php/Discrete-time_Fourier_transform_Slecture_by_Fabian_Faes Discrete Time Fourier Transform (DTFT) with example ] </font>
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• Frequency domain relation Botao Chen ECE438 slecture review
  ...ked how you illustrated the changes the frequency axis goes through in the Fourier transform. I think this is a really important concept which you illustrated
  4 KB (621 words) - 05:40, 15 October 2014
• Questions and Answers for Fourier Transform of a Rep and Comb
  ...ojectrhea.org/rhea/index.php/Fourier_Transform_rep_com_Ben_ECE438_slecture Fourier Transform of a Rep and Comb ] ...a.org/rhea/index.php/Fourier_Transform_rep_com_Ben_ECE438_slecture Back to Fourier Transform of a Rep and Comb ]
  2 KB (431 words) - 05:33, 15 October 2014
• HW6ECE438F14 Soln
  [[Category:fourier transform]]
  7 KB (1,201 words) - 12:28, 14 October 2014
• HW7ECE438F14
  [[Category:fourier transform]]
  2 KB (255 words) - 05:50, 22 October 2014
• Lecture24ECE438F14
  ...ce_z_transform_computation_3_ECE438F13|Compute this z-transform and obtain Fourier transform]]
  4 KB (446 words) - 05:56, 22 October 2014
• HonorsContractECE438Fall14
  Topic 3: [[ECE438HonorsContractFST|Fourier Slice Theorem (FST)]]
  2 KB (259 words) - 19:30, 9 February 2015
• HW7ECE438F14 Soln
  [[Category:fourier transform]]
  7 KB (1,222 words) - 09:11, 3 November 2014
• HW8ECE438F14
  [[Category:fourier transform]]
  4 KB (640 words) - 06:37, 3 November 2014
• HW9ECE438F14
  [[Category:fourier transform]]
  1 KB (210 words) - 07:28, 10 November 2014
• QE637 2013 Pro1
  Using the definitions of the Fourier transform, derive an expressoin for&nbsp;<span class="texhtml">''F''(''u'',
  6 KB (1,018 words) - 22:10, 2 December 2015
• Lecture33ECE438F14
  ...fter the phase of speech production we call "excitation". We looked at the Fourier transform of x(t).
  2 KB (255 words) - 06:36, 12 November 2014
• HW10ECE438F14
  [[Category:fourier transform]] ...the spectrum.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?
  3 KB (462 words) - 07:25, 17 November 2014
• HW9ECE438F14 Soln
  [[Category:fourier transform]]
  5 KB (860 words) - 10:26, 20 November 2014
• Lecture37ECE438F14
  ...e Fourier transform of a pulse-train (a sequence of impulses multiplied by Fourier series coefficients). After discretizing the voiced phoneme, we saw that th
  2 KB (329 words) - 06:44, 24 November 2014
• HW11ECE438F14
  [[Category:fourier transform]]
  5 KB (545 words) - 12:20, 9 December 2014
• Lecture38ECE438F14
  ...the separability of the filter greatly facilitated the computation of its Fourier transform.
  3 KB (373 words) - 07:08, 24 November 2014
• HW10ECE438F14 Soln
  [[Category:fourier transform]] ...the spectrum.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?
  6 KB (1,031 words) - 11:27, 29 November 2014
• HW11ECE438F14 Soln
  [[Category:fourier transform]]
  10 KB (1,181 words) - 16:07, 2 December 2014
• ECE438HonorsContractFST
  <font size="5">Fourier Slice Theorem (FST)</font> ...CTFT) is taken. Then according to the theorem, an inverse Continuous Space Fourier Transform (CSFT) can be used to form the original object,<math>f(x,y)</math
  8 KB (1,252 words) - 19:26, 9 February 2015
• Embedded Fixed Point FFT
  [[Category:Fourier transform]]
  9 KB (1,362 words) - 18:06, 23 February 2015
• HonorsContractECE438CBP
  <font size="5">Convolution/Fourier Back Projection Algorithm</font> ...that is not computationally expensive. Although the method is based on the Fourier Slice Theorem, there's never a transformation to the frequency domain. Theo
  6 KB (927 words) - 19:26, 9 February 2015
• ECE438HonorsContractMRI
  ...of the object evaluated at specific phases. Essentially a MRI scan is the Fourier Transform of a person.
  14 KB (2,487 words) - 19:26, 9 February 2015
• Lecture Schedule ECE438Fall15 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  10 KB (1,356 words) - 13:19, 19 October 2015
• 2015 Spring ECE 438 Ersoy
  ..._extended_fourier_transform_rep_comb_ECE438F14|great explanation of how to Fourier transform a "rep" and a "comb"]], by ECE student Ben Capano. This is the ke
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• ECE438 Lab Spring 2015
  ::[https://www.projectrhea.org/rhea/images/f/f7/Fourier_series_expansion.pdf Fourier Series Example]
  2 KB (384 words) - 11:44, 21 April 2015
• Capano project slecture extended fourier transform rep comb ECE438F14
  The Fourier transform of "rep" and "comb" of a signal
  660 B (92 words) - 09:51, 14 March 2015
• 2014 Fall ECE 438 Boutin digital signal processing slectures
  ...nsform as a function of frequency <span class="texhtml">"ω"</span> versus Fourier transform as a function of frequency <span class="texhtml">''f''</span> (in *[[Slecture Fourier transform w f ECE438|Text slecture]] by Dauren
  3 KB (409 words) - 15:48, 24 March 2015
• ECE438 digital signal processing slectures
  ...ransform as a function of frequency <span class="texhtml">ω</span> versus Fourier transform as a function of frequency <span class="texhtml">''f''</span> (in **[[Slecture Fourier transform w f ECE438|Text slecture]] by Dauren
  3 KB (389 words) - 19:26, 16 March 2015
• ECE-QE CS1-2011 solusion-4
  ...linear time-invariant system with impulse response <math>h(t)</math> whose Fourier transform <math>H(\omega)</math> has the ideal low-pass characteristic
  8 KB (1,336 words) - 01:53, 31 March 2015
• 2015 Summer ECE 301 Jang
  ...tter size both-sided crib sheet is allowed. Closed-book and no calculator. Fourier Transform Tables (both CTFT and DTFT) will be given. Chap 3. Fourier Series for Periodic Signals
  6 KB (748 words) - 21:35, 10 August 2015
• 2015 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  6 KB (845 words) - 15:37, 4 November 2016
• Lecture2ECE438F15
  ...of the CTFT (duality, multiplication, and convolution) and we computed the Fourier transform of some basic signals (Dirac delta and complex exponential.) Some
  3 KB (445 words) - 08:57, 28 August 2015
• HW1ECE38F15
  [[Category:fourier transform]] ...a|table of CT Fourier transform pairs and properties]], which lists the CT Fourier transform in terms of <math>\omega</math> in radians. (You should have seen
  2 KB (296 words) - 08:56, 26 August 2015
• Lecture3ECE438F15
  **[[practice_CTFT_computation_rect_and_sinc_ECE438F11|Compute the Fourier transform of a rect and a sinc]]
  3 KB (398 words) - 10:38, 28 August 2015
• Lecture5ECE438F15
  * About the Discrete-time Fourier transform (DTFT) of a sampled cosine:
  3 KB (487 words) - 11:09, 2 September 2015
• Lecture4ECE438F15
  ...he definition, but we found a way around that problem by using the inverse Fourier transform formula to guess the answer. *[[Table DT Fourier Transforms|Table of DT Fourier transform pairs and properties]]
  3 KB (382 words) - 16:41, 31 August 2015
• HW2ECE38F15
  [[Category:fourier transform]]
  2 KB (395 words) - 12:13, 7 September 2015
• HW3ECE38F15
  [[Category:fourier transform]] '''a)''' Obtain the Fourier transform X(f) of the signal and sketch the graph of |X(f)|.
  3 KB (554 words) - 12:10, 11 September 2015
• HW1ECE438F15 Soln
  [[Category:fourier transform]] where <math>a_k</math> are the Fourier Series coefficients of the function.
  5 KB (812 words) - 13:08, 19 October 2015
• HW4ECE38F15
  [[Category:fourier transform]]
  3 KB (499 words) - 16:04, 22 September 2015
• HW2ECE438F15 Soln
  [[Category:fourier transform]]
  4 KB (536 words) - 15:54, 25 September 2015
• HW5ECE38F15
  [[Category:fourier transform]] a) What is the relationship between the DT Fourier transform of x[n] and that of y[n]=x[4n]? (Give the mathematical relation a
  5 KB (779 words) - 18:19, 25 September 2015
• HW4ECE438F15 Soln
  [[Category:fourier transform]]
  3 KB (475 words) - 15:23, 20 October 2015
• HW6ECE38F15
  [[Category:fourier transform]] ...following signals x[n] (if possible). How does your answer relate to the Fourier series coefficients of x[n]?
  2 KB (373 words) - 11:36, 5 October 2015
• HW3ECE438F15 Soln
  [[Category:fourier transform]] a) Obtain the Fourier transform X(f) of the signal and sketch the graph of |X(f)|.
  7 KB (1,181 words) - 19:17, 19 October 2015
• HW7ECE38F15
  [[Category:fourier transform]]
  2 KB (243 words) - 15:09, 20 October 2015
• HW6ECE438F15 Soln
  [[Category:fourier transform]] ...following signals x[n] (if possible). How does your answer relate to the Fourier series coefficients of x[n]?
  9 KB (1,594 words) - 15:36, 20 October 2015
• HW5ECE438F15 Soln
  [[Category:fourier transform]] a) What is the relationship between the DT Fourier transform of x[n] and that of y[n]=x[4n]? (Give the mathematical relation a
  6 KB (945 words) - 11:40, 19 October 2015
• HW7ECE438F15 Soln
  [[Category:fourier transform]]
  6 KB (971 words) - 15:24, 20 October 2015
• HW10ECE38F15
  ...r |f|>2.5KHz.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?
  3 KB (449 words) - 11:39, 20 November 2015
• 2015 Fall ECE 438 Boutin Constant Q Transform Robert Schwieterman
  ...br />assumes you are already comfortable with the concepts of the Discrete Fourier Transform. The Constant Q Transform (CQT) is closely related to the Discrete fourier Transform (DFT). But where the DFT has <br />
  4 KB (655 words) - 23:26, 22 November 2015
• HW9ECE438F15 Soln
  [[Category:fourier transform]]
  11 KB (1,782 words) - 00:17, 23 November 2015
• FFT- BFSK case study ECE438F15
  The Fast Fourier Transform (FFT) algorithm enables the rapid demodulation of Binary Frequenc ==2. Background (''Binary Frequency Shift Keying & Fast Fourier Transform'')==
  4 KB (546 words) - 19:34, 29 November 2015
• 2015 Fall ECE 438 Boutin Digital Signal Processing With Application
  The Fast Fourier Transform (FFT) algorithm enables the rapid demodulation of Binary Frequenc ==2. Background (''Binary Frequency Shift Keying & Fast Fourier Transform'')==
  3 KB (417 words) - 04:38, 29 November 2015
• 2015 Fall ECE 438 Boutin A visual explanation of aliasing and repetition with the DTFT Erik Swan
  ...is the Discrete Time Fourier Transform (DTFT). Unlike the Continuous Time Fourier Transform (CTFT), the DTFT of a signal is periodic with period <math>2\pi</ ...we'll assume the reader has a good intuitive understanding of the CTFT and Fourier series, and is generally familiar with the DTFT.
  12 KB (2,004 words) - 20:37, 2 December 2015
• RTG-Chicago-2016
  Introduction to Fourier Series (by R. Fefferman)
  1 KB (180 words) - 15:24, 16 February 2016
• ECE301Su2016 Notes
  ** Fourier series representation of CT periodic signals and FS properties.
  2 KB (358 words) - 21:09, 1 August 2016
• HW05ECE301Su2016
  Fourier Series Representation:
  607 B (86 words) - 00:27, 6 July 2016
• HW06ECE301Su2016
  Using the Fourier integral:
  499 B (69 words) - 00:24, 12 July 2016
• 2016 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  4 KB (622 words) - 09:42, 8 January 2017
• Lecture Schedule ECE438Fall16 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  10 KB (1,357 words) - 17:02, 14 September 2016
• HW1ECE38F16
  [[Category:fourier transform]] ...a|table of CT Fourier transform pairs and properties]], which lists the CT Fourier transform in terms of <math>\omega</math> in radians. (You should have seen
  2 KB (298 words) - 10:32, 24 August 2016
• HW1ECE438F16
  [[Category:fourier transform]] ...a|table of CT Fourier transform pairs and properties]], which lists the CT Fourier transform in terms of <math>\omega</math> in radians. (You should have seen
  2 KB (308 words) - 19:02, 30 August 2016
• HW2ECE438F16
  [[Category:fourier transform]]
  2 KB (398 words) - 11:41, 2 September 2016
• HW3ECE438F16
  [[Category:fourier transform]] '''a)''' Obtain the Fourier transform X(f) of the signal and sketch the graph of |X(f)|.
  3 KB (460 words) - 09:11, 7 September 2016
• HW4ECE438F16
  [[Category:fourier transform]]
  2 KB (346 words) - 11:10, 16 September 2016
• HW5ECE438F16
  [[Category:fourier transform]] *understand the effect of downsampling and upsampling (in the Fourier domain);
  4 KB (636 words) - 08:16, 21 September 2016
• HW6ECE438F16
  [[Category:fourier transform]]
  3 KB (485 words) - 17:11, 27 September 2016
• HW7ECE438F16
  [[Category:fourier transform]]
  2 KB (313 words) - 10:53, 14 October 2016
• Introduction of Optical Character Recognition (ORC)
  ...o transform the data in some way to get the statistical value, such as the Fourier Transformation if we want to get the formants from the audio signal.
  8 KB (1,405 words) - 22:56, 27 November 2016
• HW8ECE438F16
  [[Category:fourier transform]]
  3 KB (481 words) - 15:35, 8 November 2016
• HW9ECE438F16
  [[Category:fourier transform]]
  3 KB (503 words) - 15:44, 8 November 2016
• Neil Armstrong Moon Landing Speech Analysis
  ...ents time, y-axis represents frequency and z-axis represents the FFT (fast fourier transform) at each short period of time. It tells us what is the overall di
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• Mock up midterm exam with solution
  ...f the phoneme. How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?
  8 KB (1,336 words) - 15:40, 27 November 2016
• HW10ECE438F16
  [[Category:fourier transform]] ...r |f|>2.5KHz.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?
  3 KB (460 words) - 13:20, 18 November 2016
• HW9ECE438F16sln
  [[Category:fourier transform]] ...\delta[n]</math> to get the unit impulse response h[n] of the system. Then Fourier transform $h[n]$ to get the frequency response.
  9 KB (1,559 words) - 14:33, 24 November 2016
• HW10ECE438F16sln
  [[Category:fourier transform]] ...the spectrum.) How does it compare to the graph of the magnitude of the DT Fourier transform of the digital recording of the phoneme?
  7 KB (1,236 words) - 17:19, 29 November 2016
• Lecture Schedule ECE438Spring17 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  10 KB (1,357 words) - 09:45, 8 January 2017
• 2017 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  3 KB (421 words) - 16:18, 10 December 2017
• HW3ECE438S17
  [[Category:fourier transform]] '''a)''' Obtain the Fourier transform X(f) of the signal and sketch the graph of |X(f)|.
  2 KB (383 words) - 17:35, 25 January 2017
• 2017 Spring ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  3 KB (448 words) - 23:55, 23 April 2017
• HW4ECE438S17
  [[Category:fourier transform]]
  4 KB (658 words) - 14:50, 1 February 2017
• X-Ray Crystallography
  A Brief Overview of X-Ray Crystallography and how Spatial Fourier Transforms are Applicable in the Method.
  351 B (57 words) - 16:24, 23 April 2017
• The Laurent Series in DSP
  ...'z''') as well. The Laurent Series is the link in DSP between the Discrete Fourier Transform ('''DFT''') and the Z-Transform.
  6 KB (931 words) - 23:40, 23 April 2017
• 3D Visualization of Z-Transform
  ...ze the Z-Transform in 3-D domain. The relationship between Z transform and Fourier Transform will also be illustrated in 3-D form. Figure2: Fourier Transform of a high pass filter
  2 KB (310 words) - 21:40, 30 November 2017
• 3-D Visualization of Z-Transform
  ...ze the Z-Transform in 3-D domain. The relationship between Z transform and Fourier Transform will also be illustrated in 3-D form. Figure2: Fourier Transform of a high pass filter
  2 KB (310 words) - 21:44, 30 November 2017
• Digital Filters: An Overview on Design Points and Considerations
  ...impulse response is the frequency response of the filter, when we take the Fourier Transform of the zero padded impulse response, we end up with better resolu
  6 KB (897 words) - 16:44, 7 December 2017
• 2018 Spring ECE 301 Boutin
  | Table of CT Fourier series coefficients and properties (include some computations and proofs if | Table of DT Fourier series properties with proofs (yes! I'm fearless ;D ) and list of common DT
  4 KB (618 words) - 12:12, 1 May 2018
• MathSquadPages
  *[[Fourier_analysis_in_Music| Fourier Analysis in Music]] by [[user:mbell|Maria Bell]]
  3 KB (370 words) - 09:55, 12 January 2018
• Discrete Time Fourior Transfrom Properties and Proofs
  == '''<big> Discrete-Time Fourier Transform Properties with Proofs''' </big>''' == == '''<big>List of Common Coefficients of Discrete-Time Fourier Transform''' </big>''' ==
  7 KB (1,166 words) - 13:20, 26 March 2018
• 2019 Spring ECE 301 Boutin
  |[[2019_Spring_ECE301_Boutin_Fourier_series_coefficients| Fourier Series Coefficients ]]
  3 KB (374 words) - 10:53, 30 April 2019
• ECE301Spring18-DeterminingSignalPropertiesThroughFourierExam
  == ''Determining the Properties of a Signal Based on its Fourier Transform'' == As part of this course, it is important to be able to examine the Fourier Transform of a signal, and tell if the original signal is real, pure imagin
  6 KB (1,010 words) - 18:04, 20 April 2018
• Proof of Fourier Series Property table
  =Proof of Fourier Series Property table=
  183 B (22 words) - 13:54, 21 April 2018
• Manipulate piano sounnd with Matlab
  ...of the sound. To manipulate the sound of the piano, first need to find the Fourier Analysis of piano.
  2 KB (355 words) - 16:22, 21 April 2018
• Approximating Periodic Signals with Finite Fourier Series
  =Approximating Periodic Signals with Finite Fourier Series= ...his project, a matlab function will be used to show how a finite number of Fourier Series coefficients can approximate a periodic signal.
  1 KB (226 words) - 16:42, 21 April 2018
• CT Fourier Proofs Pranith Lomada Spring18 Boutin
  = Table of CT Fourier Series Coefficients and Properties = == Fourier series Coefficients ==
  3 KB (669 words) - 22:52, 22 April 2018
• Fourier transform yoga ECE301S18project
  [[Category:Fourier transform]] =Fourier Transform Yoga=
  423 B (59 words) - 12:50, 25 April 2018
• FourierSeriesConvergenceBonusProject
  =Convergence of Parametric Fourier Series Approximations= ...y(t)), which are steadily reconstructed using more and more terms of their Fourier Series and displayed graphically via MATLAB.<br />
  2 KB (403 words) - 23:36, 11 November 2018
• 2018 Fall ECE 301 Boutin Fourier Transforms in MP3 Audio Compression Shubham Bhokare comments
  ...CE _301_Boutin_Fourier Transforms in MP3 Audio Compression_Shubham Bhokare|Fourier Transforms in MP3 Audio Compression]] ...CE _301_Boutin_Fourier Transforms in MP3 Audio Compression_Shubham Bhokare|Fourier Transforms in MP3 Audio Compression]]. Please leave me a comment below if y
  990 B (139 words) - 11:04, 28 November 2018
• 2018 Fall ECE 301 Boutin Fourier Transforms in MP3 Audio Compression Shubham Bhokare
  <center><font size= 4>Fourier Transforms in MP3 Audio Compression</font size>
  2 KB (216 words) - 11:04, 28 November 2018
• Moving between the Time Domain and Frequency Domain
  ...w \phantom{aaa} \downarrow \phantom{aaa} \downarrow \phantom{aaa} \textrm{Fourier transform} </math> ...ely, can be multiplied together to obtain Y(ω), and Y(ω) can be inverse Fourier transformed to find y(t). Though this process requires more steps, its comp
  5 KB (865 words) - 16:23, 2 December 2018
• The 2-D Fourier Transform and Images
  =The 2-D Fourier Transform and Images= ...as image processing. Let’s examine the physical meaning of an image’s Fourier Transform and what such a transformed image looks like.
  2 KB (402 words) - 20:47, 1 December 2018
• Use of Fourier Transforms in MP3 Audio Compression
  =Use of Fourier Transforms in MP3 Audio Compression= With MP3, the sound samples are transformed using methods that involve Fourier Series Transformations. A frequency analysis of the sound is the basis for
  5 KB (752 words) - 17:40, 2 December 2018
• Use of FFT in MATLAB
  FFT is Fast Fourier Transform. The FFT is a faster version of the Discrete Fourier Transform (DFT). The time taken to evaluate a DFT on computer depends on nu
  3 KB (555 words) - 22:02, 2 December 2018
• Filtering Sound with Adobe Audition
  Hello, and welcome to a tutorial on filtering and understanding sound using Fourier Transforms! While this tutorial will use Adobe Audition(TM), everything sho ...some exercises in '''ECE 301''', this tutorial will let you analyze visual Fourier Transforms, intelligently apply frequency filters, and gain a better unders
  6 KB (1,077 words) - 20:29, 7 April 2019
• 2019 Spring ECE301 Boutin Fourier series coefficients
  <center><font size= 4>Fourier Series Coefficients</font size> I am going to compute some Fourier series coefficients. I have done 3 in both CT and DT, with explanations as
  5 KB (951 words) - 21:55, 30 April 2019
• ECE 301 self-analysis of exam performance
  ...roving solutions is important. For example, in the case of Continuous time Fourier transforms of periodic signals, the answer is speculated then proven to be
  3 KB (583 words) - 21:07, 24 April 2019
• Practice Exam solutions with reflection ECE301S19
  ...roving solutions is important. For example, in the case of Continuous time Fourier transforms of periodic signals, the answer is speculated then proven to be
  4 KB (644 words) - 11:22, 30 April 2019
• 2019 Fall ECE 438 Boutin
  **[[CT Fourier Transform (frequency in hertz)|CTFT]] **[[Table DT Fourier Transforms|DTFT]]
  4 KB (467 words) - 02:18, 10 December 2019
• Lecture Schedule ECE438Fall2019 Boutin
  *Fourier Series **PM's discussion of Linear algebra and Fourier series: pp. 232-240, 247-253, 399-409,
  10 KB (1,356 words) - 18:52, 20 August 2019
• Ece438f19bhelfrechtbonus
  ...aliasing'', which results when two distinct frequency bands overlap in the Fourier domain. In other words, aliasing occurs when the original signal’s freque ...increase seen after downsampling. The amplitude decrease is related to the Fourier transform formula.
  16 KB (2,611 words) - 14:11, 12 November 2019
• Ece438f19glakebonus
  ==Relationship Between Fourier Transform and Z Transform==
  6 KB (1,040 words) - 00:57, 2 December 2019
• 2020 Fall MA 271 Walther
  | [[Walther_MA271_Fall2020_topic20|Fourier transforms]]
  6 KB (846 words) - 17:57, 7 December 2020
• Walther MA271 Fall2020 topic20
  = Fourier Transforms = ...representing how much of each frequency is prevalent in the function. The Fourier transform allows for signals to be broken into their individual frequency c
  12 KB (2,051 words) - 14:20, 5 December 2020
• Definition of Nyquist’s Theorem
  ...[https://en.wikipedia.org/wiki/Fourier_transform here]. As a result of the Fourier Transform, the graph of a waveform can be converted into one similar to the ...which are not equivalent at frequencies close to ''B'', have Discrete Time Fourier Transforms that are the same. This situation results because there is an ov
  4 KB (707 words) - 23:06, 6 December 2020
• Worked Examples Using Nyquist’s Theorem
  ...these example problems. For more information about Fourier Series and the Fourier Transform, click [https://www.tutorialspoint.com/signals_and_systems/fourie '''1)''' Through the Fourier Transform, it is revealed that a signal is made up of constituent frequenci
  4 KB (587 words) - 00:26, 7 December 2020
• Further Reading and References
  ...spoint.com/signals_and_systems/fourier_series.htm Fourier Analysis and the Fourier Transform] ...://en.wikipedia.org/wiki/Discrete-time_Fourier_transform The Discrete Time Fourier Transform]
  2 KB (257 words) - 00:56, 7 December 2020
• MA271Fall2020Walther Topic27 Quasicrystals
  ...be formed with five-fold symmetry using a [[Walther_MA271_Fall2020_topic20|Fourier transform]] of a Penrose tiling, first conducted by crystallographer Alan L
  4 KB (622 words) - 21:09, 8 December 2020
• ApplicationsCBCP
  ...mated sinusoidal functions. They are said to be periodic. Some examples of Fourier series can be seen below. The Wiener Algebra is simply the set of all absolutely converging Fourier series. It also is a Banach Space.
  1 KB (172 words) - 00:06, 7 December 2020