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The Boutin Lectures on Digital Signal Processing-Part 1

Slectures by Students in the Fall 2014 Class of ECE438


Topic 1: Fourier transform as a function of frequency ω versus Fourier transform as a function of frequency f (in hertz).

  • Topic 2: Definition of the "rep" and "comb" operators. (Note that there are two ways to define each of these operators: using multiplication/convolution with an impulse train, or using a summation formula without impulse-train. You should include both representations and explain how to go from one to the other.) DEADLINE September 19
  • Topic 3: Fourier transform of "rep" and "comb". (Make sure to carefully explain how to compute the Fourier transform of an impulse-train. You do not need to prove the multiplication/convolution property of the CTFT, but state it clearly whenever you need to use it.) DEADLINE October 1
  • Topic 4: Discrete-time Fourier transform (DTFT): definition, periodicity property, example (computation of DTFT of a complex exponential- no fudging!) DEADLINE October 1
  • Topic 5: Discrete-time Fourier transform (DTFT) of a sampled cosine. (Include Case 1) sampling rate above Nyquist rate, and Case 2) sampling rate below Nyquist rate.) DEADLINE October 3
  • Topic 6: Nyquist Theorem, with proof and example DEADLINE October 6
  • Topic 7: Frequency domain view of the relationship between a signal and a sampling of that signal. DEADLINE October 6
  • Topic 8: Frequency domain view of downsampling (explain why decimator needs a lowpass filter before the downsampling). DEADLINE October 10
  • Topic 9: Frequency domain view of upsampling (explain why interpolator needs a lowpass filter after upsampling). DEADLINE October 13


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