EE313 Linear Systems & Signals - Homework 9 Hints

• Fourier transforms videos
  • "But what is the Fourier Transform? A visual introduction", by 3Blue1Brown, Jan. 26, 2018
  • Videos: Brian Douglas (13:03) - Darryl Morrell, Part 1 (9:02) - Darryl Morrell, Part 2 (11:07)

• Signals & Systems slides and handouts
  • Lecture Slides: Frequency Response - Fourier Transforms - Sampling & Reconstruction
  • Handout Q Intro to Fourier Transforms
  • Pictorial guide of Fourier transform pairs in Hz and rad/s in Appendix D of Michael Roberts' Fundamentals of Signals & Systems (course Canvas site only). Continuous-time Fourier transforms in terms of w in rad/s will have the same shape as those in terms of Hz; the ony difference is a scaling of the frequency axis by w = 2 pi f.

• Plotting Magnitude and Phase Responses in the Frequency Domain
  For the MATLAB plot of the magnitude response, you could modify the code from Lecture Slide 14-5 to match the range of frequencies for a particular problem:

  fmaxplot = 20;
  wmaxplot = 2*pi*fmaxplot;
  w = -wmaxplot : 0.01 : wmaxplot;
  H = 2 ./ (2 + j*w);
  Hmag = abs(H);
  Hphase = phase(H);
  figure;
  plot(w, Hmag);
  title('Magnitude Response');
  figure;
  plot(w, Hphase);
  title('Phase Response');
  

  You'll need to put in your formula for H.

• Problem 9.3(d). An impulse train in the time domain models instantaneous sampling in time. The Fourier transform of an impulse train is an impulse train. Please see lecture slides 16-3 and 16-4 on Sampling & Reconstruction and homework #8 solutions in Fall 2017 for a solution.

bevans@ece.utexas.edu