E71 Assignment 4

Problem 1:

For the periodic function x(t), with period = w, and defined as

  1. What can you say about the ck before starting (i.e., real vs complex vs imaginary, odd vs even).
  2. Determine the Fourier coefficients, ck.
  3. Make a plot of ck for k=-10 to 10.
  4. For w=1, what is F0?
  5. Plot  for m=0, 1 and 3 if A=1, w=1.

Problem 2:

For the function, y(t), defined below:

  1. Find the Fourier Transform, Y(F), by integration.
  2. The function x(t) is simply the periodic extension of y(t), with period = w.  Show w·ck=Y(k·F0)
  3. Plot Y(F) if A=1, w=1 for F=-10 to 10.

Problem 3:  From text, 4.4

Problem 4:  From text, 4.6 a-d

Problem 5:  From text, 4.6 e-h