# E71 Assignment 4

### Problem 1:

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

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

### Problem 2:

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

- Find the Fourier Transform, Y(F), by integration.
- The function x(t) is simply the periodic extension of
y(t), with period = w. Show w·c
_{k}=Y(k·F_{0})
- 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