## EE 451

Homework Assignment 3
Due Sep. 15, 1999

1. Look at Lab 3
1. Find the impulse response h[n] for the difference equation.
2. Find the frequency response H(ejw).
3. Use MATLAB to plot the magnitude and phase of the frequency response.

2. Problem 2.44, parts (a) - (d). This should be easy using the symmetry properties of the Fourier transform. If you are doing a lot of math, you are approaching the problem in the wrong way. Hint: Look for symmetry and time shifts in x[n].

1. Find the impulse response for a system which has the following frequency response:
-
/     0   |w| < pi/4
H = -
\      1   pi/4 < |w| < pi
-

2. Use MATLAB to plot h[n] for n = -20 to 20.

1. Determine the Fourier transform of
-
/     1   -N <= n <= N
h[n] = -
\     0   otherwise
-

2. Use MATLAB to plot the frequency response of h[n] for N = 10. You should be able to get this into a nice closed form.

3. Problem 2.52. Again, this is very easy using properties of the Fourier transform, and should involve very little math.

4. Problem 2.53

Bill Rison, <rison@ee.nmt.edu >