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(e^jw).
   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].

3. 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.

4. 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.

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

6. Problem 2.53