Homework Assignment 2
Due Sept. 6, 2000

1. Problem 2.7 (a) (c) (d) (j) (m)

2. Problem 2.29 (a) (c). If x(n) has N terms and h(n) has M terms, how many terms does y(n) = x(n) * h(n) have?

3. Problem 2.30. Use MATLAB to plot the impulse responses of the two systems.

4. Consider the three systems shown in Figure P2.48 (page 145).
   1. Write difference equations for each of the systems.
   2. Redraw the systems using the Direct Form II stucture.
   3. Classify the systems as FIR or IIR.

5. Consider the system described by the difference equation

       y[n] = y[n-1] + y[n-2] + x[n-1]

   1. Find the first 10 values of the impulse response of the system. Note that this is the Fibonnaci sequence, where f[n] = f[n-1] + f[n-2], with f[0] = 0, and f[1] = 1.

   2. Find an analytical expression for impulse response of the system.

   3. Find the value of f[25] from the expression in (b).