Rich Kozick
Spring, 1997

## EE 329: Homework 5

Date Assigned: Friday, February 21, 1997
Date Due: Wednesday, February 26, 1997

Below are some problems to help you work with discrete-time systems and Z transforms. Note that we will have our first exam next Friday, February 28.

1. Analyze the system y(n) = x(n) + 0.9 * y(n-1) from as many points of view as you can. Include a block diagram of the system, and be sure to look at the impulse response (formula and a plot), the frequency response (formula and a plot), transfer function, and poles/zeros of the transfer function.
1. Can this system be classified as a low-pass or high-pass filter? Write out the convolution sum for this system, and try to interpret the convolution as a filtering operation.
2. In what ways does this autoregressive (AR) / feedback / all-pole system differ from the moving average (MA) / feedforward / all-zero system y(n) = [x(n) + x(n-1)]/2 that we considered in class? Can you explain why the terms used to describe each system are appropriate?

2. Consider the problem formulated in the Fun Assignment relating to the growth of rabbit populations. Let r(n) denote the number of rabbit pairs at month n. Find R(z), the Z transform of r(n), and then find r(n) by an inverse Z transform operation. Compute r(12), the number of rabbit pairs after 12 months, two ways: manually from the difference equation, and using your formula for r(n). Do your answers agree?
Thank you.