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 discretetime
systems and Z transforms.
Note that we will have our first exam next Friday, February 28.

Analyze the system y(n) = x(n) + 0.9 * y(n1)
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.

Can this system be classified as a lowpass or highpass filter?
Write out the convolution sum for this system, and try to
interpret the convolution as a filtering operation.

In what ways does this
autoregressive (AR) / feedback / allpole system differ
from the moving average (MA) / feedforward / allzero
system y(n) = [x(n) + x(n1)]/2 that we considered in class?
Can you explain why the terms used to describe each system
are appropriate?

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.