ECE438 Week10 Quiz - Rhea

Quiz Questions Pool for Week 10

Q1. Consider the following difference equation

y[n]=ay[n-1]+x[n]-x[n-1]\,\!

a. Compute the transfer function

$ H(z) $

, and find its poles and zeros.

b. Compute the impulse response

$ h[n] $

using a ROC of

$ |z|>a $

. For what values of

$ a $

is the system stable?

c. Compute the impulse response

$ h[n] $

using a ROC of

$ |z|<a $

. For what values of

$ a $

is the system stable?

Q2. The condition for the discrete-time signal $$ x[n] $$ to be real is

$x[n]=x^{\ast}[n]$

Then, what is the condition of the frequency response $$ X(w) $$ for $$ x[n] $$ to be real?

(Hint: Apply DTFT to the above equation)

Q3.

Q4.

Q5.