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. When we have a LTI system, the impulse response $ h[n] $ must be real
in order for $ y[n] $ to be real whenever $ x[n] $ is real.
The condition for $ h[n] $ to be real is
$ h[n]=h^{\ast}[n] $
Then, what is the condition of the frequency response $ H(w) $ for $ h[n] $ to be real?
(Hint: Apply DTFT to the above equation)
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