I want to learn that how can ı solve only part(a).I could not simplify the equation with a sensible result.

Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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I want to learn that how can ı solve only part(a).I could not simplify the equation with a sensible result.

Q2.
A DT LTI system has frequency response
4 – 9e-j2
H(e?) =
4 cos 2+ 2e-j2 – 9
(a) The rational system function H(z) corresponding to the frequency response
above can be written as
a2
H(z)
z-4
Find aj and az and specify the ROC.
(b) Is the system causal?
(c) What is the system's impulse response h[n]?
(d) Suppose the input to the system is the signal x[n] = 3" for all n. What is the
corresponding output, y[n]?
(e) Suppose the input to the system is the signal x[n] = 3"u[n], where u[n] is the
unit step function. As n → -00, y[n] → Bz%. What is zo?
Transcribed Image Text:Q2. A DT LTI system has frequency response 4 – 9e-j2 H(e?) = 4 cos 2+ 2e-j2 – 9 (a) The rational system function H(z) corresponding to the frequency response above can be written as a2 H(z) z-4 Find aj and az and specify the ROC. (b) Is the system causal? (c) What is the system's impulse response h[n]? (d) Suppose the input to the system is the signal x[n] = 3" for all n. What is the corresponding output, y[n]? (e) Suppose the input to the system is the signal x[n] = 3"u[n], where u[n] is the unit step function. As n → -00, y[n] → Bz%. What is zo?
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