Question

What is the frequency response of the system described by the system function H(z)=\(\frac{1}{1-0.8z^{-1}}\)?

(a) \(\frac{e^{jω}}{e^{jω}-0.8}\)

(b) \(\frac{e^{jω}}{e^{jω}+0.8}\)

(c) \(\frac{e^{-jω}}{e^{-jω}-0.8}\)

(d) None of the mentioned

I got this question in exam.

This question is from Frequency Domain Characteristics of LTI System in division Frequency Analysis of Signals and Systems of Digital Signal Processing

Answer 1

Correct answer is (a) \(\frac{e^{jω}}{e^{jω}-0.8}\)

The explanation is: Given H(z)=\(\frac{1}{1-0.8z^{-1}}\)=z/(z-0.8)

Clearly, H(z) has a zero at z=0 and a pole at p=0.8. Hence the frequency response of the system is given as

H(ω)=\(\frac{e^{jω}}{e^{jω}-0.8}\).