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 mentionedI 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

What is the frequency response of the system described by the system f

1.	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 mentionedI 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» 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)=\(\frac{e^{jω}}{e^{jω}-0.8}\).

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