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An LTI system is given by the block-diagram below: +1 x(n) Z-1 N Z-1 -1 (+) y(n) a) Write the difference equation that corresponds to the system and the impulse response of the system h(n) b) What is the frequency response H(w) of the system? (simplify as much as possible - hint: us symmetry) c) Write the expression for the magnitude |H(w)|. What is the phase response ZH(w)?

An LTI system is given by the block-diagram below: +1 x(n) Z-1 N Z-1 -1 (+) y(n) a) Write the difference equation that corresponds to the system and the impulse response of the system h(n) b) What is the frequency response H(w) of the system? (simplify as much as possible - hint: us symmetry) c) Write the expression for the magnitude |H(w)|. What is the phase response ZH(w)?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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An LTI system is given by the block-diagram below: +1 x(n) N N -1 (++) y(n) a) Write the difference equation that corresponds to the system and the impulse response of the system h(n) b) What is the frequency response H(w) of the system? (simplify as much as possible - hint: use symmetry) c) Write the expression for the magnitude |H(w). What is the phase response ZH(w)? d) What discrete frequency/frequencies are completely blocked by this system? e) If the input is a complex sinusoid x(n) = ejwon, where wo, what is the output of the system y(n)? What is the output when wo = 7 Hint: use |H(w)|, ZH(w) f) i. Assume you are given a function H(z) as a ratio of 2 polynomials in z - how could you tell if this is a low-pass/high-pass or a band-pass filter? ii. Assume you are given some H (w) (this time, assume also you can access python/matlab or some other numerical software) - how could you quickly tell if H (w) represents a low-pass/high-pass or a band-pass filter? Explain both cases briefly in no more than 2-3 sentences
Transcribed Image Text:An LTI system is given by the block-diagram below: +1 x(n) N N -1 (++) y(n) a) Write the difference equation that corresponds to the system and the impulse response of the system h(n) b) What is the frequency response H(w) of the system? (simplify as much as possible - hint: use symmetry) c) Write the expression for the magnitude |H(w). What is the phase response ZH(w)? d) What discrete frequency/frequencies are completely blocked by this system? e) If the input is a complex sinusoid x(n) = ejwon, where wo, what is the output of the system y(n)? What is the output when wo = 7 Hint: use |H(w)|, ZH(w) f) i. Assume you are given a function H(z) as a ratio of 2 polynomials in z - how could you tell if this is a low-pass/high-pass or a band-pass filter? ii. Assume you are given some H (w) (this time, assume also you can access python/matlab or some other numerical software) - how could you quickly tell if H (w) represents a low-pass/high-pass or a band-pass filter? Explain both cases briefly in no more than 2-3 sentences
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