An LTI system is given by the block-diagram below: +1 x(n) IN Z 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) = jwon, 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
An LTI system is given by the block-diagram below: +1 x(n) IN Z 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) = jwon, 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
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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