5.47. A linear-phase FIR system has a real impulse response h[n] whose z-transform is known to have the form H(2) = (1 – az-l)(1 – ei™ /2,-1>(1 – bz-)(1 – 0.52-1)(1 – cz-1) where a, b, and c are zeros of H(z) that you are to find. It is also known that H(el") =0 for w = 0. This information and knowledge of the properties of linear-phase systems are suf- ficient to completely determine the system function (and therefore the impulse response) and to answer the following questions: (d) Determine the unknown zeros a, b, and c. (The labels are arbitrary, but there are three more zeros to find.) (e) Determine the values of the impulse response and sketch it as a stem plot.

5.47. A linear-phase FIR system has a real impulse response h[n] whose z-transform is known to have the form H(2) = (1 – az-l)(1 – ei™ /2,-1>(1 – bz-)(1 – 0.52-1)(1 – cz-1) where a, b, and c are zeros of H(z) that you are to find. It is also known that H(el") =0 for w = 0. This information and knowledge of the properties of linear-phase systems are suf- ficient to completely determine the system function (and therefore the impulse response) and to answer the following questions: (d) Determine the unknown zeros a, b, and c. (The labels are arbitrary, but there are three more zeros to find.) (e) Determine the values of the impulse response and sketch it as a stem plot.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

5.47. A linear-phase FIR system has a real impulse response h[n] whose z-transform is known
to have the form
H(2) = (1 – az-)(1 – eia2;-1)(1 – bz-1)(1 – 0.5z-1)(1 – ez-1)
where a, b, and c are zeros of H(z) that you are to find. It is also known that H(ej") = 0 for
w = 0. This information and knowledge of the properties of linear-phase systems are suf-
ficient to completely determine the system function (and therefore the impulse response)
and to answer the following questions:
(d) Determine the unknown zeros a, b, and c. (The labels are arbitrary, but there are three
more zeros to find.)
(e) Determine the values of the impulse response and sketch it as a stem plot.

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