Answered: The impulse response of a linear phase…

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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The impulse response of a linear phase FIR and LTI system is given as
h[n]={2, -1, 3, -1, 2}.

a) Calculate the frequency response of the system with DFT. Give the amplitude and phase responses and the group delay.

b) Let h'[n]={ 2, -1, 3, -1, 2, 0} be the periodic state of h[n] with N=6. Give the DFS coefficients of h'[n]. Compare the computational load for DFT and FFT algorithms.

c) The input sign x[n]={1, 2} is applied to the system in (a). Calculate the 5-point circular convolution of x[n] and h[n]: c[n] = x[n] ⊗ 5 h[n]

d) Now calculate the output y[n] of the system first by linear convolution: y1[n] = x[n] * h[n], then by circular convolution: y2[n] = x[n] ⊗ h [n]. Compare the results.

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