3) Impulse response of an FIR and LTI system with linear phase is given as: h(n)={1, -1/2, 2, -1/2, 1}, n=0,1,2,3,4. a) Calculate the frequency response of the system using DFT. Write the magnitude response, phase response and the group delay of the system. b) Let h'(n)={1, -1/2, 2, -1/2, 1, 0} signal be the periodic version of h(n) with period N=6. Find DFS coefficients of h’(n). Find and compare the computational loads of DFT and FFT algorithms. (Computational load for DFT is N²,and for FFT is Nlog2N.) c) The input signal x(n)={1, 2} is applied to the system in (a). Find the 5 points circular convolution of x(n) and h(n) in time domain: c(n) = x(n) *5 h(n) d) Now, calculate the output of the system, y(n), firstly with linear convolution: yı(n) = x(1n) * h(n), then calculate the output with 6 points in time domain: y2(n) = x(n) *6 h(n). Compare the results. %3D

3) Impulse response of an FIR and LTI system with linear phase is given as: h(n)={1, -1/2, 2, -1/2, 1}, n=0,1,2,3,4. a) Calculate the frequency response of the system using DFT. Write the magnitude response, phase response and the group delay of the system. b) Let h'(n)={1, -1/2, 2, -1/2, 1, 0} signal be the periodic version of h(n) with period N=6. Find DFS coefficients of h’(n). Find and compare the computational loads of DFT and FFT algorithms. (Computational load for DFT is N²,and for FFT is Nlog2N.) c) The input signal x(n)={1, 2} is applied to the system in (a). Find the 5 points circular convolution of x(n) and h(n) in time domain: c(n) = x(n) 5 h(n) d) Now, calculate the output of the system, y(n), firstly with linear convolution: yı(n) = x(1n) h(n), then calculate the output with 6 points in time domain: y2(n) = x(n) *6 h(n). Compare the results. %3D

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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