b3 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, phaseresponse 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 DFScoefficients 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 convolutionof x(n) and h(n) in time domain: c(n) = x(n) *s h(n)d) Now, calculate the output of the system, y(n), firstly with linear convolution: yı(n) = x(n) * h(n),then calculate the output with 6 points in time domain: yz(n) =x(n) *6 h(n). Compare the results.

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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.

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.

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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Concept explainers

Nodal Analysis

In the analysis of any electric circuit, nodal analysis is the method of determining the potential difference or voltage between different nodes in an electric circuit. A node is a point where two or more branches connect each other. In the nodal analysis, the voltages are determined in the terms of branch currents. The nodal analysis is also known as the node voltage method or branch current method. The nodal analysis method is one of the several applications of Kirchhoff's Current Law (KCL).

Question

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) *s h(n)
d) Now, calculate the output of the system, y(n), firstly with linear convolution: yı(n) = x(n) * h(n),
then calculate the output with 6 points in time domain: yz(n) =x(n) *6 h(n). Compare the results.

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