QB2a) A digital filter is described by the following linear differenceequation:y(n) = 0.2[x(n) + x(n – 1) + x(n – 2) + x(n – 3) + x(n – 4)]-i) What is the main function of this filter?ii) Present the filter structure diagram, transfer function, andfrequency response of the filter.ii) Determine the sequential 6 output values for the input ofa unit step sequence:u[n] = {oS1n 2 0n < 0%3Db) In order to reduce the amount of memory and processingtime, a recursive solution is required in which previouscalculated averages (i.e., previous output samples) are usedto determine the present output.i) For the digital filter described in a), show that the recursivetransfer function is given by:Y (Z)[1 – z-5]0.2X (Z)[1 – Z-1]ii) Determine the transfer function poles and zeros and checkthe stability.

A linear equation is one that has only one degree as its maximum. A nonlinear equation is one with a…

Answered: a) A digital filter is described by the…

a) A digital filter is described by the following linear difference equation: y(n) = 0.2[x(n) +x(n – 1) + x(n – 2) + x(n – 3) + x(n – 4)]

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

QB2
a) A digital filter is described by the following linear difference
equation:
y(n) = 0.2[x(n) + x(n – 1) + x(n – 2) + x(n – 3) + x(n – 4)]
-
i) What is the main function of this filter?
ii) Present the filter structure diagram, transfer function, and
frequency response of the filter.
ii) Determine the sequential 6 output values for the input of
a unit step sequence:
u[n] = {o
S1
n 2 0
n < 0
%3D
b) In order to reduce the amount of memory and processing
time, a recursive solution is required in which previous
calculated averages (i.e., previous output samples) are used
to determine the present output.
i) For the digital filter described in a), show that the recursive
transfer function is given by:
Y (Z)
[1 – z-5]
0.2
X (Z)
[1 – Z-1]
ii) Determine the transfer function poles and zeros and check
the stability.

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