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The input output relation for a discrete time system is expressed by the following difference equation: y(n)=ax(n)+bx(n-1)+cx(n-2)+dy(n-1)+ey(n-2) where a,b,c,d,e are non zero coefficients.  Find out the two intermediate transfer functions if the system is to be realised by direct form 1.

The input output relation for a discrete time system is expressed by the following difference equation: y(n)=ax(n)+bx(n-1)+cx(n-2)+dy(n-1)+ey(n-2) where a,b,c,d,e are non zero coefficients.  Find out the two intermediate transfer functions if the system is to be realised by direct form 1.

Introductory Circuit Analysis (13th Edition)
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 input output relation for a discrete time system is expressed by the following difference equation:

y(n)=ax(n)+bx(n-1)+cx(n-2)+dy(n-1)+ey(n-2) where a,b,c,d,e are non zero coefficients. 

Find out the two intermediate transfer functions if the system is to be realised by direct form 1. 

Expert Solution
Step 1

In direct form 1 of realization, the general expression of the transfer function H(z) is given as

Electrical Engineering homework question answer, step 1, image 1

 

Step 2

In direct form 1, the intermediate transfer functions are defined as

Electrical Engineering homework question answer, step 2, image 1

Step 3

In this case, the difference equation of the system is given as

Electrical Engineering homework question answer, step 3, image 1

Taking Z transform on both sides of equation (4) gives

Electrical Engineering homework question answer, step 3, image 2

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