Question

using matlab

Show the two formals or figures in time domin and z dominclc

clear all

b=[1,-4,5]

a=[1,-6,11,-6]

[R,P,C]=residuez(b,a)

Ez=tf(b,a,1,'variable','z')

zplane(b,a)

Answer 1

Overall Code used including the above given to Represent the Ez in Z and t domain

b=[1,-4,5];
a=[1,-6,11,-6];
[R,P,C]=residuez(b,a);
Ez=tf(b,a,1,'variable','z');
zplane(b,a)
syms z t
s = (z^2 - 4*z + 5)/(z^3 - 6* z^2 + 11 *z - 6);
iztrans(s,t)

This above given code produces the Transfer function in Z domain as

Ez =

z^2 - 4 z + 5
----------------------
z^3 - 6 z^2 + 11 z - 6

Ans there pole zero plot

To convert it into time domain we will use Invert Z Transform using code

syms z t

s = (z^2 - 4*z + 5)/(z^3 - 6* z^2 + 11 *z - 6);

iztrans(s,t)

In Time domain E(t) =

3^t/3 - 2^t/2 - (5*kroneckerDelta(t, 0))/6 + 1

OR

3^t/3 - 2^t/2 - (5*(t))/6 + 1

Working Screenshot