Question

5. The transfer function of a system is given by Z Н(2) (z2-0.8z+ 0.15) -0.4n for n2 0. Find the response of To such a system we apply an input of the type x [n] the system in n domain using MATLAB for obtaining the partial fraction expansion and then manually inverting the output using z-transform tables.

Please show all the steps clearly.

Answer 1

Solution:

Enexp4) takig hanfomm exp-04)2 ()X exp (a4) 2-0.67 Naw 2 z042-t 15 Y(2) X) 2-0320.15 ,2 -042015) (t>0-2) e(E

(2-0.) (2-05) (2-0 3) B2 A2 2-0.3 2-0.67 2-05 foamt B partic frdim A B 147 C405 Carusna e Y(2).651-0 672 1h.7 - 0.32 1-0527 tabim ise 2tarsfonm SLnJ= Lo.C5 (0-)"-14-7 (0-5)"+ 4.05 (o-3)" Hence the response L.C5( -147 (0-5)+ 4.05 (o 3)

%%----------- MATLAB CODE-----------------%%

close all
clear all
syms z
H=z.^2/((z-0.67)*(z.^2-0.8*z+0.15))
iztrans(H)

%%------------------- END -----------------------%%

Simulated output:

ans =
(150*(3/10)^n)/37 - (250*(1/2)^n)/17 + (6700*(67/100)^n)/629