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Can someone explain how to solve 1c). I started the question but got stuck.

1. System Transfer Functions: (20 Pis)
Given below are the difference equations for several linear time-invariant systems. As-
sume that all of the systems are causal and right sided. Perform the following for each
System:
. Find the Z-transform, #(z), of the impulse response of the system.
. Give the region of convergence of the system. Is the system stable?
. If the system is unstable, write (ONLY) the xeros and/or pokes of a stablized
system that would result in the same magnitude response.
(a) y(n) = r(n) - 2.5x(n - 1) + r(n -2) + wy(n - 1) - ly(n -2)
(b) y(n) = x(n) - 2- v2x(n - 1) + 2r(n -2)
(c) y(n) = r(n) + 2x(n - 1) + x(n - 2) + 2. /2y(n - 1) - 4y(n-2)
NOTE: The roots of a general polynomial or' + be + c is given as 312 =
by lac

1 ) c ) you ) = x (n)+ 2x (n-1 ) + 2 (1- 2) + 2. 52 y (n-1) -4y(4-2)
-Applying 2 - transform
Y ( z ) = X ( 2 ) + 2z X ( 2 ) + 2 x ( 2 ) +2.8 y (2 ) 2 + 42 7 ( 2)
[ . : 2(2 (4-1) ) = 2-/(2)]
Y ( 2 )...

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