Question

3. Use partial-fraction expansion to find the inverse z-transform of the following. You need to simplify your results so that r{n] is a real signal. (a) 22 X(z) 2-1)(2-0.5)(2-2) EECS 50, Fall 2019 2 (b) X(2)2221

Answer 1

a) -)(t-0.5) (z-2) (a) -i) (E-0,5)(E-2) APplyng Parthal fratons oxpansion A C -(E-0.5)(2-2) - -2-0.5 E-2 = A (t-) (t-i) + B(2+)(2-i)+ c (a-)(t-2) put 0.5 => 0.5= B(-0.5)-1.5) 3 Put - A -2. Put 2 c Co() c 43 23 - 2 чз t E-0.) (-2) 2-0 5 2 4 2 + X ()- 2 2-2 2-D.5 - APplying f vevse -tansfdn ,

IET an u(n) 2-a) -2 (u(n) + CO.5 un) un) (n)

(b X () We know that Standard fomulas ayy sfn (a)z stη (a ) 2 Cos a z + By Comparing on 60 z-2 Cosat 2 Cos a Sn(a) Cosa Substitetny a 3 1.= ए/5

. x(zCan be earangcd ag written belo 2 Na2. 근 2 2. By Applyny -trafn ue get nNesse 2 Cn) sntnun) xa= sin()un)

Answer 2

1/1-1.5z^-1+0.5z ^-2