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 Determine inverse z-transform x(z)=110.5z1+0.5z2 for (i) R:|z|>1 (ii) R0C+1<0.5 (iii) ROC 0.5<|2|<1
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Solution:

Step 1: Convert x(z) to positive powers of z

x(z)=z2z21.5z+0.5

x(z)z=zz21.5z+0.5=z(z1)(z0.5)

Step 2 =: Partal Fraction

x(z)z=Az1+Bz0.5

A=(z1)z(z1)(z0.5|z=1=110.5=2

B=(z0.5)z(z1)(z0.5)|z=0.5=.5.51=1

x(z)z=zz11z0.5

$ \begin{aligned} x(z) & …

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