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Determine inverse z-transform x(z)=11−0.5z−1+0.5z−2 for (i) R∝:|z|>1 (ii) R0C+1<0.5 (iii) ROC 0.5<|2|<1
1 Answer
written 2.3 years ago by |
Solution:
Step 1: Convert x(z) to positive powers of z
x(z)=⋅z2z2−1.5z+0.5
x(z)z=zz2−1.5z+0.5=z(z−1)(z−0.5)
Step 2 =: Partal Fraction
x(z)z=Az−1+Bz−0.5
A=(z−1)⋅z(z−1)(z−0.5|z=1=11−0.5=2
B=(z−0.5)z(z−1)(z−0.5)|z=0.5=.5.5−1=−1
x(z)z=zz−1−1z−0.5
$ \begin{aligned} x(z) & …