Determine Z-transform for the sequence \(\displaystyle{x}{\left[{n}\right]}={\left({\frac{{{1}}}{{{4}}}}\right)}^{\nu}{\left[{3}-{n}\right]}\)

Nathen Peterson

Nathen Peterson

Answered question

2022-03-25

Determine Z-transform for the sequence
x[n]=(14)ν[3n]

Answer & Explanation

Aaliyah Phillips

Aaliyah Phillips

Beginner2022-03-26Added 9 answers

x[n]=(14)ν[3n]
Apply Z transform of x[n]
Z(z)=n=x[n]zn
=n=(14)ν[3n]xn
=n=3(14)nzn
=n=3(14z1)n
=(14z1)3+(14z1)2+(14z1)1+1+(14z1)1+
=(14z1)31(14z1)1
=164z314z
Thus, X(z)=164z314z
Region of convergence |4z|<1|z|<14
14z=0z=14 is pole

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