Find z-transform of the sequence \(\displaystyle{x}{\left[{n}\right]}={\left({\frac{{{1}}}{{{2}}}}\right)}^{{n}}{u}{\left[{n}+{3}\right]}\)

Ramiro Grant

Ramiro Grant

Answered question

2022-04-08

Find z-transform of the sequence
x[n]=(12)nu[n+3]

Answer & Explanation

granfury90210birm

granfury90210birm

Beginner2022-04-09Added 10 answers

Given: x[n]=(12)nu[n+3]
X(z)=n=3(12)nzn
=n=3[12z1]n
n=N1N2an=aN1aN2+11a
X(z)=(12z1)3(12z1)+11(12z1)
=(12z1)3z30112z1
=8z3×zz12
=8z4z12
Poles:
z12=0
z=0.5
Zeros:
8z4=0
z=0
Thus, |12z1|<1
|z|>12

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