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

zatajuxoqj

zatajuxoqj

Answered question

2022-03-26

Determine the Z-transform for the sequence
x[n]=(1)ν[n]

Answer & Explanation

Cason Singleton

Cason Singleton

Beginner2022-03-27Added 13 answers

x[n]=(1)ν[n]
Apply Z-transform to the sequence
z[(1)ν[n]]=n=(1)ν[n]zn
n=0
Hence, z[(1)ν[n]]=n=(1)nz1
=n=((1)nz1)n
=n=(z1)n
=1z1+z2z3+
z[(1)ν[n]]=11+z1
Thus, z-transform of (1)ν[n]
z[(1)ν[n]]=1(1+z1)
|z|>1
The z-transform of (1)ν[n] has zero at z=0 and pole at z=1

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