Determine the Z-transform for the sequence \(\displaystyle{x}{\left[{n}\right]}={\left({\frac{{{1}}}{{{3}}}}\right)}^{{{n}-{2}}}{u}{\left[{n}-{2}\right]}\)

Blackettyl2j

Blackettyl2j

Answered question

2022-03-26

Determine the Z-transform for the sequence
x[n]=(13)n2u[n2]

Answer & Explanation

pautmndu

pautmndu

Beginner2022-03-27Added 10 answers

x[n]=(13)n2u[n2]
u[n2]={1,n20,n<2
Calculate the z-transform of the sequence
X(z)=n=((13)n2u(n2))zn
=n=(13)n2zn (Putting the value of u(n2))
Let n1=n2 in the second term
X(z)=n=(13)n1×zn12
=z2n=(13)n1×zn1
z2n=(13z1)n1
Apply the sum of an infinite sequence
=z2(1113z1)
Since the sequence converges if |z|>13, the radius of convergence is |z|>13

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