SeriousTyro
Member level 2
Given \[x[n]=a^nu[n]\], find the Z-transform and ROC of \[b^{2(n+1)}x[n/5]\].
I know that the Z-transform of \[x[n]=a^nu[n] \leftrightarrow \frac{1}{1-az^{-1} \] and the ROC is \[|z|>|a|\].
I was thinking of setting \[f[n]=b^{2(n+1)}\] and \[g[n]=[n/5]\] then calculate the Z-transform of \[f[n]g[n]\]. I wasn't sure of the property for this as compared to f[n]*g[n] <-> F(z)G(z).
If I were to do that then I was thinking of using the formal definition of the Z-transform for \[b^{2(n+1)}\] and I wouldn't be sure how to calculate that.
The way I'm thinking seems arduous and to be the long route of doing this.
What other way is there to do this?
Not "simple" for me
I know that the Z-transform of \[x[n]=a^nu[n] \leftrightarrow \frac{1}{1-az^{-1} \] and the ROC is \[|z|>|a|\].
I was thinking of setting \[f[n]=b^{2(n+1)}\] and \[g[n]=[n/5]\] then calculate the Z-transform of \[f[n]g[n]\]. I wasn't sure of the property for this as compared to f[n]*g[n] <-> F(z)G(z).
If I were to do that then I was thinking of using the formal definition of the Z-transform for \[b^{2(n+1)}\] and I wouldn't be sure how to calculate that.
The way I'm thinking seems arduous and to be the long route of doing this.
What other way is there to do this?
Not "simple" for me
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