8. (10 pts.) Suppose $x[n]$ has Z transform $\frac{1 - z^{-3}}{1 + z^{-4}}$ with ROC $|z| > 1$. What is $y[n] = x[n] + x[n - 4]$? Hint: Calculate Z transforms.
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The Z-transform of 1[n] is given by: Z{1[n]} = ∑(1[n] * z^(-n)) Since 1[n] is equal to 1 for all n >= 0, the sum becomes: Z{1[n]} = ∑(1 * z^(-n)) = ∑(z^(-n)) Now, let's find the Z-transform of 1[n-4]. The Z-transform of 1[n-4] is given by: Z{1[n-4]} = Show more…
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