Question

Given the z-transform pair $x[n] \leftrightarrow X(z) = 1/(1 - 2z^{-1})$ with ROC: $|z| < 2$, use the z-transform properties to determine the z-transform of the following sequences: (a) $y[n] = x[n - 3]$, (b) $y[n] = (\frac{1}{3})^n x[n]$, (c) $y[n] = x[n] * x[-n]$, (d) $y[n] = nx[n]$, (e) $y[n] = x[n - 1] + x[n + 2]$, (f) $y[n] = x[n] * x[n - 2]$.

          Given the z-transform pair $x[n] \leftrightarrow X(z) = 1/(1 - 2z^{-1})$ with ROC: $|z| < 2$, use the z-transform properties to determine the z-transform of the following sequences:
(a) $y[n] = x[n - 3]$,
(b) $y[n] = (\frac{1}{3})^n x[n]$,
(c) $y[n] = x[n] * x[-n]$,
(d) $y[n] = nx[n]$,
(e) $y[n] = x[n - 1] + x[n + 2]$,
(f) $y[n] = x[n] * x[n - 2]$.

Given the z-transform pair x[n] ↔ X(z) = 1/(1 - 2z^-1) with ROC: |z| < 2, use the z-transform properties to determine the z-transform of the following sequences:
(a) y[n] = x[n - 3],
(b) y[n] = ((1)/(3))^n x[n],
(c) y[n] = x[n] * x[-n],
(d) y[n] = nx[n],
(e) y[n] = x[n - 1] + x[n + 2],
(f) y[n] = x[n] * x[n - 2].

Added by Matthew L.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

06/23/2023

Step 1

Step 1: Using the property of the z-transform, we have the following: (a) y[n] = x[n-3] corresponds to Y(z) = z^3X(z) (b) y[n] = x[n] corresponds to Y(z) = X(z) (c) y[n] = x[n]*x[-n] corresponds to Y(z) = X(z)X(1/z) (d) y[n] = nx[n] corresponds to Y(z) = Show more…

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Qz5 Given the z-transform pair x[n] > X(z) = 1/(1 - 2z-1) with ROC: |z] < 2, use the z-transform properties to determine the z-transform of the following sequences: (a) y[n]=x[n-3], (b) y[n]= x[n], (c) y[n]=x[n]*x[-n] (d) y[n]=nx[n], (e) y[n]=x[n-1]+x[n+2] (f)y[n]=x[n]*x[n-2].