Given the Z-transform 5z-4 X(z) = %3D z²+z-2 What are the 3 possible regions of convergence for this X(z)? a) Using contour integration in the region of convergence that has a shape |z|>R (R depends on X(2), invert X(z) to obtain the time domain signal x(n) b) Using contour integration in the region of convergence that has a shape of a disk, invert X(z) to obtain the time domain signal x(n) c) Using contour integration in the ROC that has a shape |z|

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**Given the Z-transform**

\[ X(z) = \frac{5z - 4}{z^2 + z - 2} \]

**What are the 3 possible regions of convergence for this \(X(z)\)?**

a) Using contour integration in the region of convergence that has a shape \(|z| > R\) (R depends on \(X(z)\)), invert \(X(z)\) to obtain the time domain signal \(x(n)\).

b) Using contour integration in the region of convergence that has a shape of a disk, invert \(X(z)\) to obtain the time domain signal \(x(n)\).

c) Using contour integration in the ROC that has a shape \(|z| < R\), invert \(X(z)\) to obtain the time domain signal \(x(n)\).
Transcribed Image Text:**Given the Z-transform** \[ X(z) = \frac{5z - 4}{z^2 + z - 2} \] **What are the 3 possible regions of convergence for this \(X(z)\)?** a) Using contour integration in the region of convergence that has a shape \(|z| > R\) (R depends on \(X(z)\)), invert \(X(z)\) to obtain the time domain signal \(x(n)\). b) Using contour integration in the region of convergence that has a shape of a disk, invert \(X(z)\) to obtain the time domain signal \(x(n)\). c) Using contour integration in the ROC that has a shape \(|z| < R\), invert \(X(z)\) to obtain the time domain signal \(x(n)\).
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