The Region of Convergence (ROC) for the signal x(n) = δ (n-5) is the entire z-plane, except at z=∞.

Here's why:

The given signal x(n) = δ (n-5) is a discrete time unit impulse signal delayed by 5 units. The z-transform of a delayed unit impulse δ (n-k) is z^-k. So, the z-transform of the given signal is z^-5.

The ROC of a z-transform is the set of values for which the z-transform converges. For a finite duration discrete signal like a unit impulse, the ROC is the entire z-plane except possibly at z=0 or z=∞.

In this case, since the signal is a right-sided sequence (as the impulse occurs at n=5), the ROC does not include z=∞. Therefore, the ROC of the signal x(n) = δ (n-5) is the entire z-plane, except at z=∞.

Question

The Region of Convergence (ROC) for the signal x(n) = δ (n-5) is the entire z-plane, except at z=∞.

Here's why:

The given signal x(n) = δ (n-5) is a discrete time unit impulse signal delayed by 5 units. The z-transform of a delayed unit impulse δ (n-k) is z^-k. So, the z-transform of the given signal is z^-5.

The ROC of a z-transform is the set of values for which the z-transform converges. For a finite duration discrete signal like a unit impulse, the ROC is the entire z-plane except possibly at z=0 or z=∞.

In this case, since the signal is a right-sided sequence (as the impulse occurs at n=5), the ROC does not include z=∞. Therefore, the ROC of the signal x(n) = δ (n-5) is the entire z-plane, except at z=∞.

Knowee AI · Accepted Answer

The Region of Convergence (ROC) for the signal x(n) = δ (n-5) is the entire z-plane, except at z=∞.

Here's why:

The given signal x(n) = δ (n-5) is a discrete time unit impulse signal delayed by 5 units. The z-transform of a delayed unit impulse δ (n-k) is z^-k. So, the z-transform of the given signal is z^-5.

The ROC of a z-transform is the set of values for which the z-transform converges. For a finite duration discrete signal like a unit impulse, the ROC is the entire z-plane except possibly at z=0 or z=∞.

In this case, since the signal is a right-sided sequence (as the impulse occurs at n=5), the ROC does not include z=∞. Therefore, the ROC of the signal x(n) = δ (n-5) is the entire z-plane, except at z=∞.

ROC of the signal x(n) = δ (n-5) is1 pointz=∞Entire z-plane, except at z=∞Entire z-plane, except at z=0z=0

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ROC of the signal x(n) = δ (n-5) is

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