A discrete-time all-pass system has two of its poles at 0.25∠0° and 2∠30°. Which one of the following statements about the system is TRUE?

It has two more poles at 0.5∠30° and 4∠0°.
It is stable only when the impulse response is two-sided.
It has constant phase response over all frequencies.
It has constant phase response over the entire z-plane.

Correct answer: It is stable only when the impulse response is two-sided.

Solution

The correct option is true because a discrete-time all-pass system can be stable only if its impulse response is two-sided, ensuring that the system's output remains bounded for all inputs, particularly in the case of poles located outside the unit circle.

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