[amp_mcq option1=”It has two more poles at 0.5<30° and 4<0°" option2="It is stable only when the impulse response is two-sided" option3="It has constant phase response over all frequencies" option4="It has constant phase response over the entire z-plane" correct="option3"]
The correct answer is: C. It has constant phase response over all frequencies.
An all-pass filter is a linear time-invariant (LTI) filter with a constant group delay. This
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means that the phase response of the filter is constant over all frequencies. The poles of an all-pass filter are located on the unit circle in the z-plane.
In this case, the system has two poles at 0.25<0° and 2<30°. These poles are located on the unit circle in the z-plane, which means that the system is an all-pass filter. The phase response of an all-pass filter is constant over all frequencies, so the system has constant phase response over all frequencies.
The other options are incorrect. Option A is incorrect because the system does not have two more poles at 0.5<30° and 4<0°. Option B is incorrect because the system is stable regardless of whether the impulse response is two-sided or one-sided. Option D is incorrect because the system does not have constant phase response over the entire z-plane.