GATE 2020 EC – Question 63
The transfer function of a stable discrete-time LTI system is $H(z)=\dfrac{K(z-\alpha)}{z+0.5}$, where $K$ and $\alpha$ are real numbers. The value of $\alpha$ (rounded off to one decimal place) with $|\alpha|>1$, for which the magnitude response of the system is constant over all frequencies, is ________.
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Correct answer: -2
Explanation
A first-order all-pass system has its zero at the conjugate reciprocal of its pole. The pole is at $-0.5$, so the zero is at $\alpha=\frac{1}{-0.5}=-2$, which has $|\alpha|>1$ as required.