GATE EE 2014 Set 3 — Question 43
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Signals & Systems → Fourier Analysis & Sampling → Frequency Response
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Question
A continuous-time LTI system with system function has the following pole-zero plot. For this system, which of the alternatives is TRUE?
Correct answer
(D) H(ω) = constant; -∞ < ω < ∞
Solution
The provided pole-zero plot shows a set of poles in the left-half of the -plane and a corresponding set of zeros in the right-half of the -plane. Specifically, for every pole located at , there is a corresponding zero located at . This mirror-image symmetry about the imaginary () axis is the defining characteristic of an all-pass filter. For an all-pass filter, the magnitude of the frequency response remains constant for all frequencies. This can be seen by considering a single pole-zero pair: . On the imaginary axis ():Since the magnitude is constant for each pair, the overall magnitude response of the system is constant for all . Therefore, option (D) is correct.
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