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
In the pole-zero plot, every pole has a zero at its mirror image about the axis: the pole near on the left is paired with the zero near on the right, the pole at the right near with the zero at the left near , and similarly for the lower half. So for every pole at there is a zero at .For one such pair evaluated on the axis:because the zero and the pole are at the same distance from every point on the imaginary axis.Multiplying over all pairs, equals a constant (the gain factor) for all : the system is all-pass. Hence has no maxima and is neither larger nor smaller at , so (A), (B) and (C) are false.Answer: (D)
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