GATE EE 2015 Set 1 — Question 63
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Signals & Systems → Laplace & Z Transforms → Transfer Function & Pole-Zero
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Question
The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at . List all the poles and zeroes.
Correct answer
(D) Poles at (2 ± j3), zeroes at (-2 ± j3).
Solution
A system with a perfectly flat magnitude response of unity is an all-pass filter. For a real system, the transfer function must have poles and zeros in complex conjugate pairs. For an all-pass filter, if there is a pole at , there must be a zero at .
Given a pole at :
Given a pole at :
1.Since the system is real, there must be a conjugate pole at .
2.The corresponding zeros for an all-pass filter are:
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