GATE EE 2017 Set 2 — Question 4
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Signals & Systems → Fourier Analysis & Sampling → Frequency Response
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Question
The pole-zero plots of three discrete-time systems P, Q and R on the -plane are shown below.
Which one of the following is TRUE about the frequency selectivity of these systems?
Correct answer
(B) All three are band-pass filters.
Solution
The frequency response is the transfer function evaluated on the unit circle, , with . The point corresponds to (DC) and corresponds to (the highest discrete-time frequency).System P has zeros at and and a double pole at :The gain is zero at and at and is maximum at , so P is a band-pass filter.System Q has zeros at and poles at :The zeros again force zero gain at and , while the poles, which lie at angle , raise the response near . So Q is a band-pass filter.System R has zeros at and poles at , i.e. on the unit circle:The gain is zero at and and grows without bound at , so R is also a band-pass filter.Every one of the three systems rejects both DC and and passes the band around .Answer: (B) All three are band-pass filters.
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