GATE EE 2022 Set 1 — Question 11
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Signals & Systems → Fourier Analysis & Sampling → Frequency Response
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Question
The transfer function of a real system, , is given as:where and are positive constants. This system cannot operate as
- A.low pass filter.
- B.high pass filter.
- C.band pass filter.
- D.an integrator.
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Correct answer
(B;D)
Solution
The transfer function is given by where .
1.Low Pass Filter (LPF): At , (finite non-zero value). As , . This characteristic is consistent with a low-pass filter.
2.High Pass Filter (HPF): For a high-pass filter, the gain at DC () must be zero. Since , the system cannot operate as an HPF.
3.Band Pass Filter (BPF): For a band-pass filter, the gain must be zero at both and . Since , it technically cannot be a BPF.
4.Integrator: An ideal integrator has a transfer function of the form , which requires a pole at the origin (). The poles of the given system are the roots of . Since , is not a root, and there is no pole at the origin. Thus, the system cannot operate as an integrator.
According to the official GATE 2022 answer key, both options (B) and (D) are accepted as correct.Continue learning with Success Tracker
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