GATE EE 2014 Set 2 — Question 45
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Signals & Systems → Fourier Analysis & Sampling → Fourier Series (CT & DT)
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Question
A 10 kHz even-symmetric square wave is passed through a bandpass filter with centre frequency at 30 kHz and 3 dB passband of 6 kHz. The filter output is
Correct answer
(C) a nearly perfect cosine wave at 30 kHz.
Solution
A square wave of frequency kHz contains odd harmonics: kHz.
An even-symmetric square wave has a Fourier series consisting only of cosine terms.
The bandpass filter is centered at 30 kHz with a bandwidth of 6 kHz, meaning its passband is from 27 kHz to 33 kHz.
Only the 3rd harmonic (30 kHz) falls within this passband.
Since the original signal was even-symmetric (cosine terms), the output will be a nearly perfect cosine wave at 30 kHz.
An even-symmetric square wave has a Fourier series consisting only of cosine terms.
The bandpass filter is centered at 30 kHz with a bandwidth of 6 kHz, meaning its passband is from 27 kHz to 33 kHz.
Only the 3rd harmonic (30 kHz) falls within this passband.
Since the original signal was even-symmetric (cosine terms), the output will be a nearly perfect cosine wave at 30 kHz.
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