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GATE 2014 EE (EE2) – Question 45

Signals and Systems · Fourier series representation of continuous and discrete time periodic signals, Sampling theorem · 2 marks · Multiple choice

A 10 kHz even-symmetric square wave passes through a bandpass filter centered at 30 kHz with 3 dB passband 6 kHz. Output is ______.

  1. a highly attenuated 10 kHz square wave
  2. nearly zero
  3. a nearly perfect 30 kHz cosine wave
  4. a nearly perfect 30 kHz sine wave

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Show answer and explanation

Correct answer: (C) a nearly perfect 30 kHz cosine wave

Explanation

An even square wave has cosine harmonics at odd multiples of its10kHzfundamental. The27–33kHzpassband isolates its third harmonic at30kHz while rejecting the10and50kHzcomponents. The resulting waveform is approximately a **30kHzcosine,C**,up to gain and any filter phase convention.