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GATE 2014 EE (EE1) – Question 20

Signals and Systems · Fourier series representation of continuous and discrete time periodic signals, Sampling theorem · 1 mark · Multiple choice

Which statement about a periodic square wave is true?

  1. Fourier-series coefficients do not exist.
  2. Coefficients exist but reconstruction converges at no point.
  3. Coefficients exist and reconstruction converges at most points.
  4. Coefficients exist and reconstruction converges at every point.

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Correct answer: (C) Coefficients exist and reconstruction converges at most points.

Explanation

A square wave satisfies the usual Dirichlet conditions, so its Fourier coefficients exist. The series converges to the waveform at continuity points and to the midpoint of the left and right limits at jumps. Thus it reconstructs the original square-wave values at **most points,C**. The series itself also converges at jumps, but need not equal the assigned discontinuity value there.