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GATE 2026 AE – Question 12

Engineering Mathematics · Special topics: Fourier series, complex numbers, analytic functions and Cauchy-Riemann equations · 1 mark · Multiple choice

The Fourier series representation of a square wave is shown in the figure below. The fluctuations seen near x = $\pm 1$ are named after which one of the following scientists?

A truncated Fourier series of a square wave between -1.5 and 1.5, with overshoots and ripples near x = -1 and x = 1.
  1. Cauchy
  2. Fourier
  3. Gibbs
  4. Laplace

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Correct answer: (C) Gibbs

Explanation

The overshoot and ripples that a truncated Fourier series shows near a jump discontinuity are the Gibbs phenomenon.