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Where does the gibbs phenomenon occur?

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in Signals and Systems by (1.2m points)
Where does the gibbs phenomenon occur?

(a) Gibbs phenomenon occurs near points of discontinuity

(b) Gibbs phenomenon occurs only near points of discontinuity

(c) Gibbs phenomenon occurs only ahead of points of discontinuity

(d) Gibbs phenomenon does not occur near points of discontinuity

I had been asked this question during a job interview.

The origin of the question is Gibb’s Phenomena, Convergence of Fourier Series topic in division Fourier Series of Signals and Systems

1 Answer

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The correct answer is (b) Gibbs phenomenon occurs only near points of discontinuity

Explanation: The gibbs phenomenon present in a signal x(t), only when there is a jump discontinuity in the signal. Gibbs phenomenon occurs only near points of discontinuity that is approximated by a fourier series in which only a finite number of terms are kept constant.

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