The Gibbs' phenomenon from a signal processing point of view |
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Authors: | Temple H Fay Klaus Gunther Schulz |
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Institution: | College of Business Administration, Pennsylvania State University , University Park, Pennsylvania 16802, U.S.A. |
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Abstract: | Recently, Fay and Kloppers gave two proofs to show that the well-known Gibbs' phenomenon for Fourier series at a jump discontinuity depends only on the size of the jump and is a multiple of the integral 1/π ∫0 π (sin x / x) dx. We give another proof, based upon low-pass filtering of the Fourier transform, that uses the observation that a truncated Fourier series for a function ? (x) is ‘very nearly’ equal to the convolution integral 1/π ∫ -∞ +∞ ? (x - t)(sin nt / t) dt. |
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Keywords: | group work undergraduate mathematics interactive groups student voice |
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