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We should mention at the outset that the well-known Gibbs phenomenon was first discovered analytically by Henry Wilbraham  in 1848. This was a half century before the famous mathematical physicist Josiah W. Gibbs [2,3] explained its presence in the output of the supposedly extremely accurate harmonic analyzer of Albert A. Michelson and S.W. Stratton in 1898  (see also Michelson , ). As we elaborate on the historical development in Section 2.7, it seems that the results of Wilbraham were almost forgotten for about eighty years until Carslaw  brought it to some light in his short historical note in 1925 (see also Carslaw , ). This raises the legitimate question of whether the phenomenon should be re-named as “Gibbs-Wilbraham Phenomenon?”. Such a question of credit and priority may be still a subject of discussion among the concerned researchers. In the meantime, and for using the name familiar to most, we shall use “The Gibbs Phenomenon”; besides telling the story that recognizes Wilbraham’s effort, which is long overdue. Fortunately, this story is well told by E. Hewitt and R. Hewitt  in 1980.
KeywordsFourier Series Jump Discontinuity Convolution Product Convolution Theorem Gibbs Phenomenon
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