On the Gibbs Phenomenon for the Shannon Sampling Series in Wavelet Subspaces and a Way to go Around
Commun. Korean Math. Soc. 1998 Vol. 13, No. 1, 181-193
Hong-Tae Shim
Sun Moon University
Abstract : The Shannon sampling series is the prototype of an interpolating series or sampling series. Also the Shannon wavelet is one of the protypes of wavelets. But the coefficients of the Shannon sampling series are different from those of the Shannon wavelet expansions. By giving different function values at the point of discontinuity, we analyze the Gibbs phenomenon for the Shannon sampling series. We also find a way to go around this overshoot effect.
Keywords : scaling function, wavelet, sampling interpolation, the Gibbs phenomenon
MSC numbers : 40A05, 41A30, 41A58
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