Even though the Shannon wavelet is a prototype of wavelets, it lacks condition on decay which most wavelets are assumed to have. By providing a sufficient condition to compute the size of Gibbs phenomenon for the Shannon wavelet series, we can see the overshoot is propotional to the jump at discontinuity. By comparing it with that of the Fourier series, we also see that these two have exactly the same Gibbs constant.
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Shim, H. On Gibbs constant for the Shannon wavelet expansion. Korean J. Comp. & Appl. Math. 4, 469–473 (1997). https://doi.org/10.1007/BF03014493
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Key words and phrases
- Shannon wavelet
- Gibbs phenomenon
- Gibbs constant