On Gibbs constant for the Shannon wavelet expansion
Copyright policy )On Gibbs constant for the Shannon wavelet expansion
Summary: 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 proportional 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.
- Sun Moon University Korea (Republic of)
Signal theory (characterization, reconstruction, filtering, etc.), Spline approximation, Shannon wavelet series, Gibbs phenomenon, Nontrigonometric harmonic analysis involving wavelets and other special systems, Fourier series, Approximation by other special function classes, Gibbs constant
Signal theory (characterization, reconstruction, filtering, etc.), Spline approximation, Shannon wavelet series, Gibbs phenomenon, Nontrigonometric harmonic analysis involving wavelets and other special systems, Fourier series, Approximation by other special function classes, Gibbs constant
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