Spline harmonic analysis and wavelets

Valery A. Zheludev

doi:10.1117/12.188785

11 October 1994 Spline harmonic analysis and wavelets

Valery A. Zheludev

Proceedings Volume 2303, Wavelet Applications in Signal and Image Processing II; (1994) https://doi.org/10.1117/12.188785
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

We present here a new approach to wavelet transforms based on techniques of SHA. It is a version of HA which operates in spline spaces. SHA enjoys various applications but here we outline a recent application of SHA techniques, namely, accomplishing on the base of periodic splines the wavelet transforms of periodic signals as well as the remarkable informative digital representation of the signals. SHA approach to wavelets yields a tool just as for the constructing a diversity of spline wavelet bases, so for a fast implementation of a decomposition of a function into a fitting wavelet representation and its reconstruction. This approach allows to construct WP bases for refined frequency resolution of signals.

Citation Download Citation

Valery A. Zheludev "Spline harmonic analysis and wavelets", Proc. SPIE 2303, Wavelet Applications in Signal and Image Processing II, (11 October 1994); https://doi.org/10.1117/12.188785

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