Wavelet filtering in the scale domain

Gerald Kaiser

doi:10.1117/12.255234

23 October 1996 Wavelet filtering in the scale domain

Gerald Kaiser

Proceedings Volume 2825, Wavelet Applications in Signal and Image Processing IV; (1996) https://doi.org/10.1117/12.255234
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

For a given basic wavelet (psi) (t), two distinct correspondences (called C1 and C2) are established between frequency filters, defined in the frequency domain through multiplication by a transfer function W(f), and scale filters, defined in the wavelet domain through multiplication by a scale transfer function w((sigma) ). W(f) is obtained by performing a scaling convolution of w((sigma) ) with (psi) (f)* (for C1) or its spectral energy density (psi) (f) ² (for C2). For a large class of transfer functions W(f), this relation can be solved for w((sigma) ) by applying the Mellin transform. We call such frequency filters and their associated time-domain convolution operators C1- or C2-admissible with respect to (psi) . In particular, the identity operator (W(f) equalsV 1) is C2-admissible if and only if the wavelet (psi) is admissible in the conventional sense. The implementation of the correspondence C1 is computationally simpler than C2, but C2 can be generalized to time-dependent filters. Applications are proposed to the analysis of atmospheric turbulence data and wideband Doppler filtering.

Citation Download Citation

Gerald Kaiser "Wavelet filtering in the scale domain", Proc. SPIE 2825, Wavelet Applications in Signal and Image Processing IV, (23 October 1996); https://doi.org/10.1117/12.255234

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