Hyperbolic wavelet function

Khoa Nguyen Le; Kishor P. Dabke; G. K. Egan

doi:10.1117/12.421221

26 March 2001 Hyperbolic wavelet function

Khoa Nguyen Le, Kishor P. Dabke, G. K. Egan

Proceedings Volume 4391, Wavelet Applications VIII; (2001) https://doi.org/10.1117/12.421221
Event: Aerospace/Defense Sensing, Simulation, and Controls, 2001, Orlando, FL, United States

Abstract

A survey of known wavelet groups is listed and properties of the symmetrical first-order hyperbolic wavelet function are studied. This new wavelet is the negative second derivative function of the hyperbolic kernel function, [sech((beta) (theta) )]ⁿ where n equals 1, 3, 5,... and n equals 1 corresponds to the first-order hyperbolic kernel, which was recently proposed by the authors as a useful kernel for studying time-frequency power spectrum. Members of the 'crude' wavelet group, which includes the hyperbolic, Mexican hat (Choi-Williams) and Morlet wavelets, are compared in terms of band-peak frequency, aliasing effects, scale limit, scale resolution and the total number of computed scales. The hyperbolic wavelet appears to have the finest scale resolution for well-chosen values of (beta)

Citation Download Citation

Khoa Nguyen Le, Kishor P. Dabke, and G. K. Egan "Hyperbolic wavelet function", Proc. SPIE 4391, Wavelet Applications VIII, (26 March 2001); https://doi.org/10.1117/12.421221

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