Hyperbolic wavelet function
Khoa Nguyen Le, Kishor P. Dabke, G.K. Egan · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2001
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)