Hyperbolic wavelet family

This article reports early results on digital implementation of first- and nth-order hyperbolic wavelets whose important parameters are explicitly expressed and numerically estimated. The first-order hyperbolic, Morlet and Choi-Williams wavelets are compared in detail by numerically calculating their band-peak frequencies, minimum numbers of sampling points, scale resolutions, and maximum numbers of scales. One of the main aims is to show that there exists a strong link among time-frequency kernels and wavelets. This relationship helps to expand and link time-frequency and wavelet approaches to signal analysis. One example of using the hyperbolic wavelet for speech recognition is also given.