Design of wavelets adapted to signals and application

This paper addresses the design of wavelets adapted to the processed signals and the considered application. Our approach consists of parameterizing a mother wavelet, and defining a quality criterion for the optimization of the parameters, according to the context. The first parameterization, leading to orthogonal wavelets, considers the coefficients of the scaling filter as the parameters. A second parameterization, leading to semiorthogonal wavelets, consists of convolving an existing wavelet (or scaling function) by a given sequence. In this paper, we explore these two methods and apply them to the supervised classification of signals made of waveform trains.