Wavelet transformations in signal detection

It is pointed out that in the analysis of transient signals such as those encounters in speech, or in certain kinds of image processing, standard Fourier analysis is often non satisfactory because the basic functions of the Fourier analysis (sines, cosines, complex exponentials) extend over infinite time, whereas the signals to be analyzed are short-time transients. Reference is made to a method for dealing with transient signals which has recently appeared in the literature. The basis functions are referred to as wavelets, and they utilize time compression (or dilation) rather than a variation of frequency of the modulated sinusoid. Hence, all the wavelets have the same number of cycles. The analyzing wavelets must satisfy a few simple conditions, but are not otherwise specified. There is a wide latitude in the choice of these functions and they can be tailored to specific applications. The wavelets are founded on rigorous mathematical theory, and the expansions are robust. They are applied to detect ventricular delayed potentials (VLP) in the electrocardiogram