Using the wavelet transform for the detection of magnetic underwater transient signals

In the analysis of transient signals such as those encountered in underwater observations (sonar, magnetic signals) standard Fourier analysis is often not satisfactory. This is because the basis functions of Fourier analysis (sines cosines, complex exponentials) extend over infinite time whereas the signals to be analysed are short-time transients. A new method of dealing with transient signals has recently appeared in the literature. The basis functions are referred to as wavelets, and they employ 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 therefore a wide latitude in the choice of these functions and they can be tailored to specific applications. The wavelets are well founded on rigorous mathematical theory, and the expansions are robust. We have applied them to detect magnetic underwater signals