The Signal Processing (SP) domain is a well delimited branch with strong connexions in both Applied Mathematics and Electronics. The present viewpoint is rather mathematics-Oriented than electronics-Oriented. After the main SP problem statement - in a mathematical manner-a new approach of this problem is made (from a software or engineering viewpoint ). Problem-solving by classical harmonic analysis - based on Fourier's ideas- resulted in a certain type of algorithms called "Fast Fourier Transform (FFT). This class of algorithms is used for a large set of usual signals and it is very productive. However, this tool seems to be inadequate for several signals, including non-stationary signals. Signals of a certain type, as those associated with seismology, cardiography, speech processing or image processing, are improper for frequency modelling based on the Fourier's series because of theirnot few high instantaneous frequencies. The number of computations which these signals are subject to in the Fourier analysis is large enough and the slow convergence of this series makes the results be not so precise as they usually are. The proposed solution for error recovery is that of the "wavelets" ("ondelettes" (Fr), "undine" (Rom)) - a new family of functions by means of which the signals can be represented more exactly. It is not the differential equations or the differences that do this representation more exactly, but the "Biscalar Dilation Equations" (BDE) or "Two Scale Difference Equations", as in the following example:
harmonic analysis, Fast Fourier Transform, non-stationary signals, instantaneous frequency, wavelets, Biscalar Dilation Equations, scaling function, wavelet-mother, finite energy signals.
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