A NEW METHOD OF SIGNAL DESCRIPTION AND ITS APPLICATIONS TO SIGNAL-PROCESSING

Signal processing is performed by using a mathematical description of signals (processes). The description is realized by the signal itself or a mathematical image of it. The most often used images are the Laplace-Fourier transforms, the images in the forms of series and polynomials, Poincare's phase trajectories and so on. We propose to use the image in the form of a suitable generating differential equation, i.e., the signal is considered to be one of the partial solutions of the chosen equation. For this approach it is necessary to represent differential equations in new concise nonlinear forms and to introduce some new notions and a suitable mathematical apparatus. The proposed method of signal description has some advantages and gives new possibilities for signal processing. We present in this paper the theoretical basis and short descriptions of some applications: the measurement of signal parameters, amplitude and frequency detection, data compression, rejection and filtering, malfunction diagnosis, identification and extrapolation. The properties of the images in the form of generating differential equations are called 'structural properties', whereas the properties of the signal itself or its spectrum are called 'contour properties'.