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SYNTHESIS OF DISCRETE FILTERS BY METHODS OF INVARIANT DIFFERENTIAL AND INTEGRAL EQUATIONS

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Design of discrete filters on the base of invariant differential and integral equations of analogous continuous filters is considered. Method of invariant differential equations uses substitution of the differential equations by final differences. When synthesis based on invariant integral equations method is realized, integral equations are substituted by sums. The proposed methods make it possible to synthesize a variety of discrete low-pass and high-pass filters, bandpass and notch filters. With the correct choice of the discreteness period, the frequency properties of the synthesized discrete filters agree well enough with the frequency properties of the continuous analog filters. The choice of the method of synthesis of discrete filters by their continuous analogs is determined by the parameter specified by the continuous filter, e.g. frequency transfer function, pulse or transient response, differential or integral equation.

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