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ANALYSIS OF COMPLEX FILTERS WITH THE USE OF TRANSITION CHARACTERISTICS

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A method for studying complex filter with the use of the transition characteristics is developed. Presentation of input signal as a sum of step functions shifted relative to each other leads to a new form of complex superposition integral allowing to determine the filter output signal for a given complex-valued input and a known complex transition characteristic. Application of complex filters is shown to enable variation of their frequency settings without a change in shape of the amplitude and phase-frequency characteristics. The concepts of complex delta function and complex transition characteristics are introduced; the concepts are employed in the study of dynamic properties of the filters and transmission of various signals. In contrast to the known method of analysis of linear systems based on the pulse characteristic, the proposed method may be used to synthesize complex discrete filter with dynamic properties coinciding with those of a continuous filter-analog. The developed theoretical principles are confirmed by presented examples.

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