Effect of feedback on the frequency responses of systems containing nonrecursive digital filters

Abstract

Nonrecursive digital filters (NDF) constitute a widely used element in systems for digital signal processing. They are implemented by means of integrated circuits, solid-state devices based on surface acoustic waves (SAW), and devices with charge coupling (see [1]). In a number of cases the necessity arises of controlling the amplitude- frequency response (AFR) of systems, which is usually carried out by changing the coefficients of the NDF; this is difficult from the engineering standpoint, especially for solid-state implementations. Therefore, methods which allow the AFR of a system to be varied without altering the internal structure of the NDF are of interest. Such a result may be achieved by commutation of filters having known AFR (see [2]), but under these conditions hardware expenditures increase. The control of the system passband by means of quadrature processing of the input signal may be effectively accomplished only for NDF which are close to ideal differentiators or Hilbert converters and requires the presence of two such filters (see [3]). In radioelectronics, extensive use is made of feedback (FB) in order to control AFR. The use of FB converts an NDF into a recursive filter, but the AFR of such a structure has not been considered in the theory of recursive filters.