Optimization of the FIR filter structure in finite residue field algebra

Abstract

This paper introduces a method for optimizing non-recursive filtering algorithms. A mathematical model of a non-recursive digital filter is proposed and a performance estimation is given. A method for optimizing the structural implementation of the modular digital filter is described. The essence of the optimization is that by using the property of the residue ring and the properties of the symmetric impulse response of the filter, it is possible to obtain a filter having almost a half the length of the impulse response compared to the traditional modular filter. A difference equation is given by calculating the output sample of modules p1 … pn in the modified modular digital filter. The performance of the modular filters was compared with the performance of positional non-recursive filters implemented on a digital signal processor. An example of the estimation of the hardware costs is shown to be required for implementing a modular digital filter with a modified structure. This paper substantiates the expediency of applying the natural redundancy of finite field algebra codes on the example of the possibility to reduce hardware costs by a factor of two. It is demonstrated that the accuracy of data processing in the modular digital filter is higher than the accuracy achieved with the implementation of filters on digital processors. The accuracy advantage of the proposed approach is shown experimentally by the construction of the frequency response of the non-recursive low-pass filters.