Development of a method for synthesis the FIR filters with a cascade structure based on genetic algorithm

Abstract

The object of research is the process of digital signal processing. The subject of research is methods of synthesis of digital filters with a finite impulse response based on a genetic algorithm. Digital filtering is one of the tasks of digital signal processing. FIR filters are always stable and provide a constant group delay. There are various methods for synthesizing digital filters, but they are all aimed at synthesizing filters with a direct structure. One of the most problematic areas of a digital filter with a direct structure in digital processing is the high sensitivity of the filter characteristics to inaccuracies in setting the filter coefficients. Genetic algorithm-based filter synthesis methods use an ideal filter as the approximated filter. This approach has a number of disadvantages: it complicates the search for an optimal solution; computation time increases. The study used random search method, which is the basis of genetic algorithm (used for solving optimization problems); theory of digital filtering in filter analysis; numerical methods for modeling in a Python program. Prepared synthesis method FIR filter with the cascade structure, which is less sensitive to the effect of finite bit width. Computation time was reduced. This is due to the fact that the proposed method searches for the most suitable filter coefficients based on a genetic algorithm and has a number of features, in particular, it is proposed to use a piecewise-linear function as an approximated amplitude-frequency response. This makes it possible to reduce the number of populations of the genetic algorithm when searching for a solution. The synthesis of an FIR filter with a cascade structure based on a genetic algorithm showed that for a 24-order filter it took about 30–40 generations to get the filter parameters close to the optimal values. In comparison with classical methods of filter synthesis, the following advantages are provided: calculations of the coefficients of a filter with a cascade structure directly, the possibility of optimizing coefficients with limited bit depth.