Ordering the cascades of a nonrecursive digital filter in a sequential form of implementation using a genetic algorithm

Abstract

The paper proposes an algorithm for minimizing the output error of a FIR filter caused by quantization of the results of multiplication operations by optimizing the arrangement of filter cascades. Digital filters are widely used in various fields of science and technology. FIR filters have some advantages over other types of filters. To implement FIR filters, a sequential form is often used, which provides smaller deviations of the zeros of the transfer function. The quantization effect leads to an increase in the output error of the filter, which will depend on the arrangement of the cascades. Choosing the optimal order of the cascades is a difficult challenge, as it belongs to the class of NP-complete problems. The noise model of the sequential form of the FIR filter implementation was chosen. In accordance with the noise model, an algorithm for ordering the filter cascades based on a genetic algorithm was developed. To solve this problem, a genetic algorithm was used because it allows us to obtain a quasi-optimal solution in less time compared to algorithms that allow us to obtain exact solutions. In addition, the use of a genetic algorithm has an advantage over other heuristic methods. In this paper, a fitness function is proposed to minimize the error in the ordering of FIR filter cascades. A detailed analysis of the methods of selection, crossing, and mutation is carried out, and the methods that are most suitable for solving the problem are selected. The hyperparameters of the genetic algorithm were adjusted to obtain greater efficiency. A number of experiments were conducted to test the algorithm. Several FIR filters of different types and orders were synthesized.As a result of experimental studies, it was found that the developed algorithm really has high performance compared to algorithms that allow obtaining exact solutions. The proposed algorithm is more effective in ordering a large number of cascades, as it significantly reduces the time spent on finding a solution to the problem.

Keywords

• ordering of fir filter cascades
• sequential form of fir filter implementation
• fir filter design
• genetic algorithm