Features of creation and application of multidimensional adaptive filtering algorithms in time and frequency domains. Part 1. Filtering
Authors: Vinokurov A.D. , Kupriyanov N.A. , Makarenkov V.V. , Ulyanov G.N. , Shatalov A.A. , Shatalova V.A. 
Published: October 2024

Problem statement. In the modern literature devoted to digital signal processing (DSP), the basics of constructing linear non-recursive (transversal with finite impulse response (FIR)) are discussed in detail and recursive (with infinite impulse response (IIR)) filters. Much attention is also paid to the synthesis and analysis of their characteristics, as well as issues of convergence and noise immunity. However, there are few publications on the comparative analysis of the characteristics and complexity of the implementation of numerous varieties of these devices. There is also not enough work devoted to the implementation of adaptive filters, the results of their modeling and practical application. It is noted that adaptive IIR filters have a number of advantages over adaptive FIR filters, one of which is significantly faster convergence, but at the same time they have increased computational complexity and stability. Not enough attention is paid to the issues of adaptation related to their functioning, increasing throughput, speed, accuracy and mass-dimensional characteristics of the systems created on their basis. The available developments on the construction of nonlinear adaptive FIR and IIR filters either do not guarantee the finding of a global optimum, or require preliminary studies to determine the appropriate criteria for the adequacy of the solutions obtained. At the same time, in order to solve the spectrum of actual problems of radar, radio navigation, television and communications in conditions of interference, due to the large number of calculations at various stages, it seems optimal to use adaptive FIR and IIR filters. Goal. Consideration and comparative analysis of the features of the creation and application of algorithms for the operation of a number of multidimensional linear adaptive FIR and IIR filters that perform filtering, smoothing and extrapolation operations, largely determining the characteristics of the systems being developed, as well as the quality of functioning and features of their application. In this part of the work, the main attention is paid to adaptive filtering algorithms implemented in the time and frequency domain. Results. The results of the study of the possibilities of creating adaptive algorithms for optimal signal processing against the background of interference and noise based on adaptive FIR and IIR filters have shown that in order to achieve the maximum throughput of the created information processing systems, it is necessary to create adaptive algorithms that ensure the maximum possible speed, accuracy and reliability of equipment, as well as minimum weight and size characteristics and power consumption of DSP computing systems. It is advisable to use promising methods and computing systems that eliminate the effect of the effect of finite-bit numbers on the accuracy of calculations, providing high performance by achieving the maximum possible parallelism of calculations to achieve the final result of the DSP. Practical significance. The results of the study of the possibilities of using algorithms of multidimensional adaptive filtering for the study of random processes have shown that the basis of the algorithms being created should be based on the methods of developing FIR and IIR filters made in accordance with one of the 6 possible forms of their implementation.