Algorithms for Direct and Inverse Parametric Fast Fourier Transform

Abstract

Русский Main page New issue Archive of articles Editorial board For the authors Publishing house ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES". No. 1. Vol. 28. 2022 DOI: 10.17587/it.28.9-19 O. V. Ponomareva, Dr. Sc., Tech., Professor, A. V. Ponomarev, PhD, Econ., Associate Professor, Kalashnikov Izhevsk State Technical University, Izhevsk, 426069, Russian Federation, N. V. Smirnova, PhD, Tech., Associate Professor, Sevastopol State University, Sevastopol, 299053, Russian Federation Algorithms for Direct and Inverse Parametric Fast Fourier Transform Classical Fourier processing of finite information discrete signals (FID signals) is the most important method of digital analysis, modeling, optimization, improvement of control and decision making. The theoretical basis of classical Fourier processing of FID signals is the discrete Fourier transform (DFT). The practical basis of classical Fourier processing of FID signals is the Fast Fourier Transform (FFT). The practice of using classical Fourier processing of FID signals, having confirmed its effectiveness, revealed a number of negative effects inherent in this type of digital signal processing (DSP). The aliasing effect, scalloping effect, picket fence effect, significantly affect the effectiveness of analysis, modeling, optimization, improvement of management and decision making. To increase the efficiency of Fourier processing of FID signals, the authors of the paper have developed a generalization of DFT in the form of a parametric DFT (DFT-P). Since the direct application of parametric Fourier processing of FID signals (as well as the use of classical Fourier processing of FID signals) requires complex multiplications, fast procedures are required for the practical implementation of this type of FID signals. Purpose of the research is to develop algorithms for the fast parametric discrete Fourier transform (FFT-P). The work developed fast procedures for the implementation of DFT-P by time decimation. Parametric FFT-P with substitution (in place) and without substitution (no place) are proposed. The estimation of the efficiency of the FFT-P algorithms is given. The practical significance of the work is in the fact that developing algorithms for the parametric fast Fourier transform can reduce the computational costs of performing parametric discrete transformations by three or more orders of magnitude.