Mathematical Model of Multistage Fourier Transform Based on Deductive Processing of Digital Signals

Abstract

Issues related to the mathematical modeling of the discrete Fourier transform of digital signals are considered. This study is motivated by the demand for research into additional optimization possibilities for digital signal processing algorithms. The purpose of the study is to reduce the computational complexity of the multistage Fourier transform. The study is based on difference digital filtering and the multistage Fourier transform. The results demonstrate and confirm the possibility of reducing the computational complexity of this transform based on deductive processing of digital signals. The concept of deductive signal processing is defined and described. We propose reducing the error of the multistage Fourier transform of digital signals by increasing their sampling frequency while decreasing the computational complexity of recurrent numerical algorithms for this transform by reducing the bit depth of difference samples of signals and difference samples of the impulse response of difference digital filtering. The practical significance of the research results consists in determining an additional reserve for improving the accuracy of the discrete Fourier transform of digital signals by applying their multistage Fourier transform based on deductive signal processing algorithms with an increase in the sampling frequency.