Efficient Method for Fast Discrete Fourier Transform of Finite Signals with High Frequency Resolution

The paper is devoted to the development of methods and algorithms for fast Fourier transforms of discrete finite signals. For this purpose, a generalization of classical discrete Fourier transforms has been carried out by introducing parameters in the time and frequency domains into their bases. The paper is a continuation of the authors' research in the field of spectral analysis. We emphasize the role of work in such areas as vibroacoustic functional diagnostics of objects in mechanical engineering, medicine, sonar, as well as in the detection and classification of surface and underwater vessels. A theoretical and experimental justification is given for the effectiveness and efficiency of the proposed method and algorithm for fast Fourier transform of discrete finite signals with high frequency resolution.

I. Introduction

A researcher faces an important and urgent problem of identifying hidden periodicities in many subject areas, when solving various classes of both theoretical and applied problems [1]. The development of various information technologies in signal processing plays a decisive role in solving the problems of this issue. Particularly noteworthy is the contribution to the development of theory and methods, algorithms and tools for digital (computer) signal processing (DSP) of intensively evolving discrete Fourier transforms [2]–[5].