Fast Discrete Fourier Transform of Complex Finite Signals with a Number of Samples Not Equal to a Power of Two with Limited Computing Function

The article is devoted to the development of the theoryfor digital processing of finite discrete signals, the method and algorithm for the fast discrete Fourier transform of complex finite signals with a number of samples not equal to a power of two, with limited computing function. The development of the method and algorithm is implemented on the internal structure analysis of the discrete Fourier transform basis - a system of discrete exponential functions. Structure analysis of the discrete Fourier transform basis made it possible to eliminate a significant drawback of fast Fourier transform algorithms: limited durations of finite discrete signals that allow fast procedure application. The work is a continuation of the authors' research in the field of digital spectral and vector analysis; in particular, it considers a new basis for the discrete Fourier transform, which provides for a transition to the frequency domain with a selected parameter of a finite discrete signal in the time domain. The article provides a theoretical and experimental justification for the efficiency and effectiveness of the proposed method and algorithm for the fast Fourier transform of complex finite signals with a number of samples not equal to a power of two, with limited computing function. The effectiveness and efficiency of the proposed method and algorithm of fast discrete Fourier transform are confirmed by the following proven provisions. Firstly, the range of finite discrete signaldurations studied by fast methods is significantly expanded. Secondly, the researcher can realize the advantages of the method and algorithm with limited available computing function. Thirdly, using the proposed method and algorithm of fast discrete Fourier transform, it is possible to calculate the coefficients (bins) of the DFT in the selected spectrum region of a finite discrete complex signal. The role and place of the work seems to be important and relevant in many subject areas of science and technology, such as, for example, vibroacoustic functional diagnostics of objects in mechanical engineering and medicine, as well as in the detection and classification of objects.