Application of Parametric DFT in Cepstral Method for Scales Bases Identification

Applications of cepstral analysis of energy spectra of signals (ESS), measured by the method of discrete Fourier transform (DFT) are briefly discussed. The problems of cepstral analysis of ESS, the advantages and disadvantages of this type of analysis are investigated. A comparison of the results of revealing the reverse, gear and cyclic frequencies of the gearbox with the digital cepstral method and other digital methods for identifying the bases of harmonic series is given. Based on studies of the problems of digital cepstral processing of ESS, analysis of advantages and disadvantages of this method of identifying the bases of scale (tone series), it is proposed, in order to increase the efficiency and effectiveness of cepstral analysis, that the energy spectra are not measured by the DFT method, but by the parametric DFT (DFT-P) method. The analytical properties of DFT-P are briefly considered. The existence of fast DFT-P (FFT-P) algorithms is proved. An experimental verification of the theoretical results obtained in the work was carried out by the method of numerical simulation.