Method and Algorithm for Increasing the Efficiency of Identifying Hidden Periodicities Based on Parametric Discrete Fourier Transforms

The article discusses one of the important and current applications of digital signal processing - digital spectral analysis based on discrete Fourier transforms. The classical discrete Fourier transform of finite signals and its two generalizations are analyzed: parametric discrete Fourier transform of the first type, which has a parameter in the variable responsible for the frequency; parametric discrete Fourier transform of the second type, which has a variable parameter. The theory of statistical measurements of probabilistic parameters of discrete finite random signals is briefly outlined. Applications of classical discrete periodogram analysis in identifying hidden periodicities, unharmonic signals and hidden near-periodicities in mixed signals are considered. A method and algorithm for increasing the efficiency of identifying hidden periodicities based on parametric discrete Fourier transforms is proposed.