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 Num. Meth. Prog., 2019, Volume 20, Issue 3, Pages 270–282 (Mi vmp965)

Spectral analysis of discrete signals with high frequency resolution

O. V. Osipov

Belgorod Shukhov State Technological University

Abstract: Algorithms of direct and inverse fast Fourier transforms are discussed. These algorithms allow one to process discrete signals with high frequency resolution, including with a small number of frequency samples, and to receive the frequency responses with a set length of frequencies greater than the length of the original discrete signal. The time complexity of the developed algorithms for the direct and inverse FFT is $O(N \cdot R \cdot \log_2 N)$, where $R$ is the frequency resolution of the spectral characteristic (the ratio of the length of a set of frequencies to the length N of a set of signal samples). The developed methods allow one to increase the resolution of systems of digital signal processing and can be implemented in electronic devices and in software for spectral analysis.

Keywords: fast Fourier transform (FFT), spectral analysis, high resolution, frequency shift, time-frequency resolution, digital signal processing (DSP) problems, numerical iterative FFT algorithm, forward FFT, inverse FFT, amplitude-frequency characteristic.

DOI: https://doi.org/10.26089/NumMet.v20r324

Full text: PDF file (655 kB)

UDC: 519.677

Citation: O. V. Osipov, “Spectral analysis of discrete signals with high frequency resolution”, Num. Meth. Prog., 20:3 (2019), 270–282

Citation in format AMSBIB
\Bibitem{Osi19} \by O.~V.~Osipov \paper Spectral analysis of discrete signals with high frequency resolution \jour Num. Meth. Prog. \yr 2019 \vol 20 \issue 3 \pages 270--282 \mathnet{http://mi.mathnet.ru/vmp965} \crossref{https://doi.org/10.26089/NumMet.v20r324} \elib{https://elibrary.ru/item.asp?id=39540781}