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Features of discrete Fourier transform


D.B. Rozhdestvensky

Discrete Fourier transform (DFT) is intended for the analysis and processing of a digital signal the same as continuous transformation Fourier for analogue signal. However, adequacy of results of transformations analogue and discrete are various. Such distinction speaks that DFT is approximation of continuous Fourier transform, thus DFT possesses a number of the features which ignorance leads unexpected for interested persons to apply DFT to sad results. On purpose to acquaint the reader with features DFT, the conclusion of basic formulas of transformation is spent and the analysis of features of a spectrum of trial function by means of DFT is carried out. The received spectra of the transformed signal allow to define undesirable by-effects which accompany transformation. These features DFT are connected with digitization of investigated process and presence of ruptures in time area. These features concern: 1. The effect of occurrence of false components  is caused by presence as a part of initial process of the frequency components exceeding Nyquist frequency; 2. The effect leakage spectral components - is connected with the task of initial process in the form of final number of readout; 3. The effect of «paling»  is caused by artificial reception of formation of periodic process of final initial sample; 4. The effect of «window»  is connected with digitization and limitation of a spectral interval of private spectrum DFT. The analysis, the found features allows to plan ways of their suppression by measures on ordering of spectrum DFT.
June 24, 2020
May 29, 2020

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