The Causes of Leakage Deviations from Sinc Function in DFT and Ways to Minimize Them

Karel Hájek

doi:10.3849/aimt.01375

Authors

Karel Hájek Department of Electrical Engineering, University of Defence in Brno, Czech Republic

DOI:

https://doi.org/10.3849/aimt.01375

Keywords:

aliasing, DFT, frequency estimation, leakage

Abstract

The article describes new model for a solution to the instability problem of DFT spectra leakage for the incoherent real sinusoidal signal, which is a fundamental problem, for example when solving the most accurate estimation of its frequency in various types of measurement practical tasks. It shows that the main cause of leakage deviations from the sync function is aliasing, which, together with an undefined value of the input signal phase, causes a seemingly random deviation of leakage. This paper shows it by a new form of DFT spectrum expression. It consists mainly of the spectrum of the rectangular signal in the form of the function sinc, modulated to the frequency of the tested signal in baseband. To do this, analogous spectra from other neighbouring bands formed by the sampling effect are added as aliasing. In doing so, the effect of adding or subtracting the phase of the test signal is reflected, depending on the signal parameters. Based on the analysis of these effects, some ways to minimize or correct them are shown. On the other hand, the paper shows a simpler and substantially lesser effect of aliasing in the DFT spectrum for a complex sinusoidal signal.

Author Biography

Karel Hájek, Department of Electrical Engineering, University of Defence in Brno, Czech Republic

Electrical Engineering

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