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

Abstract

The article describes a new model for the solution of the instability problem of discrete Fourier transform (DFT) spectra leakage for the incoherent real sinusoidal signal for solving the most accurate estimation of its frequency. This paper shows this phenomenon by a new form of DFT spectrum expression. It consists mainly of the spectrum of the rectangular signal in the form of the sinc function, modulated to the frequency of the tested signal in baseband. To do this, analogous spectra from other neighboring bands formed by the sampling effect are added as aliasing. The analysis shows some ways to minimize or correct it. The paper shows a simpler and substantially lesser effect of aliasing in the DFT spectrum for a complex valued sinusoidal signal.