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.
Highlights
discrete Fourier transform (DFT) or its fast variant FFT is a widely used instrument for spectral analysis in many branches
The presented model of the DFT spectrum of the incoherent sinusoidal signal shows aliasing from all partial spectra from the −F0 and +F0 sub-bands as the cause of leakage deviations from sinc
In the case of a real valued sinusoidal signal, the essential influence of ratio F0/FS is explained. This aliasing and the phase shift of the signal φ0 together with the phase jump by π between the two parts of the basic spectrum cause an unpleasant sensitivity of the spectrum module to the phase of the analyzed signal. This effect appears as a practical problem, for example when estimating the frequency of a dominant signal in the DFT analysis for many measurement tasks
Summary
DFT or its fast variant FFT is a widely used instrument for spectral analysis in many branches. For a common incoherent signal this condition cannot usually be fulfilled In this case, the result of DFT spectral analysis is not accurate. The attempt to estimate as accurately as possible the frequency of the harmonic component of the signal under testing is a typical example of this problem. This is dealt with in many publications, such as [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]
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