Open AccessEstimation of the Absolute Error of the Normalized Frequency of a Sinusoidal Signal During Its Discretization In Time
Author(s) -
В. Ігнаткін,
O. G. Saragtov
Publication year - 2020
Publication title -
metrologìâ ta priladi
Language(s) - English
Resource type - Journals
eISSN - 2663-9564
pISSN - 2307-2180
DOI - 10.33955/2307-2180(6)2019.40-44
Subject(s) - mathematics , interpolation (computer graphics) , mathematical analysis , statistics , spectral density estimation , sine wave , signal (programming language) , fast fourier transform , discretization , approximation error , fourier transform , algorithm , physics , telecommunications , computer science , frame (networking) , voltage , quantum mechanics , programming language
The influence of systematic errors due to the influence of the imaginary part in the spectrum of a sinusoidal signal on the zinc of its normalized frequency using the method of discrete Fourier transform (DFT) with interpolation with a maximum decay rate of the side lobes is analyzed.
Results are given for estimating the absolute error of the normalized frequency and conditions are found for the minimum integer number of sine wave cycles, taking into account which guarantees the value of this error is less than a certain given level.
The reliability of the results received is confirmed by computer simulation.
In practice, the frequencies of the sinusoidal signal and the sample do not satisfy the coherent sample ratio, which results in the well-known effect of erosion or «leakage» of the spectrum components. This means that the energy of the spectral lines propagates along the frequency axis. To reduce the errors associated with blurring the spectrum, leaching is used.
The best results were achieved in the case of «age» with a maximum rate of decline of the side lobes (SSBL), which include the «windows» of Rife-Vincent’s class 1 and the use of the corresponding ratios.