Algorithm of minimizing the metodical error of assessing the signal frequency by the maximum spectrum
DOI:
https://doi.org/10.15587/1729-4061.2014.24725Keywords:
space-time signal, diagnostics, reliability, weighting function, spectrum, complex systemsAbstract
The problem of selecting the weighting function and scale factor taking into account the features of the discrete signal spectrum is considered. The dependences of maximum values of methodological errors on the normalized frequency when using the Kaiser-Bessel and Dolph-Chebyshev weighting function are described. The adaptive sample optimization algorithm is given. Validating the obtained theoretical results is performed by numerical simulation, which confirmed that using the Dolph-Chebyshev weighting function provides smaller error due to the smaller width of the main lobe of the spectral density for the same maximum levels of side lobes of the Kaiser-Bessel and Dolph-Chebyshev weighting function when measuring signal frequency, containing about one oscillation period. However, with the rise in frequency, monotonous decrease in the sidelobe level of the spectral density of the Kaiser-Bessel weighting function leads to lower estimation error. As a result, with the growth of the estimated signal frequency, the Kaiser-Bessel weighting function has a significant advantage over the Dolph-Chebyshev weighting function. It is shown that, at increasing the number of samples, divergence monotonously decreases. Calculations of dependences with different sampling periods show that increasing the number of samples reduces the shift of theoretical and practical values with zero error and lowers the measurement error during simulation. The reduction rate of the error value with an increase in the relative signal sample length, obtained during the simulation is less than the reduction rate of the error, obtained from theoretical calculations. This is caused by two reasons: DFT use, and expansion of the main spectral component and the inevitable increase in noise exposure including through the signal quantization.
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