LIDFT method with classic data windows and zero padding in multifrequency signal analysis

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This paper presents a new modification of the least-squares Prony's method with reduced sampling, which allows for a significant reduction in the number of the analysed signal samples collected per unit time. The specific combination of non-uniform sampling with Prony's method enables sampling of the analysed signals at virtually any average frequency, regardless of the Nyquist frequency, maintaining high accuracy in parameter estimation of sinusoidal signal components. This property allows using the method in measuring devices, such as for electric power quality testing equipped with low power signal processors, which in turn contributes to reducing complexity of these devices. This paper presents research on a method for selecting a sampling frequency and an analysis window length for the presented method, which provide maximum estimation accuracy for Prony's model component parameters. This paper presents simulation tests performed in terms of the proposed method application for analysis of harmonics and interharmonics in electric power signals. Furthermore, the paper provides sensitivity analysis of the method, in terms of common interferences occurring in the actual measurement systems.

Section: Origin Of the Methodsmentioning

confidence: 99%

Prony’s Method with Reduced Sampling - Numerical Aspects

Zygarlicki¹,

Mroczka²

2014

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“…Some equivalent to the method being developed can be a method described in publications [13]. Unfortunately, this method has drawbacks typical for Fourier analysis [14].…”

Section: Introductionmentioning

confidence: 99%

Variable-Frequency Prony Method in the Analysis of Electrical Power Quality

Zygarlicki¹,

Mroczka²

2012

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The article presents a new modification of the the least squares Prony method. The so-called variable-frequency Prony method can be a useful tool for estimating parameters of sinusoidal components, which, in the analyzed signal, are characterized by time-dependent frequencies. The authors propose use of the presented method for testing the quality of electric energy. It allows observation of phenomena which, when using traditional methods, are averaged in the analysis window. The proposed modification of least squares Prony method is based on introduction and specific selection of a frequency matrix. This matrix represents frequencies of estimated components and their variability in time.

“…The least-squares approximation of the data window frequency characteristics with appropriate linear functions is used in the linear interpolation of the discrete Fourier transform (LIDFT) [1][2][3] and the zero padding can also be used with this approximation to increase approximation accuracy [4]. Linear approximation of the spectrum allows for linearizing relationships to determine component frequencies and this feature of the LIDFT method differs it from other methods of signal estimation [5][6][7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

“…In the methods described in [1][2][3][4] the approximation function is discontinuous, which can be inadvisable in some applications.…”

Section: Introductionmentioning

confidence: 99%

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Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method

Borkowski¹

2011

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This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.