Continuous and discontinuous linear approximation of the window spectrum by least squares method

• Autorzy: Borkowski J.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

data window; spectrum approximation; interpolated DFT; LIDFT; spectrum estimation; zero padding

• Wydawca: Komitet Metrologii i Aparatury Naukowej PAN
• Czasopismo: Metrology and Measurement Systems
• Rocznik: 2011
• Tom: Vol. 18, nr 3
• Strony: 379--390
• Opis fizyczny: Bibliogr. 15 poz., wykr., wzory

Twórcy

autor

Borkowski J.

• Wroclaw University of Technology, Chair of Electronic and Photonic Metrology, ul. B. Prusa 53/55, 50-317 Wroclaw, Poland,

Bibliografia

• [1] Borkowski, J. (2000). LIDFT - The DFT linear interpolation method, IEEE Trans. Instrum. Meas., 49, 741-745.
• [2] Borkowski, J., Mroczka, J. (2000). Application of the discrete Fourier transform linear interpolation method in the measurement of volume scattering function at small angle, Opt. Eng. 39(6), 1576-1586.
• [3] Borkowski, J., Mroczka, J. (2002). Metrological analysis of the LIDFT method, IEEE Trans. Instrum. Meas., 51, 67-71.
• [4] Borkowski, J., Mroczka, J. (2010). LIDFT method with classic data windows and zero padding in multifrequency signal analysis, Measurement, 43, 1595-1602.
• [5] Kay, S.M. (1988). Modern Spectral Estimation: Theory and Application, Englewood Cliffs, Prent.-Hall.
• [6] Zygarlicki J, Zygarlicka M, Mroczka J, Latawiec K.J. (2010). A reduced Prony’s method in powerquality analysis-parameters selection, IEEE Trans. Power Del., 25(2), 979-986.
• [7] Szmajda M, Górecki K, Mroczka J. (2010). Gabor transform, spwvd, gabor-wigner transform and wavelet transform - tools for power quality monitoring, Metrology and Measurement Systems, 17(3), 383-396.
• [8] Mroczka, J., Szczuczyński, D. (2009). Inverse problems formulated in terms of first-kind Fredholm integral equations in indirect measurements, Metrology and Measurement Systems, 16 (3), 333-357.
• [9] Duda, K., Borkowski, D., Bień, A. (2009). Computation of the network harmonic impedance with Chirp-Z transform, Metrology and Measurement Systems, 16(2), 299-312.
• [10] Agrež, D. (2002). Weighted Multipoint Interpolated DFT to Improve Amplitude Estimation of Multifrequency Signal, IEEE Transactions on Instrumentation and Measurement, 51(2), 287-292.
• [11] Belega, D., Dallet, D. (2008). Frequency estimation via weighted multipoint interpolated DFT, IET Science, Measurement and Technology, 2(1), 1-8.
• [12] Chen, K.F., Jiang, J.T., Crowsen, S. (2009). Against the long-range spectral leakage of the cosine window family, Computer Physics Communications, 180, 904-911.
• [13] Duda, K. (2010). DFT Interpolation Algorithm for Kaiser-Bessel and Dolph-Chebyshev Windows, IEEE Transactions on Instrumentation and Measurement, 60(3), 784-790.
• [14] Dehkordi, V.R., Labeau, F., Boulet, B. (2008). Piece-wise linear DFT interpolation for IIR systems: Performance and error bound computation, Proceedings of the 42nd Conference on Signals, Systems and Computers, Asilomar, Pacific Grove, CA., 588-592.
• [15] Gray, R.M. (2006). Toeplitz and Circulant Matrices: A review, Foundations and Trends in Communications and Information Theory, 2(3), 155-239.