Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30840
AC Signals Estimation from Irregular Samples

Authors: Predrag B. Petrović


The paper deals with the estimation of amplitude and phase of an analogue multi-harmonic band-limited signal from irregularly spaced sampling values. To this end, assuming the signal fundamental frequency is known in advance (i.e., estimated at an independent stage), a complexity-reduced algorithm for signal reconstruction in time domain is proposed. The reduction in complexity is achieved owing to completely new analytical and summarized expressions that enable a quick estimation at a low numerical error. The proposed algorithm for the calculation of the unknown parameters requires O((2M+1)2) flops, while the straightforward solution of the obtained equations takes O((2M+1)3) flops (M is the number of the harmonic components). It is applied in signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise RMS measurements (for power and energy) of a periodic signal based on the presented signal reconstruction. The paper investigates the errors related to the signal parameter estimation, and there is a computer simulation that demonstrates the accuracy of these algorithms.

Keywords: Signal reconstruction, Time, Band-limited signals, Fourier coefficient estimation, analytical solutions

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1424


[1] J. G. Proakis and D. G. Manolakis, Digital Signal Processing: Principles, Algorithms, Applications, 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.
[2] R. S. Prendergast, B. C. Levy, and P. J. Hurst, ÔÇ×Reconstruction of Band- Limited Periodic Nonuniformly Sampled Signals Through Multirate Filter Banks", IEEE Trans. Circ. Syst.-I,: vol. 51, no. 8, pp.1612-1622, Aug. 2004.
[3] P. Marziliano, M. Vetterli, and T. Blu, ÔÇ×Sampling and Exact Reconstruction of Bandlimited Signals With Additive Shot Noise", IEEE Trans. Inform. Theory, vol. 52, no. 5, pp.2230-2233, May 2006.
[4] E. Margolis, Y. C. Eldar, ÔÇ×Reconstruction of nonuniformly sampled periodic signals: algorithms and stability analysis", Electronics, Circuits and Systems, 2004. ICECS 2004. Proceedings of the 2004 11th IEEE International Conference, 2004, pp. 555-558.
[5] W. Sun and X. Zhou, ÔÇ×Reconstruction of Band-Limited Signals From Local Averages", IEEE Trans. Inf. Theory, vol. 48, no. 11, pp. 2955- 2963, Nov. 2002.
[6] A.K. Muciek, ÔÇ×A Method for Precise RMS Measurements of Periodic Signals by Reconstruction Technique With Correction", IEEE Trans. Instrum. Meas., vol. 56, no. 2, pp.513-516, Apr. 2007.
[7] P. Petrovic, "New approach to reconstruction of nonuniformly sampled AC signals", Proceedings of 2007 IEEE International Symposium on Industrial Electronics (ISIE 2007), Vigo, Spain, 2007, pp. 1693-1698.
[8] A.V.D.Bos, ÔÇ×Estimation of Fourier Coefficients", IEEE Trans. Instrum. Meas., vol. 38, no. 5, pp.1005-1007, Oct. 1989.
[9] A.V.D.Bos, ÔÇ×Estimation of complex Fourier Coefficients", IEE Proc.- Control Theory Appl., vol. 142, no. 3, pp.253-256, May. 1995.
[10] R. Pintelon, and J. Schoukens, ÔÇ×An Improved Sine-Wave Fitting Procedure for Characterizing Data Acquisition Channels", IEEE Trans. Instrum. Meas., vol. 45, no. 2, pp.588-593, Apr. 1996.
[11] Y. Xiao, Y. Tadokaro, and K. Shida, ÔÇ×Adaptive Algorithm Based on Least Mean p-Power Error Criteterion for Fourier Analysis in Additive Noise", IEEE Trans. Signal Proc., vol. 47, no. 4, pp.1172-1181, Apr. 1999.
[12] M. Agrawal M, S. Prasad S, and S.C.D.Roy, " A simple solution for the analytic inversion of Van der Monde and Confluent Van der Monde matrices", IETE JOURNAL OF RESEARCH, vol. 47, no. 5, pp. 217-219, Sep.-Oct. 2001.
[13] I. Gohberg and V. Olshevsky, ÔÇ×The fast generalized Parker-Traub algorithm for inversion of Van der Monde and related matrices", J. Complexity, vol. 13, no.2, pp. 208-234, June 1997.
[14] C. S. Jog, ÔÇ×On the explicit determination of the polar decomposition in n-dimensional vector spaces", JOURNAL OF ELASTICITY , vol.66, no. 2, pp.159-169, Dec. 2002.
[15] V.E. Neagoe, ÔÇ×Inversion of the Van der Monde matrix", IEEE Signal Processing Letters, vol. 3, no. 4, pp.119-120, Apr. 1996.
[16] H. C. So, K. W. Chan, Y. T. Chan, and K. C. Ho, ÔÇ×Linear Prediction Approach for Efficient Frequency Estimation of Multiple Real Sinusoids: Algorithms and Analyses", IEEE Trans. Signal Proc., vol. 53, no. 7, pp.2290-2305, July 2005.
[17] B. Wu and M. Bodson, "Frequency estimation using multiple source and multiple harmonic components", American Control Conference, 2002. Proceedings of the 2002, vol.1, 2002, pp. 21-22.
[18] G. Seber, Linear Regression Analysis, New York; Wiley, 1977.
[19] S.J.Reeves and L. P. Heck, ÔÇ×Selection of Observations in Signal Reconstruction", IEEE Trans. Signal Proc., vol. 43, no. 3, pp.788-791, Mart 1995.
[20] Y. S. Poberezhskiy and G. Y. Poberezhskiy, ÔÇ×Sampling and Signal Reconstruction Circuits Performing Internal Antialiasing Filtering and Their Influence on the Design of Digital Receivers and Transmitters", IEEE Trans. Circ. Sys.-I, vol. 51, no. 1, pp. 118-129, Jan. 2004.
[21] Y. Xiao, R. K. Ward, L. Ma, and A. Ikuta, "A New LMS-Based Fourier Analyzer in the Presence of Frequency Mismatch and Applications", IEEE Trans. Circ. Syst.-I, vol. 52, no. 1, 2005, pp.230-245, Jan. 2005.
[22] Y. Xiao, R.K. Ward, and L. Xu, "A new LMS-based Fourier analyzer in the presence of frequency mismatch", ISCAS-03, Proceedings of the 2003 International Symposium on Circuits and Systems, vol. 4, 2003, pp.369-372.
[23] P. Petrovic, ÔÇ×New Digital Multimeter for Accurace Measurement of Synchronously Sampled AC Signals", IEEE Trans. Instrum. Meas., vol. 53, no.3, 2004, pp.716-725, June 2004.
[24] T. Daboczi, "Uncertainty of Signal Reconstruction in the Case of Jitter and Noisy Measurements", IEEE Trans.on Instrum.Meas., vol. 47, no. 5, pp.1062-1066, Dec. 1999.
[25] G. Wang, W. Han, "Minimum Error Bound of Signal Reconstruction", IEEE Signal Proc. Lett., vol. 6, no. 12, pp. 309-311, Dec. 1999.
[26] N. J. Nigham, Accuracy and Stability of Numerical Algorithms, 2nd ed, SIAM, 2002.
[27] H. G. Feichtinger, ÔÇ×Reconstruction of band-limited signals from irregular samples, a short summary", 2nd International Workshop on Digital Image Processing and Computer Graphics with Applications, 1991, pp. 52-60.
[28] T. Cooklev, ÔÇ×An Efficient Architecture for Orthogonal Wavlet Transforms", IEEE Signal Proc. Lett., vol. 13, no. 2, pp. 77-79, Feb. 2006.
[29] J. Schoukens, Y. Rolain, G. Simon, and R. Pintelon, ÔÇ×Fully Automated Spectral Analysis of Periodic Signals, IEEE Trans. Instrum. Meas., vol. 52, no. 4, pp.1021-1024, Aug. 2003.
[30] S. J. Reeves, ÔÇ×An Efficient Implementation of the Backward Greedy Algorithm for Sparse Signal Reconstruction", IEEE Signal Proc. Lett., vol. 6, no. 10, pp. 266-268, Oct. 1999.
[31] P. Petrovic, ÔÇ×New procedure for estimation of amplitude and phase of compelx ac signals", in Proc. I2MTC, Austin, TX, USA, 2010, pp.464- 469.
[32] K.J.Coakley, C.M.Wang, PD. Hale and T.S. Clement, ÔÇ×Adaptive characterization of jitter noise in sampled high-speed signals", IEEE Trans. Instrum. Meas., vol. 52, no. 5, pp.1537-1547, Oct. 2003.
[33] H. Z. Hoseini, I. Kale and O. Shoaei, ÔÇ×Modeling of Switched-Capacitor Delta-Sigma Modulators in SIMULINK", IEEE Trans. Instrum. Meas., vol. 54, no. 4, pp.1646-1654, Aug. 2005.
[34] G. Vendersteen and R. Pintelon, ÔÇ×Maximum likelihood estimator for jitter noise models", IEEE Trans. Instrum. Meas., vol. 49, no. 6, pp.1282-1284, Dec. 2000.
[35] R.M. Hidalgo, J.G. Fernandez, R.R. Rivera, and H.A. Larrondo, ÔÇ×A Simple Adjustable Window Algorithm to Improve FFT Measurements", IEEE Trans. Instrum. Meas., vol. 51, no. 1, pp.31-36, Jan. 1996.
[36] N.C.F. Tse and L.L. Lai, "Wavelet-Based Algorithm for Signal Analysis", EURASIP Journal on Advances in Signal Processing, Vol. 2007, Article ID 38916, 10 pages, 2007.