Abstract
This article provides a comparative analysis of eleven major nonparametric, parametric, and subspace methods for estimation of the power spectrum. We analyze the dependence of the resolving capacity of the methods of the power’s spectrum estimation on the signal/noise ratio (SNR), the signal duration, and the amount of lost data.
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Proakis, J.G., and Manolakis, D.G., Digital Signal Processing: Principles, Algorithms and Applications, Englewood Cliffs, NJ: Printice Hall, 1996.
Kay, S.M., Modern Spectral Estimation, Englewood Cliffs, NJ: Printice Hall, 1988.
Stoica, P. and Moses, R., Introduction to Spectral Analisys, Upper Sadle River, NJ: Printice Hall, 1997.
Kay, S.M and Marple, S.L., Spectrum Analysis — a Modern Perspective, Proc. IEEE, 1981, vol. 69, pp. 1380–1419.
Thomson, D.J., Spectrum Estimation and Harmonic Analysis, Proc. IEEE, 1982, vol. 70, pp. 1055–1096.
Yule, G.U., On a Method of Investigating Periodicities in Distributed Series with Special References to Wolfer’s Sunspot Numbers, Philos. Trans. R. Soc., 1927, London, Ser. A, vol. 226, pp. 267–298.
Parzen, E., On Consistent Estimates of the Spectrum of a Stationary Time Series, Am. Math. Stat., 1957, vol. 28, pp. 329–348.
Blackman, R.B. and Tukey, J.W., The Measurement of Power Spectra, Dover, New York, 1958.
Burg, J.P., Maximum Entropy Spectral Analysis, Proc. 37th Meeting of the Society of Exploration Geophysicians, Oklahoma City, October, 1967.
Johnson, D.H., The Application of Spectral Estimation Methods to Bearing Estimation Problems, Proc. IEEE, 1982, vol. 70, pp. 1018–1028.
McClellan, J.H., Multidimensional Spectral Estimation, Proc. IEEE, 1982, vol. 70, pp. 1029–1039.
Nikias, C.L. and Scott, P.D., Energy-Weighted Linear Predictive Spectral Estimation: a New Method Combining Robustness and Hight-Resolution, IEEE Trans. Acoustics, Speech and Signal Processing, 1982, vol. 30, pp. 287–292.
Welch, P.D., The Use of Fast Fourier Transform for the Estimation of Power Spectra: a Method Based on Time Averaging over Short, Modified Periodograms, IEEE Trans. Audio Electroacoust, 1967, vol. 15, pp. 70–73.
Percival, D.B., and Walden, A.T., Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques, Cambridge University Press, 1993.
Marple, S.L., Minimum Variance Spectral Estimator Fast Algorithm Based on Covariance and Modified Covariance Methods of Linear Prediction, Signal, Systems and Computers, Conference Record of the Thirty-Fifth Asimolar Conference, Pacific Grove, C.A., 2001, vol. 1, pp. 711–714.
Lomb, N.R., Least-Squares Frequency Analysis of Unequally Spaced Data, Astrophysics and Space Science, 1967, vol. 39, pp. 447–462.
Scargle, J.D., Studies in Astronomical Time Series Analysis III. Fourier Transforms, Autocorrelation Functions, and Cross-Correlation Functions of Unevently Spaced Data, The Astrophysics Journal, 1989, vol. 343, pp. 874–887.
Broersen, P.M.T., Automatic Spectral Analysis with Time Series Models, IEEE Trans. On Instrumentation and Measurement, 2002, vol. 51, pp. 211–216.
Isaksson, A.J., Identification of ARX-models Subject To Missing Data, IEEE Trans. On Automatic Control, 1993, vol. 38, pp. 813–819.
Ljung, L., System identification: Theory for the Users, Upper Saddle River, NJ: Printiec Hall, 1999.
Wallin, R., Isaksson, A.J. and Ljung, L., An Iterative Method for Identification of ARX Models from Incomplete Data, Proc. of CDC/IEEE Conf., Sydney, Australia, 2000, pp. 203–208.
Wallin, R. and Isaksson, A.J., Multiple Optima in Identification of ARX Models Subject to Missing Data, EURASIP Journal on Applied Signal Processing, 2002, vol. 1, pp. 30–37.
Pintelon, R. and Schoukens, J., Frequency Domain System Identification with Missing Data, IEEE Trans. on Automatic Control, 2000, vol. 45, pp. 364–369.
Mirsaidi, S., Fleury, G.A. and Oksman, J., LMS-like AR Modeling in the Case of Missing Observations, IEEE Trans. on Signal Processing, 1997, vol. 45, pp. 1574–1583.
de Waele, S. and Broersen, P.M.T., The Burg Algorithm for Segments, IEEE Trans. on Signal Processing, 2000, vol. 48, pp. 2876–2880.
Boashash, B., Time-Frequency Signal Analysis, Melboume, Australia: Longman, Cheshire, 1991.
Donoho, D.L., Johnstone, G.K. and Pickard, D., Wawelet Shrinkage: Asymptotia, J. Roy. Statist. Soc., 1995, vol. 57, pp. 301–369.
Qian, S. and Chen, D., Discrete Gabor Transform, IEEE Trans. on Signal Processing, 1993, vol. 41, pp. 2429–2438.
Peleg, S., and Friedlander, B., Multicomponent Signal Analysis Using the Polynomial-Phase Transform, IEEE Trans. on Aerospace and Elec. Sys., 1996, vol. 32, pp. 378–387.
Hussain, Z.M. and Boashash, B., Adaptive Instantaneous Frequency Estimation of Multi-Component FM Signal Using Quadratic Time-Frequency Distributions, IEEE Trans. on Signal Processing, 2002, vol. 50, pp. 1866–1876.
Boashash, B. and O’shea, P.J., Use of Cross Wigner-Ville Distribution for Instaneous Frequency Estimation, IEEE Trans. on Signal Processing, 1993, vol. 41, pp. 1439–1445.
Katkovnik, V. and Stankovic, L.J., Instantaneous Frequency Estimation Using the Wigner Distribution with Varying and Data Driven Window Length, IEEE Trans. on Signal Processing, 1998, vol. 46, pp. 2315–2325.
Francos, A. and Porat, M., Analysis and Synthesis of Multicomponent Signals Using Positive TFDs, IEEE Trans. on Signal Processing, 1999, vol. 47, pp. 493–504.
Choi, H., and Williams, W., Improved Time-Frequency Representation of Multi-Components Signals Using Exponential Kernels, IEEE Trans. on Signal Processing, 1989, vol. 37, pp. 862–871.
Dubois, C., Davy, M. and Idear, J., Tracking of Time-Frequency Components Using Particle Filtering, IEEE Int.Conf. Acoustics, Speech, Signal Processing (ICASSP) 2005, Philadelphia, PA, 2005, pp.18–23.
Tsakonas, E.E., Sidiropoulos, N.D., and Swami, A., Optimal Particle Filters for Tracking a Time-Varying Harmonic or Chirp Signal, IEEE Trans. on Signal Processing, 2008, vol. 56, pp. 4598–4610.
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Original Russian Text © K. Kazlauskas, Ya. Kazlauskas, G. Petreykite, 2009, published in Avtomatika i Vychislitel’naya Tekhnika, 2009, No. 6, pp. 47–60.
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Kazlauskas, K., Kazlauskas, Y. & Petreykite, G. The comparative analysis of methods for estimation of the power spectrum. Aut. Conrol Comp. Sci. 43, 317–327 (2009). https://doi.org/10.3103/S0146411609060054
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DOI: https://doi.org/10.3103/S0146411609060054