Performance Evaluation of Music and Minimum Norm Eigenvector Algorithms in Resolving Noisy Multiexponential Signals

Authors: Abdussamad U. Jibia, Momoh-Jimoh E. Salami

Abstract:

Eigenvector methods are gaining increasing acceptance in the area of spectrum estimation. This paper presents a successful attempt at testing and evaluating the performance of two of the most popular types of subspace techniques in determining the parameters of multiexponential signals with real decay constants buried in noise. In particular, MUSIC (Multiple Signal Classification) and minimum-norm techniques are examined. It is shown that these methods perform almost equally well on multiexponential signals with MUSIC displaying better defined peaks.

Keywords: Eigenvector, minimum norm, multiexponential, subspace.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1070197

References:

[1] D.G. Gardner, J.C. Gardner, G. Lush, and W.R. Ware, "Method for the analysis of multicomponent exponential decay curves", Journ. Chem. Phys., vol. 31, 1959, pp. 978-986.
[2] M.J.E. Salami, "ARMA models in multicomponent signal analysis", Ph.D. Dissertation, Dept. of Electr. Eng., University of Calgary, Calgary, Canada. 1985.
[3] M.J.E. Salami, and S.N. Sidek, "Performance evaluation of the deconvolution techniques used in analyzing multicomponent transient signals", in Proc. IEEE Region 10 International Conference on Intelligent System and Technologies for the New Millennium (TENCON 2000), Vol. 1, 2000, Kuala Lumpur, pp. 487-492
[4] M.J.E. Salami, and S.N. Sidek, "Parameter estimation of multicomponent transient signals using deconvolution and ARMA modeling techniques", Journal of Mechanical systems and signal processing, Vol. 17, Issue 6, pp. 1201 - 1218, Academic Press, UK.
[5] M.J.E. Salami, "High-resolution decay rate estimation in multiexponential signal analysis", Pro. 3rd Intern. Conf. on Acoustical and vibratory surveillance methods and diagnostic techniques, 1998, pp. 379-388.
[6] R. Gutierrez-Osuna, A. Gutierrez-Galvez, and N. Powar,. "Transient response analysis for temperature-modulated chemoresistors", Sensors and Actuators Journal, pp. 57-66, 2003.
[7] T. K. Sarkar, and O. Pereira, "Using the matrix pencil method to estimate the parameters of a sum of complex exponentials" IEEE Antennas and Propagation Magazine, vol. 37. No.1, 1995, pp. 48-55.
[8] D. F. Eaton, "Recommended methods for fluorescence decay analysis", Journal of Pure and Applied Chemistry, vol. 62, No 8, 1990, pp. 1631- 1648.
[9] D. Lawunmi, "A theoretical analysis of exponentially decaying time series" Journal of Measurement Science and Technology, IOP Publishing Ltd., UK. 1997, pp. 703-706.
[10] G. Bienvenu, and L. Kopp, "Optimality of high resolution array processing using the eigensystem approach", IEEE Transactions on Acoustics, Speech and Signal Processing, vol. 31(10), pp. 1235-1248, 1983.
[11] M.J.E. Salami and Z. Ismail, "Analysis of multiexponential transient signals using interpolation-based deconvolution and parametric modeling techniques", in Proc. IEEE International conference on Industrial Technology, vol. 1, 2003, pp. 271-276.
[12] D.G. Manolakis, V.K. Ingle, and Kogon, S.M., Statistical and Adaptive Signal Processing, Artech House, Inc., Norwood, 2005.
[13] M.H. Hayes, Statistical Signal Processing and Modeling, John Wiley and sons, Inc., New York, 1996.
[14] S. J. Orfanidis, Optimal Signal Processing. McGraw-Hill Publishing Company, 2007.
[15] Salami M.J.E., "High-resolution decay rate estimation in multiexponential signal analysis", in Pro. 3rd Intern. Conf. on Acoustical and vibratory surveillance methods and diagnostic techniques, 1998, pp. 379-388.
[16] S.M. Kay, and S.L. Marple, "Spectrum analysis - A modern perspective", in Proc. of the IEEE. 69(11), 1981, pp. 1380-1419.
[17] M.J.E. Salami, S.T Nichols, and M.R. Smith, "A SVD-based transient error method for analyzing noisy multicomponent exponential signals", in Proc. ICASSP87, 1987, pp. 677- 680.
[18] M.R. Smith, S. Cohn-Sfetcu, and Buckmaster H.A., "Decomposition of multicomponent exponential decays by spectral analytic techniques", Technometrics, vol. 18, pp. 467-482, 1976.