Abstract
In statistical signal processing, parametric modeling of non-Gaussian processes experiencing noise interference is a very important research topic. Particularly challenging to some researchers is how to estimate signals encountering stochastic noise process exhibiting sharp spikes. The authors propose the use of systems with impulse effect along with the classic autoregressive moving average model as a novel parametric modeling tool to successfully estimate these specific processes. The proficiency of this original system is illustrated in a performance table.
Similar content being viewed by others
References
S. M. Kay and S. L. Marple, “Spectrum Analysis—A Modern Perspective,” Proc. IEEE, vol. 69, 1981, pp. 1380–1419.
S. Kay, “Modern Spectral Estimation: Theory and Application,” Prentice Hall, Englewood Cliffs, New Jersey, 1988.
J. D. Scargle, “Absolute Value Optimization to Estimate Phase Properties of Stochastic Time Series,” IEEE Trans. Inf. Theory, vol. 23, 1977, pp. 140–143.
K. S. Lii and M. Rosenblatt, “Deconvolution and Estimation of Transfer Function Phase and Coefficients for Non-Gaussian Linear Processes,” Ann. Stat., vol. 10, 1982, pp. 1195–1208.
G. B. Giannakis and J. M. Mendel, “Identification of Non-minimum Phase Systems Using Higher Order Statistics,” IEEE Trans. Acoust. Speech Signal Process., ASSP-37, no. 3, 1989, pp. 360–377.
K. S. Lii, “Identification and Estimation of Non-Gaussian ARMA Process,” IEEE Trans. Acoust. Speech Signal Process., ASSP-38, no. 7, 1990, pp. 1266–1276.
A. Al-Smadi and A. Alsamali, “Fitting ARMA Models to Linear Non-Gaussian Processing Using Higher Order Statistics,” Signal Process., vol. 82, no. 11, 2002, pp. 1789–1793.
P. D. Frazier and M. F. Chouikha, “Parametric Modeling and Application of Systems with Impulse Effect,” in Proceedings of the 2004 IEEE International Workshop on Machine Learning for Signal Processing, São Luís, Brazil, Sep. 2004, pp. 725–733.
J. A. R. Fonollosa, J. Vidal, and E. Masgrau, “Adaptive System Identification Based on Higher-order Statistics,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Toronto, Canada, May 1991, pp. 3437–3440.
J. K. Tugnait, “Order Reduction of SISO Nonminimum-phase Stochastic Systems,” IEEE Trans. Automat. Contr., vol. AC-31, no. 7, 1986, pp. 623–632.
C. L. Nikias and A. N. Venetsanopoulos, “Identification of Nonminimum Phase Communication Channels via Parametric Modeling of 3rd Moments,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Tokyo, Japan, Mar. 1986, pp. 667–670.
S. L. Bernstein, “Long-range Communication at Extremely Low Frequency,” Proc. IEEE, vol. 62, no. 3, 1974, pp. 292–312.
M. P. Shinde and S. N. Gupta, “Signal Detection in the Presence of Atmospheric Noise in the Tropics,” IEEE Trans. Commun., COMM-22, 1974, pp. 1055–1063.
E. J. Wegman, S. G. Schwartz, and J. B. Thomas, (Eds.), “Topics in Non-Gaussian Signal Processing,” Academic, New York, 1989.
D. Sengupta and S. Kay, “Efficient Estimation of Parameters for Non-Gaussian Autoregressive Processes,” IEEE Trans. Acoust. Speech Signal Process., ASSP-37, no. 6, 1989, pp. 785–794.
C. L. Nikias and M. Shao, Signal Processing with Alpha-Stable Distributions and Applications, Wiley, New York, 1994.
P. D. Frazier, “System Analysis and Modeling using Impulsive Differential Equations,” Ph.D. Dissertation, Howard University, Washington, District of Columbia, May 1998.
T. Vogel, “Systèmes Dynamiques Héréditaries à Déferlement,” Ann. Télécommun., vol. 8, 1953, pp. 354–360.
V. D. Miĺman and A. D. Myśkis, “On the Stability of Motion in the Presence of Impulses,” Sib. Math. J., vol. 1, 1960, pp. 233–267.
A. M. Samoilenko, “Application of the Averaging Method for Investigation of Oscillations Generated by Transient Impulses in Auto-oscillations in Systems of Second Order with Small Parameter,” Ukr. Math. J., vol. 13, 1961, pp. 103–109.
A. M. Samoilenko and N. A. Perestyuk, “The Stability of Solutions of Differential Equations with Instantaneous Variations,” Diff. Equ., vol. 13, no. 11, 1977, pp. 1379–1387.
D. D. Bainov and P. S. Simeonov, “Systems with Impulse Effect: Stability, Theory and Applications,” Wiley, Chichester, UK, 1989.
Z. Guan, Yong-Qing Lui, and X. Wen, “Decentralized Stabilization of Singular and Time Delay Large Scale Control Systems with Impulsive Solutions,” IEEE Trans. Automat. Contr., vol. AC-40, no. 8, 1995, pp. 1437–1441.
P. D. Frazier and M. F. Chouikha, “Control of Upright Balance via Switching State Controller,” in Proceedings of the 18th IASTED International Conference: Modelling, Identification, and Control, Innsbruck, Austria, Feb. 1999, pp. 578–581.
P. D. Frazier and M. F. Chouikha, “A Novel Control Model for Elucidating Human Postural Balance,” in Proceedings of the Fifth World Congress on Intelligent Control and Automation, Hangzhou, Peoples Republic of China, Jun. 2004, pp. 2369–2375.
H. Ye, A. N. Michel, and L. Hou, “Stability Analysis of Systems with Impulse Effect,” IEEE Trans. Automat. Contr., vol. AC-43, no. 12, 1998, pp. 1719–1723.
P. M. T. Broersen, “The Quality of Models for ARMA Processes,” IEEE Trans. Signal Process., vol. 46, no. 6, 1998, pp. 1749–1752.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Frazier, P.D., Chouikha, M.F. Effective Parametric Estimation of Non-Gaussian Autoregressive Moving Average Processes Exhibiting Noise with Impulses. J VLSI Sign Process Syst Sign Image Video Technol 45, 21–28 (2006). https://doi.org/10.1007/s11265-006-9769-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11265-006-9769-2