Abstract
In many problems of digital signal processing, it is required to determine a model matching the statistics of a given observation of a generally non-Gaussian random process. Because of the wide range of systems that can be represented by Volterra series and Wiener expansions, the discrete nonlinear second-order Wiener filter (NSWF) driven by white Gaussian noise has been used in this study to match the statistics of a discrete zero-mean stationary non-Gaussian random process. First, we derive the autocorrelation function and show that it does not provide sufficient information necessary for estimating the parameters of the proposed model. Next, we derive the third-order moment sequence and show that it provides additional information that can be used in conjunction with the autocorrelation function to solve the problem. The power spectrum and bispectrum of the discrete NSWF have been also derived.
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References
M. J. Coker and D. N. Simkins, A nonlinear cancellor, inProc. IEEE Int. Conf. on ASSP, Denver, CO, vol. 2, 1980, pp. 470–473.
T. Koh, E. J. Powers, R. W. Miksad, and F. J. Fischer, Application of nonlinear digital filters to modeling low-frequency drift oscillations of moored vessels in random seas, inProc. 1984 Offshore Tech. Conf., pp. 309–314.
O. Agazzi, D. G. Messerrschmitt, and D. A. Hodges, Nonlinear echo cancellation of data signals,IEEE Trans. Commun.,30, 2421–2433, 1982.
M. Schetzen,The Volterra and Wiener Theories of Nonlinear Systems, Wiley, New York, 1980.
P. Alper, A consideration of the discrete Volterra series,IEEE Trans. Automat. Control,10, 322–327, 1965.
N. Wiener.Nonlinear Problems in Random Theory. Wiley, New York, 1958.
S. A. Billings, Identification of nonlinear systems — A survey,Proc. IEE-D,127(6), 272–285, 1980.
C. M. Nikias and M. R. Raghuveer, Bispectrum estimation: A digital signal processing framework,Proc. IEEE,75, 869–891, 1987.
S. A. Diant and M. R. Raghuveer, Estimation of the parameters of a second-order nonlinear system, inProc. Int. Conf. on ACC, Boston Rouge, LA, Oct. 1988.
V. Z. Marmarelis and D. Sheby, Bispectrum analysis of weakly nonlinear quadratic systems, inProc. ASSP Spectrum Estimation and Modeling Workshop III, Boston, MA, Nov. 1986, pp. 14–16.
M. Schetzen, Nonlinear system modeling based on the Wiener theory,Proc. IEEE,69, 1557–1573, 1981.
S. Yasui, Stochastic functional Fourier series, Volterra series, and nonlinear system analysis,IEEE Trans. Automat. Control,24, 230–242, 1979.
W. B. Davenport and W. L. Root,An Introduction to the Theory of Random Signals and Noise, McGraw-Hill, New York, 1958.
W. J. Lawless and M. Schwartz, Binary signaling over channels containing quadratic nonlinearities,IEEE Trans. Comm.,22, 288–298, 1974.
S. Benedetto, E. Biglieri, and R. Daffara, Performance of multilevel baseband digital systems in a nonlinear environment,IEEE Trans. Comm.,24, 1166–1175, 1976.
D. D. Falconer, Adaptive equalization of channel nonlinearities in QAM data transmission systems,Bell System Tech. J.,57, 2589–2611, 1978.
B. E. A. Saleh, Optical bilinear transformation: General properties,Optica Acta,26(6), 777–799, 1979.
M. J. Hinich and D. M. Patterson, Evidence of nonlinearity in daily stock returns,J. Bus. Econ. Statist.,3, 69–77, 1985.
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Alshebeili, S.A., Venetsanopoulos, A. Parameter estimation and spectral analysis of the discrete nonlinear secondorder Wiener filter (NSWF). Circuits Systems and Signal Process 10, 31–51 (1991). https://doi.org/10.1007/BF01183239
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DOI: https://doi.org/10.1007/BF01183239