Parametric estimation of the cross-power spectral density

A new cross-spectral analysis procedure is proposed for the parametric estimation of the relationship between two time sequences in the frequency domain. In this method, the two observable outputs are modeled as a pair of autoregressive moving-average and moving-average (ARMAMA) models under the assumption that the two outputs are driven by a common input and independent ones simultaneously. Cross- and auto-power spectral densities (PSDs) of a pair of ARMAMA models can be derived as forms of rational polynomial functions. The coefficients of these functions can be estimated from the cross-correlation function or the auto-correlation functions of the two observed sequences by using the method presented in this paper. The main advantage of the present procedure is that the physical parameters of an unknown system can be easily estimated from the coefficients of the cross- and auto-PSD functions. To illustrate the effectiveness of the proposed procedure, numerical and practical examples of a mechanical vibration problem are analyzed. The results show that the proposed procedure gives accurate cross- and auto-PSD estimates. Moreover, the physical properties of the unknown system can be well estimated from the obtained cross- and auto-PSDs.

[1]  Paruchuri R. Krishnaiah,et al.  On the use of autoregressive order determination criteria in univariate white noise tests , 1988, IEEE Trans. Acoust. Speech Signal Process..

[2]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[3]  A. A. Beex,et al.  A recursive procedure for ARMA modeling , 1985, IEEE Trans. Acoust. Speech Signal Process..

[4]  G. Carter,et al.  The generalized correlation method for estimation of time delay , 1976 .

[5]  Athina P. Petropulu,et al.  Cross-spectrum based blind channel identification , 1997, IEEE Trans. Signal Process..

[6]  J. Cadzow,et al.  Singular-value decomposition approach to time series modelling , 1983 .

[7]  M. Morf,et al.  Spectral Estimation , 2006 .

[8]  J. Bendat,et al.  Random Data: Analysis and Measurement Procedures , 1971 .

[9]  B. Friedlander Instrumental variable methods for ARMA spectral estimation , 1983 .

[10]  Surendra Prasad,et al.  Multichannel ARMA modeling by least squares circular lattice filtering , 1994, IEEE Trans. Signal Process..

[11]  L. Scharf,et al.  A note on covariance-invariant digital filter design and autoregressive moving average spectrum analysis , 1979 .

[12]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[13]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[14]  Erdal Şafak Identification of Linear Structures Using Discrete‐Time Filters , 1991 .

[15]  M. Kaveh High resolution spectral estimation for noisy signals , 1979 .

[16]  S. Kay Spectral estimation , 1987 .

[17]  C. Farrar,et al.  SYSTEM IDENTIFICATION FROM AMBIENT VIBRATION MEASUREMENTS ON A BRIDGE , 1997 .

[18]  Steven Kay,et al.  A new ARMA spectral estimator , 1980 .

[19]  J. Cadzow,et al.  High performance spectral estimation--A new ARMA method , 1980 .

[20]  J. Cadzow,et al.  Spectral estimation: An overdetermined rational model equation approach , 1982, Proceedings of the IEEE.

[21]  B. Peeters,et al.  Stochastic System Identification for Operational Modal Analysis: A Review , 2001 .

[22]  Steven Kay,et al.  Modern Spectral Estimation: Theory and Application , 1988 .

[23]  M Cavacece,et al.  Analysis of Damage of Ball Bearings of Aeronautical Transmissions by Auto-Power Spectrum and Cross-Power Spectrum , 2002 .

[24]  Surendra Prasad,et al.  Improved ARMA spectral estimation using the canonical variate method , 1987, IEEE Trans. Acoust. Speech Signal Process..

[25]  Xianda Zhang,et al.  An approach to time series analysis and ARMA spectral estimation , 1987, IEEE Trans. Acoust. Speech Signal Process..