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.