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The Two-Dimensional Power Spectral Density: A Connection Between 2-D Rational Functions and Linear Systems

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1 Author(s)
Pulford, G.W. ; Underwater Syst., Brest, France

A derivation of the power spectral density (PSD) matrix of a continuous-time, linear, constant-coefficient system with white Gaussian noise input is given. The assumption of wide-sense stationarity is not made. By transforming the two-dimensional (2-D) autocorrelation function (ACF), a 2-D spectral density is obtained that takes the system's transient behavior into account. The 2-D PSD is a non-separable rational function. The results are applicable to second-order Volterra series representations of nonlinear systems. Simulations are presented for a fourth order system that compare the 2-D PSD amplitude (both theoretical and empirical) with its 1-D counterpart on 50 realizations of a short data segment containing an initial transient.

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Automatic Control, IEEE Transactions on  (Volume:56 ,  Issue: 7 )