Title :
The Two-Dimensional Power Spectral Density: A Connection Between 2-D Rational Functions and Linear Systems
Author :
Pulford, Graham W.
Author_Institution :
Underwater Syst., Brest, France
fDate :
7/1/2011 12:00:00 AM
Abstract :
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.
Keywords :
Gaussian noise; Volterra series; continuous time systems; linear systems; matrix algebra; nonlinear systems; 2D autocorrelation function; 2D rational functions; constant-coefficient system; continuous-time system; fourth order system; linear systems; nonlinear systems; second-order Volterra series representations; system transient behavior; two-dimensional power spectral density matrix; white Gaussian noise; Kernel; Laplace equations; Polynomials; Transfer functions; Transforms; Transient analysis; 2-D Laplace transform; 2-D fast Fourier transform (FFT); Autocorrelation function (ACF); S-transform; Volterra series; nonseparable rational function; nonstationary system; power spectral density (PSD); transient response;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2011.2135170
