Simulation of correlated, gaussian data from an array

A method is presented for digitally simulating zero-mean stationary Gaussian data from an array of hydrophones. The data will exhibit prescribed temporal and spatial correlation to within an arbitrarily small error. In this method a Fourier series having a period greater than twice the simulation interval is constructed at each hydrophone. At each frequency, the technique uses independent numbers from a random number generator to construct Fourier coefficients exhibiting the prescribed spatial correlation. Upper bounds on the covariance error are given as a function of the period of the series and the characteristics of the model. The error due to truncating the series is also considered. Aside from this truncation error, it is determined that the simulation can yield zero error when the period of the series is at least twice the maximum correlation-time interval in the acoustic field.