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In the development of adaptive array processing algorithms, data simulation has been a key element of testing and evaluation. It has long been known how to simulate temporally-white, Gaussian array data with a specified spatial covariance. However, with the advent of space-time array processing algorithms, it has become crucial to simulate data which has a specified joint spatio-temporal correlation. In the case where only a finite number of time correlation lags are known (say, from measured data), then a technique for generating valid data having this specified correlation relationship is required. A direct extension of the current spatial techniques fails to insure proper temporal correlation for all time samples. Techniques have been proposed for generating space-time data from correlation functions defined for a finite number of lags, but the truncated correlation function must itself be positive definite (assuming a zero extension). In general, this will not be true for measured correlation data. This paper proposes two methods of generating arbitrarily long sequences of multi-channel Gaussian data which has a specified spatio-temporal correlation function. The first method uses a matrix finite impulse response (FIR) filter approach to generate data with the approximate spatio-temporal correlation required. The second method uses a matrix infinite impulse response (IIR) filter approach, and has the capability to generate data with the exact spatio-temporal correlation function specified to a finite number of time lags. Results are shown demonstrating simulated data having a spatio-temporal correlation function equal to that measured from a GPS adaptive array mounted on an F-16 illuminated with four strong broadband sources.