Generation of random sequences with jointly specified probability density and autocorrelation functions

A new method is presented for the generation of stochastic (random) sequences with an arbitrarily specified first-order probability distribution function (PDF) and an arbitrarily specified first-order auto-correlation function (ACF). A set of numbers with the desired PDF are first generated. These are then given a white (independent) ACF by double stochastic interchange. The desired ACF is then obtained by stochastically shuffling the series to minimize a sum of squares criterion between desired and actual ACFs. The technique is particularly useful for generating experimental stimuli for system identification, sequences for numerical stimulation, and test series for evaluating signal processing algorithms when colored (non-white) non-Gaussian data are required.