An efficient source of random numbers for modeling symmetrically distributed noise

Computer simulation of signal processing algorithms inevitably requires an efficient source of pseudorandom numbers to model noise. If symmetric random noise is defined by its kurtosis rather than by its distribution, it can be simulated by simple combinations of random variates X₁, X₂, … uniformly distributed on the interval (-1, 1). A notable example is the mock-Gaussian variate Y=0.9828X₁+2.493SX₂X₃, which appears to be the simplest generator possible for giving Gaussian moments up to the fourth order