In this paper, a random number generator for simulation of speech-waveform coders was designed. A random number generator having a desired probability density function and a desired power spectral density is discussed and experimental results are presented. The technique is based on Sondhi algorithm which consists of a linear filter and a memoryless nonlinearity. Several methods of obtaining memoryless nonlinearities for some typical continuous distributions are discussed. Sondhi algorithm is analyzed in the time domain using the diagonal expansion of the bivariate Gaussian probability density function. It is shown that the Sondhi algorithm gives satisfactory results when the memoryless nonlinearity is given in an antisymmetric form as in uniform, Cauchy, binary and gamma distribution. It is shown that the Sondhi algorithm does not perform well when the corresponding memoryless nonlinearity cannot be obtained analytically as in Student-t and F distributions, and when the memoryless nonlinearity can not be expressed in an antisymmetric form as in chi-squared and lognormal distributions.