Generation of a random sequence having a jointly specified marginal distribution and autocovariance

We consider the problem of generating a random sequence with a specified marginal distribution and autocovariance. The proposed scheme for generating such a sequence consists of a white Gaussian noise source input to a linear digital filter followed by a zero-memory nonlinearity (ZMNL). The ZMNL is chosen so that the desired distribution is exactly realized and the digital filter is designed so that the desired autocovariance is closely approximated. Both analytic results and examples are included. The proposed scheme should prove useful in simulations involving non-Gaussian processes.

[1]  M. Levin Generation of a sampled Gaussian time series having a specified correlation function , 1960, IRE Trans. Inf. Theory.

[2]  J. Franklin,et al.  Numerical Simulation of Stationary and Non-Stationary Gaussian Random Processes , 1965 .

[3]  J. Cooley,et al.  Application of the fast Fourier transform to computation of Fourier integrals, Fourier series, and convolution integrals , 1967, IEEE Transactions on Audio and Electroacoustics.

[4]  U. Gujar,et al.  Generation of random signals with specified probability density functions and power density spectra , 1968 .

[5]  P. E. Valisalo,et al.  GENERATION OF RANDOM TIME-SERIES THROUGH HYBRID COMPUTATION , 1970 .

[6]  R. J. Polge,et al.  Generation of a pseudo-random set with desired correlation and probability distribution , 1973 .

[7]  John R. Fraker,et al.  A composite approach to generating autocorrelated sequences , 1974 .

[8]  P. M. Reeves,et al.  A non-Gaussian model of continuous atmospheric turbulence proposed for use in aircraft design , 1975 .

[9]  W. Whitt Bivariate Distributions with Given Marginals , 1976 .

[10]  Apostolos Traganitis,et al.  The effect of a memoryless nonlinearity on the spectrum of a random process , 1977, IEEE Trans. Inf. Theory.

[11]  W. Szajnowski The Generation of Correlated Weibull Clutter for Signal Detection Problems , 1977, IEEE Transactions on Aerospace and Electronic Systems.

[12]  Peter A. W. Lewis,et al.  Discrete Time Series Generated by Mixtures. I: Correlational and Runs Properties , 1978 .

[13]  E. Masry,et al.  On the reconstruction of the covariance of stationary Gaussian processes observed through zero-memory nonlinearities , 1978, IEEE Trans. Inf. Theory.