An isospectral family of random processes

We construct a family of random step functions whose members all have the same power spectrum and such that as converges to , the Gaussian process with the same spectrum. We illustrate the procedure for calculating the general multivariate distribution of the processes by calculating the univariate, bivariate and trivariate distributions. We show how a suitably constructed univariate entropy can serve as an index of the extent to which has approached the Gaussian limit ).