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An isospectral family of random processes

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1 Author(s)

We construct a family of random step functions {x_n (t)} whose members all have the same power spectrum and such that as n \rightarrow \infty , x_n (t) converges to x_{\infty } (t) , the Gaussian process with the same spectrum. We illustrate the procedure for calculating the general multivariate distribution of the processes {x_n(t)} 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 x_n(t) has approached the Gaussian limit x_{\infty }( t ).

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Information Theory, IRE Transactions on  (Volume:6 ,  Issue: 4 )