Generating Uncorrelated Random Outputs by Nonlinear Processing of a Single Noise Source

It will be shown that, for a single Gaussian noise source, an arbitrary number of mutually uncorrelated outputs can be produced by passing the noise through a parallel cascade of zero-memory nonlinear filters, where the output of the kth filter is related to its input by a kth-degree Hermite polynomial. This generalizes a recent finding
¹
in which four noncorrelated outputs were produced from a Gaussian source by nonlinear processing; extensions of this method to certain non-Gaussian noise sources are also indicated. The non-correlation between Gaussian input and distortion terms in the equivalent gain representation of an instantaneous non-linearity
¹
will be shown to hold for any separable random process.