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

机译：通过单个噪声源的非线性处理生成不相关的随机输出

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摘要

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 finding1 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-linearity1 will be shown to hold for any separable random process.
机译：将显示出，对于单个高斯噪声源，通过使噪声经过零内存非线性滤波器的并行级联，可以产生任意数量的互不相关的输出，其中第k个滤波器的输出与其输入有关。由k次Hermite多项式这概括了最近的发现1，其中通过非线性处理从高斯源产生了四个不相关的输出；还指出了该方法对某些非高斯噪声源的扩展。高斯输入和失真项之间的非相关性在瞬时非线性1的等效增益表示中将显示为对于任何可分离的随机过程都成立。

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