随机信号的非线性变换及其频谱特性的分析

Analysis of Nonlinear Transformations and Spectral Properties of Random Signals

本文介绍和分析平稳随机信号的非线性变换及其频谱关系。对于输入信号为高斯平稳随机过程的情况,讨论无记忆非线性系统及一类有限记忆非线性系统的响应以及经过非线性变换后的频谱特性,并详细分析非线性系统函数的特性和使用条件。另外,也对某些非高斯平稳随机信号的非线性变换及其频谱特性进行了分析。指出非线性变换对随机信号具有白化作用并给出频谱带宽的关系。最后,采用本文讨论的方法给出几组实际模拟的结果。

This paper introduces and analyzes the nonlinear transformations and spectral density properties of stationary random signals . For the Gaussian stationary random processes, the responses both of the memoryless nonlinear system and finite memory nonlinear system to a random input are discussed . The nonlinear system function and its limitation when using the methods described are analyzed in detail. Also, certain non-Gaussian processes are observed for their nonlinear transformations and spectral properties. The results indicate that the nonlinear transformations have a whitening effect on the random signals in the sense that the bandwidth of the output spectrum is larger than that of the input spectrum. Finally, some simulated examples by using the procedures developed are also presented.