非高斯噪声环境下的多项式变换方法
Polynomial Transformation Method for Non-Gaussian Noise Environment
摘要：
本文研究了非高斯噪声环境下的信号处理。对于许多现实生活中的情况下，存在于系统中的加性噪声过程被发现是占主导地位的非高斯。检测和估计被非高斯噪声污染的信号的问题很难在数学上跟踪。本文提出了一种新的非高斯噪声中信号的最优检测和估计方法。它表明，预处理数据的正交多项式逼近与最小误差方差准则转换成一个近似误差过程，这是接近高斯的加性非高斯噪声过程。利用Monte Carlo模拟方法对基于序列双相干的高斯假设进行了验证。利用直方图检验和峰度检验对高斯假设进行了验证。
英文摘要：
Signal processing in non-Gaussian noise environment is addressed in this paper. For many real-life situations, the additive noise process present in the system is found to be dominantly non-Gaussian. The problem of detection and estimation of signals corrupted with non-Gaussian noise is difficult to track mathematically. In this paper, we present a novel approach for optimal detection and estimation of signals in non-Gaussian noise. It is demonstrated that preprocessing of data by the orthogonal polynomial approximation together with the minimum error-variance criterion converts an additive non-Gaussian noise process into an approximation-error process which is close to Gaussian. The Monte Carlo simulations are presented to test the Gaussian hypothesis based on the bicoherence of a sequence. The histogram test and the kurtosis test are carried out to verify the Gaussian hypothesis.
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