高斯白噪声对PSWFs信号时频分布影响研究

Study on the Influence of Gaussian White Noise on the Time-frequency Distribution of PSWFs Signal

文中引入STFT和WVD两种时频分析方法,重点分析了高斯白噪声时频域统计特性、其对PSWFs信号时频分布的影响。理论与数值分析发现,高斯白噪声经两种时频变换后,其均值和方差均为常数,噪声能量随机平铺在整个时频域上。当噪声平均功率较小时,在两种时频域上噪声方差较为接近,随着噪声平均功率增加,在WVD时频域上噪声方差呈几何增长,加重对PSWFs信号时频分布的影响。相对于WVD,STFT能够较好地平滑高斯白噪声,降低高斯白噪声对PSWFs信号时频分布的影响。同时,对于相同阶数的PSWFs信号,随着时间带宽积的增加,信号能量聚集性不断提高,其在时频域的能量峰值增加,高斯白噪声对其影响程度不断减小。大时间带宽积和低阶PSWFs信号在噪声中更容易识别和检测。在这为下一步探索PSWFs信号时频检测的边界条件,设计新的PSWFs信号时频检测方法提供了理论依据。

In this paper,two time-frequency analysis methods,STFT and WVD,are introduced to analyze the time-frequency domain statistical characteristics of Gaussian white noise and its influence on the time-frequency distribution of PSWFs signal.Theory and numerical analysis found that after two time-frequency transformations,the mean and variance of gaussian white noise are constant,and the noise energy is randomly tiled in the whole time-frequency domain.when the average noise power is small,on the two kinds of time-frequency domain noise variance is relatively close,as average noise power increasing,the noise variance in WVD time-frequency domain geometric growth,increase impact for PSWFs signal timefrequency distribution.Compared with WVD,STFT can smooth gaussian white noise better and reduce the influence of Gaussian white noise on the time-frequency distribution of PSWFs signal.At the same time,for PSWFs signals of the same order,with the increase of time bandwidth product,the signal energy aggregation keeps increasing,its peak energy in the time-frequency domain increases,and the influence of Gaussian white noise on it keeps decreasing.Large time bandwidth product and low order PSWFs signal are easier to identify and detect in noise.This provides a theoretical basis for the next step to explore the boundary conditions of PSWFs signal time-frequency detection and design a new time-frequency detection method for PSWFs signals.