Welch功率谱估计中窗函数的选择与算法分析

Window function selection and algorithm analysis in Welch power spectrum estimation

以Matlab为平台对Welch算法中窗函数的选择与使用进行了分析。从频谱分辨率、噪声水平等方面对窗函数特性进行分析,其中矩形窗与凯撒窗频谱分辨率较高,但信号频率附近噪声水平较高。分析认为矩形窗与凯撒窗适用于高信号信噪比的高精度频谱估计。汉宁窗与切比雪夫窗对频谱泄漏抑制效果较好,信号频率附近噪声水平未受影响,但其分辨率相对较低。分析认为汉宁窗与切比雪夫窗适用于信噪比较低的信号频率的大致估计。Welch功率谱估计算法针对短信号使用的研究认为,直接对短信号进行Welch功率谱估计不仅频谱分辨率低,信号也容易被噪声干扰导致探测失败。短信号功率谱的估计无法直接通过Welch功率谱估计法来实现。

The selection and use of window function in Welch algorithm are analyzed with Matlab as the platform. The characteristics of window function are analyzed from spectrum resolution and noise level. The spectral resolution of Rectangular window and Kaiser window is higher, but the noise level near the signal frequency is higher. It is considered that Rectangular window and Kaiser window are suitable for high precision spectrum estimation of signals with high signal to noise ratio. Hanning window and Chebyshev window have better effect on spectrum leakage suppression, and the noise level near the signal frequency is not affected, but the frequency resolution is relatively low, suitable for general frequency estimation of signals with low signal to noise ratio. The study of using Welch algorithm in frequency estimation of short signals shows that it is not only the low spectrum resolution, but also the signal is easily disturbed by the noise, which leads to the failure of the detection.