短时傅里叶变换的时频聚集性度量准则研究

为了使短时傅里叶变换(short time Fourier transform,简称STFT)获得良好的时频聚集性,必须根据信号的具体特点来选择窗长。分析了现有窗长选择准则的选择机理及其优缺点,发现归一化3阶Renyi熵准则与Stankovic准则一般只会取到窗长选择范围的最大值,并分析了出现这种问题的原因,而其他准则得到的也不是最优的窗长。提出了一种新的基于对数窗能量的窗长选择准则。对数窗能量与窗长是一种非线性关系,这显著区别于普通窗能量随窗长线性增长的特性,且其增长速度与窗型无关,并在短窗和长窗具有不同的增长速度,因而能够在短窗和长窗之间取得良好的折衷。提供了仿真信号和实际信号的处理实例,其结果证明对数窗能量准则使STFT获得了良好的时频聚集性,效果优于现有的窗长选择准则。

Study on Measure Rule of Time Frequency Concentration of Short Time-Fourier Transform

To achieve good time-frequency concentration in short time Fourier transform (STFT), window length should be selected according to the characteristic of the processed signal. The selection mechanism of existing rules is analyzed and their merit and defect are discussed. It is found that normalization third order Renyi entropy rule and Stankovic rule often reach the maximum of the window length range while the window lengths determined by other rules are also not optimal. The reason for this phenomenon is analyzed. A new window length selection rule based on logarithmic window energy is put forward. The relationship between logarithmic window energy and window length is non-linear, which is quite different from the linear increase characteristic of common window energy with respect to window length. The logarithmic window energy increases with different speeds during the short and long window and the increasing speeds are independent of the type of window, thus good compromise between the short and long window length can be achieved. The processing examples of simulation and practical signals are provided, which demonstrate that STFT can obtain good time frequency concentration using the window length determined by the proposed rule,and the effect is better than that of the existing rules.