一种基于多窗宽度STFT的PSWFs信号时频分析方法

A Time-Frequency Analysis Method of PSWFs Based on Multi-window Width STFT

固定窗宽度的短时傅里叶变换(Short Time Fourier Transform,STFT)时频分辨率是固定的,难以对频率时变的椭圆球面波函数(Prolate Spheroidal Wave Functions,PSWFs)信号的时频分布特性进行全面分析。剖析了窗宽度对不同参数PSWFs信号STFT时频分布的影响,并提出了一种基于多窗宽度STFT的PSWFs信号时频分析方法。该方法基于PSWFs信号阶数、时间带宽积,计算PSWFs信号时域、频域零点间距离,根据零点间距离与STFT时频分辨率的关系,选取多个STFT窗宽度分别对PSWFs信号整体时频分布范围、时间轴方向的时频特征以及频率轴方向的时频特征进行分析。数值分析表明,相对于固定窗宽度的STFT,该方法兼顾时间分辨率与频率分辨率,能够更为全面地分析PSWFs信号整体时频分布范围情况以及时间轴方向与频率轴方向的时频特征情况。

Time-frequency resolution of Short Time Fourier Transform(STFT)with a fixed window width is fixed.And it is difficult to analyze comprehensively the time-frequency distribution characteristics of Prolate Spheroidal Wave Functions(PSWFs)with time-varying frequency.This paper analyzes the influence of different window widths on time-frequency distribution characteristics of different parameters of PSWFs.And a time-frequency analysis method for PSWF signals based on multi-window width STFT is proposed.This method first calculates the distance between time domain and frequency domain zero points of the PSWFs based on the order and time bandwidth product.Then,according to the relationship between the distance and the time-frequency resolution of the STFT,it selects multiple STFT window widths to analyze the overall time-frequency distribution range of the PSWF signal,time-frequency characteristics of the time axis,and time-frequency characteristics of frequency axis.Numerical analysis shows that,compared with the fixed window width STFT,this strategy takes into account time resolution and frequency resolution,and can analyze the overall time-frequency distribution range of the PSWF signal,the time-frequency characteristics of the time axis,and the time-frequency characteristics of frequency axis respectively.