基于小波包分解的自适应同步压缩短时傅里叶变换

Adaptive synchro-squeezed short time Fourier transform by wavelet packet decomposition

获得同时含有稳态频率和瞬态频率成分信号的高分辨率时频分布是时频分析的重点与难点,为了解决此类信号进行同步压缩短时傅里叶变换(synchro-squeezed short time Fourier transform,SSTFT)时窗长受限的问题,提出了基于小波包分解的自适应同步压缩短时傅里叶变换(adaptive synchro-squeezed short time Fourier transform by wave packet decomposition,WPD-ASSTFT)方法。首先,借助小波包分解将信号分解为若干个子信号;之后,对不同的子信号进行自适应窗长选择,确定使子信号进行短时傅里叶变换(short time Fourier transform,STFT)的时频分布Renyi熵值最小时对应的窗长——最优窗长;然后,将各个子信号在最优窗长下进行SSTFT;最后,将所有子信号的时频分布相加得到原始信号的时频分布。通过小波包分解,将信号分解为不同频率范围的子信号,通过自适应窗长选择,使得SSTFT的时频图分辨率最佳。利用该方法对仿真信号和铁路轴箱加速度信号进行分析,结果表明:由WPD-ASSTFT得到的时频分布具有良好的分辨率。

Obtaining the high-resolution time-frequency distribution with both steady and transient frequency components was the key of time-frequency analysis.In order to solve the limitation of window of synchro-squeezed short time Fourier transform(SSTFT)for thus signals,and obtain a signal time-frequency distribution with better resolution,an adaptive synchro-squeezed short time Fourier transform by wavelet packet decomposition(WPD-ASSTFT)was proposed.Firstly,the wavelet packet decomposition method was used to decompose the signal into several sub signals.Then the adaptive window length was selected for different sub signals to determine the optimal window length which corresponding to the minimum Renyi entropy of the time-frequency amplitude of the sub signal after short time Fourier transform(STFT).Then the sub signals were subjected to SSTFT to obtain the time-frequency image with the best resolution of each sub signal.Finally,the time-frequency distribution of original signal was obtained by adding the time-frequency amplitudes of all the sub signals.After wavelet packet decomposition,the signal was decomposed into different sub-signals with different frequency ranges.After adaptive window length selection,the time-frequency distribution resolution of SSTFT was the best.The simulation signal and railway axle box acceleration signal were analyzed by this method.The results show that the time-frequency distribution obtained by WPD-ASSTFT has good resolution.