基于多分辨分析的时频分析

短时傅里叶变换由于采用固定宽度的时域窗，在缓变与瞬变信号共存的宽频带信号分析中，其时间与频率分辨力矛盾突出。采用Mallat算法的小波变换能够将信号正交分解成多尺度的信号分量，然而所提供的时频信息不很直观，难以识别其时频谱。通过对短时傅里叶变换和小波变换在时频分析中的优缺点分析，发现两者具有互补性。因此本文提出基于多分辨分析的短时傅里叶变换（取名为WAVSTFT），即采用Mallat算法将信号分解成多个尺度信号分量，再对各分量分别做与其尺度相适应的短时傅里叶变换，最后把得到的各时频谱在同一个不相平面上叠加，从而得到信号的总体时频构造。经理论分析与实例验证，该方法有效可行，为工程测试中的时频分析提供了一种有效的手段。

Time frequency Analysis Based on Multi_resolution Analysis

The contradiction stands out between the time_resolution and frequency_resolution when STFT is used to analyse the multi_scale signal.especially when the difference is great between the largest scale and the smallest scale of the signal.Wavelet transform with Mallat algorithm can decompose the signal into several orthonormal signal component in multi scales.But due to that WT can only provide time_scale information of the signal,it is hard,sometimes even impossible,to understand the time_frequency information from the decomposition directly.After analyzing the advantages and disadvantages of the WT and STFT when used in getting the time_frequency information of a multi_scale signal,it can be found betweew them mutual complementarity evists.Accordingly in the paper it puts forward a new idea of STFT based on multi_resolution analysis called WAVSTFT,namely decomposing the signal by Mallat algorithm into several orthonormal signal components first,then applying STFT to every signal component with the width of the window matching the scale of the signal component and finally piling up all the spectrums of the signal components in a same phase plane and the whole time_frequency information can thas be got.After theoretical analysis and experimental simalation WAVSTFT is proved to be efficient and can provide the engineering world good means for time_frequency analysis.