基于动态规划提取信号小波脊和瞬时频率

Wavelet ridge and instantaneous frequency extraction based on dynamic optimization

提出一种基于动态规划提取信号小波脊和瞬时频率的方法,其基本思路是:对信号进行连续复Morlet小波变换,由变换得到的小波系数的局部模极大值初步提取其小波脊;为降低噪音影响,在初步提取的各小波脊附近选取部分小波系数,通过施加罚函数平滑噪音干扰引起的小波脊变化的不连续性,将小波脊的提取问题转变为最优化问题,采用动态规划方法计算得到新的小波脊;根据小波尺度与频率的关系由提取的小波脊识别出信号的瞬时频率。将提出的方法运用于含噪调频信号进行数值模拟分析和实测索冲击响应信号分析。研究结果表明,基于连续小波变化的模极大值可以有效提取信号小波脊和瞬时频率;采用施加罚函数的方法可有效降低噪音的影响;基于动态规划的方法可有效提高计算效率。

A new method of extracting signal wavelet ridge and instantaneous frequency based on dynamic optimization was presented. Its basic ideal was as follows： First, wavelet ridges were extracted initially based on maximum value of modulus of wavelet coefficients, then some coefficients near the initially wavelet ridges were chosen and penalty function was introduced. So the problem was transformed to an optimization problem. Finally, new wavelet ridges were extracted by using dynamic optimization method. According to the relation between wavelet scale and frequency of signal, the instantaneous frequency of signal was obtained. A frequency modulated signal with noise and impulse response signal of cable tested in laboratory were simulated and analyzed using the method. The results show that the present algorithm can be used to extract wavelet ridges and instantaneous frequency of signal. It can decrease influence of noise validly. In addition, the algorithm has high efficiency in computing.