小波变换作为新的信号分析工具,受到学者们的重视,然而如何将小波尺度与频率联系起来,是一个亟待解决的问题.为了求解小波的中心频率,提出了一种基于正弦波的模型,并将模型推广到任意采样间隔与任意小波尺度.由于模型的非凸性,传统的基于梯度的优化方法容易陷入局部最优,因此提出了一种基于Rossler吸引子的粒子群算法.实验给出了常见小波的频率值,并通过一个通信信号检测的例子证明了该方法的有效性.%As a latest signal analysis toolkit,wavelet transform receives increasing interest from scholars. However, the correlation between the wavelet scale and frequency is an outstanding problem. This paper proposed a sinusoid model to estimate the central frequency of mother wavelets, besides, the model is generalized to the situation of arbitrary sample interval and arbitrary scale of wavelet. Moreover, traditional gradient-based optimization method will find local optimum due to the non-convex property of the model, therefore, a novel Rossler-attractor based Particle Swarm Optimization( RPSO) method was proposed. Experiments gave the center frequencies of all common wavelets , and applied the proposed method in the field communication signal detection to validate its effectiveness and efficiency.
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