基于局部频率约束的动态快速匹配追踪方法

Dynamic and fast matching pursuit method based on local frequency constraints

传统的动态匹配追踪将原始信号中蕴含的瞬时属性作为其自适应分解的先验信息,而Hilbert变换求取的瞬时频率会出现"负频率",且极易受到噪声的干扰。首次将局部频率引进匹配追踪领域,局部频率采用最小二乘估计策略,综合数据点局部邻域内的瞬时信息,进而避免计算结果出现负异常现象。通过设计多个信号验证局部频率的合理性与稳定性。所提方法以局部频率替换瞬时频率来确定冗余字典搜索范围,与传统的动态匹配追踪相比,运算效率明显提高。理论模型验证了该方法具有较强的可行性和稳定性,并通过某研究区的瞬时谱尖灭点识别说明了该方法的实用性。

Traditional dynamic matching pursuit algorithm takes the instantaneous characteristics of the signal as a priori information for its adaptive greed decomposition.However,the instantaneous frequency obtained by Hilbert transform always exhibits"negative frequency"phenomenon,which is susceptible to noise interference.In this paper,the use of local frequencies was introduced into the matching pursuit field for the first time.The method adopts a least squares inversion strategy and combines the instantaneous information in the neighbors of the data point,avoiding negative anomalies in the calculation.The method replaces the instantaneous frequency with the local frequency to determine the redundant dictionary search range,and the computational efficiency is improved noticeably.The stability and feasibility of the approachwere verified by multiple designed signals and theoretical models,andtested in recognizing tip point of instantaneous spectrum in real data cases.