一种基于自适应遗传算法的高斯FM^mlet变换最优时频原子搜索算法

A Search Algorithm of Optimal Time-frequency Atom of Gaussian FM^mlet Transform Based on Adaptive Genetic Algorithm

时频分析方法是当前非平稳信号分析与处理的研究热点,基于高斯FMmlet变换的信号表示方法成为目前分析具有线性和非线性频率切变信号的重要工具。高斯FMmlet变换在信号分析与处理中的应用面临的一个主要问题就是匹配追踪方法的数字实施方法。针对现有算法精度不高、收敛性差的问题,提出了一种基于自适应遗传算法的高斯FMmlet变换最优时频原子搜索算法。首先详细推导了时频原子有限长序列的离散公式,接着详细讨论了自适应遗传算法,然后给出了一种利用自适应遗传算法搜索高斯FMmlet变换最优时频原子的算法及其实现方法,最后结合实例对该算法进行了仿真研究。结果表明,该算法不但搜索精度很高,而且具有较好的收敛性和鲁棒性。

Time-frequency analysis method was one of important research areas in the analysis and processing of nonstationary signals and the signal representation method based on the Ganssian FM^mlet transform has become an important technique to analyses the signals consists of linear and non-linear frequency-shear components. One of the major problems of the application of Gaussian FM^mlet transform in signal processing was its digital realization method of matching pursuit. Aimed at the problems such as low accuracy and poor convergence in existing algorithms, a new optimal Ganssian FM^mlet time-frequency atom search method based on the adaptive genetic algorithm was proposed. Firstly a discrete formula of finite length time-frequency atom sequence was derived. Secondly an algorithm based on adaptive genetic algorithm was described in detail. Then a Gaussian FM^mlet time-frequency atom search algorithrn and its digital implement method based on the adaptive genetic algorithm were presented. Finally a simulation result of practiced example shows that the algorithm not only has high search precision but also has good convergence and robustness.