分数阶Fourier变换域极值搜索的混沌优化算法研究

正如傅里叶变换采用正弦基,单频信号能够在频域形成峰值,分数阶Fourier变换采用线性调频基,线性调频(LFM)信号能够在分数阶Fourier域上实现聚焦,利用此聚焦性通过搜索峰值可实现LFM信号检测和参数估计.通常采用步进式搜索方法,效率低下.为了克服该缺点,通过对分数阶Fourier域优化问题本质的研究,将混沌优化算法引入到分数阶Fourier域极值搜索中.仿真结果表明:本文的方法优于传统的步进式搜索法.

Study of chaos optimization algorithm in the fourier domain for extremum searching

As the sinusoidal signal can be concentrated in the Fourier domain due to the orthonormal sine basis of the Fourier transform. The linear frequency modulation (LFM) signal can be concentrated in the fractional Fourier domain due to its orthonormal chirped basis of the fractional Fourier transform. So the detection and parameter estimation of LFM signal is usually completed by step-based searching method for extremum searching in the fractional Fourier domain. In order to resolve the disadvantage of inefficiency of step-based searching method, Chaos optimization algorithm is introduced to the fractional Fourier transform for extremum searching based on the study for the nature of fractional Fourier optimization problem. Simulation results show that the performance of Chaos optimization algorithm is better than that of the traditional step-based method.