分数阶Fourier变换中量纲归一化因子的选取  

Selection of dimensional normalization parameters in fractional Fourier transform

作　　者：刘锋[1] 徐会法[1] 陶然[2] 

机构地区：[1]海军航空工程学院电子信息工程系,山东烟台264001 [2]北京理工大学信息科学技术学院,北京100081

出　　处：《系统工程与电子技术》2011年第2期237-241,共5页Systems Engineering and Electronics

基　　金：国家杰出青年科学基金(60625104)资助课题

摘　　要：针对分数阶Fourier变换数值计算中量纲归一化因子的优化选取,分析了量纲归一化对chirp信号的调频率和初始频率的影响,以及chirp信号在(p,u)平面上的尖峰位置的影响,推导了两个chirp信号的尖峰在p轴和u轴上的投影距离与量纲归一化因子的关系。发现两个尖峰的距离随着量纲归一化因子的变化而变化,并且具有极大值。提出一种量纲归一化因子选取的方法,通过调节信号的观测时间和采样频率,选择合理的量纲归一化因子,增大两个信号尖峰间的距离,减小多分量chirp信号在分数阶Fourier域的相互影响。仿真结果验证了该方法的有效性。Dimensional normalization is required in the digital computation of the fractional Fourier transform,but how to select a suitable dimensional normalization parameter is not studied yet.For this reason,the influence of the dimensional normalization on the initial frequency,the chirp rate and the peak＇s position on the（p,u） plane is analyzed.And the relationship between the dimensional normalization parameter and the distance between two chirp signals＇ peaks at the p axis and the u axis is deduced.It is discovered that the distance between two peaks varies with the dimensional normalization parameter and it has maximums.A method is presented to choose the dimensional normalization parameter.By changing signals＇ observation time and sampling frequency,a suitable dimensional normalization parameter is selected to increase the distance between two signals＇ peaks and reduce the mutual influence among multi-component chirp signals.The effectiveness of this method is verified by the simulation results.

关 键 词：分数阶FOURIER变换 CHIRP信号 量纲归一化因子选取 

分 类 号：TN957.51[电子电信—信号与信息处理]