线性正则变换域的复能量密度函数  

The Complex Energy Density Function Associated with the Linear Canonical Transform

作　　者：赵志纯[1] 郭艳芬[2] 李炳照[1] 

机构地区：[1]北京理工大学数学学院,北京100081 [2]北京工业职业技术学院基础部,北京100042

出　　处：《数学的实践与认识》2014年第9期259-264,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61072097;61171195);教育部新世纪优秀人才支持计划(NCET-12-0042)

摘　　要：线性正则变换是经典Fourier变换的广义形式,目前在非平稳信号的参数检测与估计方面取得了优异的应用效果,但线性正则变换理论体系还不完善.探讨了线性正则变换相关的复能量密度函数的基本概念,并详细推导研究了其基本的数学性质与特点,在上述理论的基础上,通过仿真实验来验证所得到结论的准确性.为其在实际应用中发挥更大的作用奠定了基础.Linear canonical transform is the classical form of generalized Fourier transform, which has been played a very important role in modern applied mathematics. Especially it has achieved excellent application effect in detection of non-stationary signal and parameters estimation. For the condition of the theory of linear canonical transform is not perfect, we discussed the basic conception of the complex energy density function associated with the linear canonical transform, and studied the framework in detail. Based on the above, we operated the simulation to verify the accuracy of the conclusions which we have obtained. The simulation experiment shows that the theory would be playing bigger role in practical application in the future.

关 键 词：线性正则变换 复能量密度函数 线性调频信号 

分 类 号：O174.22[理学—数学]