一种全新的积分变换——双正交梅林变换  

A new integral transform: biorthogonal Mellin transform

作　　者：张亮 陈辉[1] 杜庆磊[1] 王永良[1] Liang ZHANG;Hui CHEN;Qinglei DU;Yongliang WANG(Department of Early Warning Technology,Air Force Early Warning Academy,Wuhan 430019,China)

机构地区：[1]空军预警学院预警技术系,武汉430019

出　　处：《中国科学：信息科学》2023年第10期2034-2052,共19页Scientia Sinica(Informationis)

基　　金：国家自然科学基金(批准号:62271498,62001510)资助项目。

摘　　要：针对调频(frequency modulation, FM)类信号处理问题,提出一种全新的积分变换——双正交梅林变换(biorthogonal Mellin transform, BMT).该变换与傅里叶变换(Fourier transform, FT)、双正交傅里叶变换(biorthogonal Fourier transform, BFT)、梅林变换(Mellin transform, MT)、分数阶傅里叶变换(fractional Fourier transform, FRFT)存在密切关系,能够解决指数为整数或者分数的幂函数调频(power frequency modulation, PFM)信号检测、参数估计、滤波等问题.文中给出了BMT定义、基本性质和典型函数变换结果,设计了一种基于指数采样理论的离散BMT快速计算方法.实验结果表明, BMT构思新颖,理论完备,具有广阔应用前景.A new integral transform,called the biorthogonal Mellin transform(BMT),is proposed to deal with the frequency modulation signals.The transform is closely related to the Fourier transform,the biorthogonal Fourier transform,the Mellin transform,and the fractional Fourier transform and can solve the problems of detection,parameter estimation,and ltering for power-function frequency modulation signals,whose instantaneous frequency is a power function,whether their exponent is a positive integer or fraction.In this paper,the de nition of the BMT,its basic properties,and typical transformation results are given,and a fast calculation method of discrete BMT is designed based on the exponential sampling theorem.The experimental results show that the proposed BMT has the prospect of a broad in uence,with a novel conception and complete theory.

关 键 词：双正交梅林变换 双正交傅里叶变换 梅林变换 分数阶傅里叶变换 数值计算 

分 类 号：TN911.7[电子电信—通信与信息系统]