一种全新的积分变换——双正交梅林变换

A new integral transform: biorthogonal Mellin transform

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.