信号处理
信號處理
신호처리
SIGNAL PROCESSING
2010年
4期
569-572
,共4页
交换矩阵%酉特性%傅立叶变换%分数阶傅立叶变换
交換矩陣%酉特性%傅立葉變換%分數階傅立葉變換
교환구진%유특성%부립협변환%분수계부립협변환
Commuting matrix%Unitary%Fourier transform%Fractional Fourier transform
分数阶傅立叶变换比傅立叶变换更具有一般性,多年来引起人们深入研究.由于连续的分数阶傅立叶变换在工程实现时都要抽样离散化,直接对连续分数阶傅立叶变换的核离散化会失去很多重要的性质,因此人们研究它的离散实现并保持它具有与连续分数阶变换同样的性质.本文提出了一种新的交换矩阵实现离散分数阶傅立叶变换,其变换的离散核矩阵与连续变换的分数阶傅立叶变换核有相似性,诸如酉特性、可加性、正交性和可逆性.仿真结果证实了所提出的分数阶傅立叶变换核与连续分数阶傅立叶变换核的相似性以及两种变换对矩形信号这种典型信号的分数阶傅立叶变换的相似性.
分數階傅立葉變換比傅立葉變換更具有一般性,多年來引起人們深入研究.由于連續的分數階傅立葉變換在工程實現時都要抽樣離散化,直接對連續分數階傅立葉變換的覈離散化會失去很多重要的性質,因此人們研究它的離散實現併保持它具有與連續分數階變換同樣的性質.本文提齣瞭一種新的交換矩陣實現離散分數階傅立葉變換,其變換的離散覈矩陣與連續變換的分數階傅立葉變換覈有相似性,諸如酉特性、可加性、正交性和可逆性.倣真結果證實瞭所提齣的分數階傅立葉變換覈與連續分數階傅立葉變換覈的相似性以及兩種變換對矩形信號這種典型信號的分數階傅立葉變換的相似性.
분수계부립협변환비부립협변환경구유일반성,다년래인기인문심입연구.유우련속적분수계부립협변환재공정실현시도요추양리산화,직접대련속분수계부립협변환적핵리산화회실거흔다중요적성질,인차인문연구타적리산실현병보지타구유여련속분수계변환동양적성질.본문제출료일충신적교환구진실현리산분수계부립협변환,기변환적리산핵구진여련속변환적분수계부립협변환핵유상사성,제여유특성、가가성、정교성화가역성.방진결과증실료소제출적분수계부립협변환핵여련속분수계부립협변환핵적상사성이급량충변환대구형신호저충전형신호적분수계부립협변환적상사성.
For many years, the fractional Fourier Transform (FRFT) is deep investigated because of a generalization of the conventional Fourier transform. The engineering realization of the continuous FRFT has to be sampled and discretized, and such an achieved core matrix will lose many important properties. Thus, people have done many researches on the discrete realization of the core matrix of the continuous FRFT. In this paper, a newly commuting matrix is proposed to implement the discrete fractional transform (DFRFT). The core matrix of the DFRFT resulted from the presented commuting matrix has the similar properties with the core of the continuous fractional Fourier transform, such as unitary, additive, orthogonal, reversible. Finally, the simulation results have shown the similarity of the core matrix of the proposed DFRFT and the core function of continuous FRFT, and the similarity of two FRFTs of rectangular signal