Studying the Two New Convolutions of Fractional Fourier Transform by Using Dirac Notation  

作　　者：Ying Cai Cuihong Lv Nan Huang Nan Jin 

机构地区：[1]School of Physics and Electronic Engineering,Jiangsu University,Zhenjiang 212013,Jiangsu Province,China

出　　处：《Journal of Contemporary Educational Research》2022年第5期38-47,共10页当代教育研究（百图）

基　　金：National Natural Science Foundation of China(Grant Number:11304126);College Students' Innovation Training Program(Grant Number:202110299696X)。

摘　　要：Based on quantum mechanical representation and operator theory,this paper restates the two new convolutions of fractional Fourier transform(FrFT)by making full use of the conversion relationship between two mutual conjugates:coordinate representation and momentum representation.This paper gives full play to the efficiency of Dirac notation and proves the convolutions of fractional Fourier transform from the perspective of quantum optics,a field that has been developing rapidly.These two new convolution methods have potential value in signal processing.

关 键 词：Fractional Fourier transform Convolution theorem Quantum mechanical representation Dirac notation 

分 类 号：O17[理学—数学]