傅里叶变换基本性质的物理诠释  

PHYSICAL EXPLANATION FOR THE BASIC PROPERTIES OF FOURIER TRANSFORM

作　　者：唐荣安[1] 洪学仁[1] 徐红萍[1] 高吉明[1] 豆福全[1] 

机构地区：[1]西北师范大学物理与电子工程学院,甘肃兰州730070

出　　处：《物理与工程》2016年第2期51-53,共3页Physics and Engineering

基　　金：国家自然基金项目(11365020;2014.1-2017.12);甘肃省高等学校基本科研业务费项目(极端条件下电子;离子及原子动力学特性研究;2013.1-2015.12);西北师范大学教学研究重点项目(物理学专业"云亭班"教学计划实施效果跟踪;2013.7-2015.7);西北师范大学教学研究项目(少数民族学生"数学物理方法"多元模式教学探究;2013)

摘　　要：数学物理方法是物理学专业基础课,其中的积分变换部分也是工程技术专业的基本教学内容.在该课程中,傅里叶变换往往是积分变换法教学的首要内容,而傅里叶变换的基本性质则是该部分的重点,也是其产生广泛应用的关键原因.本文从振动的合成与分解、物理学量纲分析等角度对傅里叶变换的线性定理、延迟定理、位移定理、标度变换定理、微分定理及卷积定理共6条基本性质进行了物理学诠释.对学生深刻理解和灵活运用傅里叶变换法解决物理问题、进行信号频谱分析大有裨益;对学生学习后续的量子力学、信号与系统等课程亦有帮助.Methods of mathematical physics is a basic professional course in physics, In which the integral transform is the basic teaching content in the field of engineers technology. In the course, Fourier transform is always arranged as the primary content in the chapter of integral transforms. Basic properties of Fourier transform are the key points in this part and the criti- cal reason for its wide range of applications. By using the synthesis and decomposition of vi- bration and the physics dimension analysis, this paper presents the physical interpretation of six basic properties of Fourier transform consisting of linearity theorem, shifting theorem, translation theorem, scaling theorem, derivative theorem and convolution theorem. The dis- cussion and results can not only help the students easily use Fourier transform in physics and signal analysis, but also help them understand the subsequent contents learned in the quantum mechanics, signals and systems, and other physical theories.

关 键 词：傅里叶变换 物理诠释 数学物理方法 

分 类 号：O411.1-4[理学—理论物理] G652[理学—物理]