傅里叶变换基本性质的物理诠释

PHYSICAL EXPLANATION FOR THE BASIC PROPERTIES OF FOURIER TRANSFORM

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.