基于LabVIEW验证典型波形的傅里叶级数合成  

Verification of the Fourier Series Synthesis of Several Typical Waveforms Based on LabVIEW

作　　者：狄静宇 申剑辉 DI Jingyu;SHEN Jianhui(Department of Transportation and Vehice Engineering,Tangshan University,Tangshan Hebei 063000,China)

机构地区：[1]唐山学院交通与车辆工程系,河北唐山063000

出　　处：《河北软件职业技术学院学报》2024年第1期16-19,共4页Journal of Hebei Software Institute

摘　　要：基于经典傅里叶级数理论,任意周期信号都可分解为一系列不同频率和幅值的正弦或余弦信号,称之为信号傅里叶级数的分解;反之,称之为信号傅里叶级数的合成。故可在推导几种典型周期信号的傅里叶级数展开式的基础上,使用LabVIEW软件进行程序设计:将不同频率和幅值的正弦或余弦信号进行相互叠加,从而验证几种典型波形的傅里叶级数合成;同时,也显示并验证了吉布斯现象,即在信号波形的不连续点会出现“毛刺”的现象。Based on the classical Fourier series theory,any periodic signal can be decomposed into a series of sine and cosine signals with different frequency and amplitude,which is called Fourier series decomposition of signal;conversely,it is called Fourier series synthesis.Therefore,based on the derivation of Fourier series expansions for several typical periodic signals,LabVIEW software can be used for program design,the Fourier series synthesis of several typical signal waveforms is verified by superposition of sine and cosine signals with different frequencies and amplitudes.Meanwhile,it also displayed and verified the Gibbs phenomenon,which is the phenomenon of burrs appearing at discontinuous points in the synthetic waveforms.

关 键 词：傅里叶级数 LabVIEW三角波 方波 锯齿波 

分 类 号：TN911.6[电子电信—通信与信息系统]