积分变换的电学应用

Electrical Application of Integral Transformation

通过非周期函数Fourier变换式的三角函数形式与周期函数的Fourier级数对比,指出两者都是无穷多项正弦谐波的叠加:后者是可数无穷多项的叠加,前者是不可数无穷多项的叠加,从而指出了Fourier变换的电学背景及非周期电路的分析方法。单位阶跃函数的一个表现为电路中电容上电压(或电感中电流)的跳跃变化,这将引起电容中电流(或电感上电压)的巨变,而单位脉冲函数体现了这一特点。综述了Fourier变换、单位脉冲函数、卷积、Laplace变换在电路分析中的应用。

Through the contrast between the triangle function of non-period function of Fourier transformation and the Fourier series of the period functions.It was pointed out that both are all the addition of the endless several sine waves. The latter is countable,infinite and polynomial;the former is uncountable.Thus it discussesd the electrical backgrounds of Fourier transformation and the analytical method of the non- period electric circuits. An expression of the unit rank jumping function is the jumping variety of the electric voltage in the electric capacity （or the electric current in electricity feeling）, which will cause a huge change in the electric current（ or the electric voltage）, but the unit pulse function gave this characteristics.It also enumerated application of the Fourier transformation, unit pulse function, convolution and Laplace transformation in circuit analysis.