建立在付里叶变换理论上的相量法原理

Mathematics Principle of the Phsor Established on the Fourier Transform Theory

在系统理论中,付里叶分析与付里叶变换的工具使我们能够对一个线性时不变系统在正弦激励下的响应进行分析,比如一个电路对正弦输入下的响应。但是在电路理论中,电路在正弦输入下的响应分析法主要是应用相量法。在教科书中,这种方法常常通过尤拉公式或旋转矢量来引出,这与付里叶分析或付里叶变换无任何联系。既然电路分析也是系统分析,因此,在正弦输入下的分析方法应是统一的,即相量法一定与付里叶变换有必然的联系。根据付里叶变换讨论了相量法的数学原理。建立了付里叶变换和相量法之间的对应关系。在此基础上,定义了符号变换,讨论了符号变换的若干性质。应用符号变换于正弦激励下系统分析,其传输值和相移的概念与系统理论是一致的。

In the theory of the system, the tools of Fourier analysis or Fourier transform enable us to analyze the response of a LTI system, such as a circuit, to such sinusoidal inputs. But in the theory of the circuit, the main approach to analyze the response of a circuit to sinusoidal inputs is phsor. The phsor is often introduced by the Euler formula or by rotate vector on the text books, which do not have any relation with Fourier analysis or Fourier transform. Since the circuit analysis must be the system analysis. It is must be unity of analysis approach to sinusoidal inputs. That is, phsor must be related to Fourier transform. The paper discussed the mathematics principle in light of Fourier transform and established the corresponding relation between phsor and Fourier transform. On the basis of this, the sign transform has been defined and some of characters of the sign transform have been discussed. Applied the sign transform on the system analysis which encouraged by the sinusoidal, the results of the concepts of the transmission value and phase shift are identical with system theory.