从向量到实函数的傅里叶变换探析

Analysis of Fourier transform from vector to real function

从介绍向量空间中内积引申出向量的傅里叶展开,然后从向量空间过渡到实函数空间,从可积函数内积得到实函数的傅里叶展开.探讨向量空间中向量和实函数空间中函数的傅里叶展开,并讨论二者之间的联系,对理解基向量、基函数和傅里叶变换有一定的价值.

From the introduction of inner product in vector space,the Fourier expansion of vector is extended,then from vector space to real function space,the Fourier expansion of real function is obtained from the inner product of integrable function.The Fourier expansion of vector in vector space and the Fourier expansion of function in real function space is discussed,and the relationship between them is discussed,which is of certain value to understand the basis vector,basis function and Fourier transform.