【摘要】 提出了将序列信号分解成正交序列集表示,证明了正交序列集{ej2πNkn(n=0,1,…,N-1),(k=0,1,…,N-1)}是完备正交序列集,将周期序列信号x(n)分解成完备正交序列集{ej2πkNn(n=0,1,…,N-1),(k=0,1,…,N-1)}表示而定义为离散傅里叶级数,由离散傅里叶级数导出离散傅里叶变换定义.更多还原

【Abstract】 It is presented that the sequence signal is expressed by orthogonal sequence set.It is proved that the orthogonal sequence set {e^j2πknN（n=0,1,...,N-1）,（k=0,1,...,N-1）} is a complete set of orthogonal sequence set.The periodic sequence signal x（n） is decomposed to a complete orthogonal sequence set {e^j2πknN（n=0,1,...,N-1）,（k=0,1,...,N-1）} to define it as discrete Fourier series.And then,the definition of discrete Fourier transform is derived from discrete Fourier series.更多还原