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{e^j2πkn/N(n=0,1,…,N-1),(k=0,1,…,N-1)}是完备正变序列集,将周期序列信号x(n)分解成完备正交序列集{e^j2πkn/N(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。
It is presented that the sequence signal is expressed by orthogonal sequence set. It is proved that the orthogonal sequence set {e^j2πkn/N(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^j2πkn/N(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.