8.1 Representation of Periodic Sequence: the discrete fourier series 2丌 2丌 2丌 k+mN)n 2mn Due to the periodicity of the complex exponential we only need n exponentials for discrete time Fourier series 小]=∑[k]e0xA nk=07 8.1 Representation of Periodic Sequence: the Discrete Fourier Series ◆Due to the periodicity of the complex exponential we only need N exponentials for discrete time Fourier series   (2 ) 1 0 1 / [ ] N k j N kn x n X k e N  − = =  ◆No need   1 (2 / ) [ ] j N kn k x n X k e N  =  ( ) ( ) 2 2 2 2 j k n j kn j kn N mN N N j mn e e e e     + = =