5 The discrete-time fourier transform 5. The Discrete time Fourier Transform 5.0 Introduction (1)Fourier series (periodic signal xn jk(2I/N)n k=<N> k(2T/N) N ∑ (2) Fourier transform(aperiodic signal) [n]= X(e )endo X(e)=∑xnk5 The discrete-time Fourier transform 5.0 Introduction (1) Fourier series (periodic signal) 5. The Discrete time Fourier Transform      = =   =  − =  n N j k N n k k N j k N n k x n e N a x n a e (2 / ) (2 / ) [ ] 1 [ ]   (2) Fourier transform (aperiodic signal)      = = − + =−   j n N j j j n X e x n e x n X e e d       ( ) [ ] [ ] ( ) 2