2. 3. 1 Discrete Fourier transform DFT uFig 2.63(c): the Fourier transform of a nonperiodic discrete signal The Fourier transform of an infinite-length discrete time sequence is a periodic continuous spectrum FT:X()=∑ x(t, e2m (2203) IFT:x(t, 乙X(/2d 2.204) Whee〃sn△(n=0,±1+2…) At is the sampling period; fs is the sampling frequency of the time sequence❑Fig. 2.63 (c): the Fourier transform of a nonperiodic discrete signal. The Fourier transform of an infinite-length discrete time sequence is a periodic continuous spectrum. where Δt is the sampling period; fs is the sampling frequency of the time sequence. 2.3.1 Discrete Fourier Transform (DFT) ( )  ( )  =− − = n j f t n n FT X f x t e 2 : (2.203) ( ) ( ) − = 2 2 1 2 : s s n f f j ft s n X f e df f IFT x t  (2.204) t = nt(n = 0,1,2, ) n s f t 1  =