上海交通大学：《数字信号处理 Digital Signal Processing（B）》教学资源_Handouts_ch9 DFT

DTFT Digital Signal Processing--DFT/FFT Algorithms XGo)=∑xn)eom tm=27,ee一dn n=-c0 (2)=FE.()]=Fx,()Mt)]=x,()M()ed M)=7之em, x(1)emveRdt m=- =7三0 ed (2)=于∑X,2-jm2,) 上游充通大学

Digital Signal Processing—— DFT/FFT Algorithms DTFT (j ) ( )e j n n X x n        1 ( ) (e )e 2 j j n x n X d          ( ) ˆ ( )  ( ) ( ) ˆ X j F x t F x t M t a   a  a                           M j m t a j t m jm t a j t a x t e dt T x t e e dt T x t M t e dt s s ( ) ( ) 1 ( ) 1 ( ) ( )        m a a s X j jm T X j ( ) 1 ( ) ˆ      m jm t e s T M t 1 ( )

FT、FS、DTFT Digital Signal Processing--DFT/FFT Algorithms )()e XG2)=∫x0eodi x0=∑XUk2,)ea 0=2元XUD)e严d0 XGo)=∑x(m)em DTFS? 11=-00 m=2aXee“da 上游充通大￥

Digital Signal Processing—— DFT/FFT Algorithms FT、FS、DTFT (j ) ( )e j n n X x n        1 ( ) (e )e 2 j j n x n X d          (j ) (t)e j t X x dt        1 ( ) ( )e 2 j t x t X j d          0 / 2 0 / 2 1 (jk ) (t)e p p T jk t T p X x dt T       0 0 ( ) ( )e jk t k x t X jk       DTFS?

DFS Digital Signal Processing--DFT/FFT Algorithms (n)=x(n+kN) ,(0）=∑Xe=X(k2,ea I cT/2 X,=X(2)=T∫T(ea 2 t= 2π nAT= 2π △T 2t= n T N△T N T=NAT el2t→eN t=n△T e→e0 上游充通大学

Digital Signal Processing—— DFT/FFT Algorithms DFS x n x n kN ( ) ( )   1 1 1 ( ) ( ) jk t jk t T k k k x t X e X k e            1 / 2 1 / 2 1 ( ) ( ) T jk t k T T X X k x t e dt T        T T N T   t n T   1 2 2 2 t t n T n T N T N          1 2 j n j t N e e    1 2 2 2 j n j t N e e    1 2 j kn jk t N e e   

DFS Digital Signal Processing--DFT/FFT Algorithms )m hn N e N =e NK-0 2π (k-r)n n=0 n=0 1 k-r=mN 0 others 上游交通大学

Digital Signal Processing—— DFT/FFT Algorithms DFS 2 2 2 2 2 ( ) 2 j k lN n j kn j Nln j kn j kn N N N N N j ln e e e e e e           1 2 0 1 ( ) ( ) N j kn N k x n X k e N      1 1 1 2 2 ( ) 0 0 0 1 ( ) ( ) N N N j rn j k r n N N n n k x n e X k e N               1 2 ( ) 0 1 1 0 N j k r n N k k r mN e N others            1 1 2 ( ) 0 0 1 ( ) N N j k r n N k n X k e N               

DFS Digital Signal Processing--DFT/FFT Algorithms 交哈空1-)r=w 0 others X(k)()e n=0 Kk+=2me导a-艺e。京 n=0 n=0 0me原- W-1 = k=0 上游充通大￥

Digital Signal Processing—— DFT/FFT Algorithms DFS 1 1 2 ( ) 0 0 1 ( )[ ] N N j k r n N k n X k e N         ( ) 0 X k k r mN others       1 2 0 ( ) ( ) N j nk N n X k x n e      1 1 2 2 2 ( ) 0 0 ( ) ( ) ( ) N N j k lN n j kn j lNn N N N n n X k lN x n e x n e e                 1 2 0 ( ) ( ) N j kn N k x n e X k       