Representation of X(e)in terms of X,(j),X.(j) impulse train sampling x,(t)=x(t)s(t)=>x.(nT)(t-nT) 用连续时间傅里叶变换定义求X(①) X.(j2)-x(nT)(-nT)edt =x(nT)J6(-nT)edt -oo=-0 =∑x.(nT)en let xn]=x(nT),T=@ o:digital frequency数字角频率，rad DTFT 2:analog frequency模拟角频率，rad/s =之nile-jom=-Xem)）=X(en =x.U2-7∑x.U2-k2》 是X(2) 的周期延拓 三-00 Sampling frequency采样频率，rad/s 7[ ] ( ) j n j n x n e X e    =− − = =  7 s c ( ) c ( ) ( ) ( ) ( ) n x t x n x t s t T t n  T  =− = = − c ( ) n j Tn x nT e  =− −  = ( ) c ( ) ( ) n s j t X j x nT t  nT e dt  =−  −  −   =  −  let [ ] ( ), x n x nT = c  =T  DTFT Representation of in terms of , ( ) j X e  X j s ( ) X j c ( ) 2 , s T   =( ) ( ( )) 1 s c s k X j T X j k  =− =   =  −  Sampling frequency 采样频率, rad/s 用连续时间傅里叶变换定义求 X j s ( )  : 是 X j c ( ) 的周期延拓 ( ) j T X e  = ( ) ( ) j t c n x Tn  t nT e dt  =−  −   − = −   ω: digital frequency数字角频率, rad Ω: analog frequency模拟角频率, rad/s 冲激串采样) impulse train sampling