Frequency-Selective Filters Ideal lowpass filter(discrete-time system) W<w 0,1。<lw<兀 SIn w n 0<n<O 元- 2丌
7 Frequency-Selective Filters ◆Ideal lowpass filter (discrete-time system) ( ) = w w w w H e c j w c l p 0, 1, 0 wc − 2 − − wc 2 ( ) jw H e 1 ( ) = − n n w n h n c l p , sin
Frequency-Selective Filters Ideal highpass filter(discrete-time system 0 W<<兀 h(n)=8[n 0<1<00 H 2丌 2丌 8
8 Frequency-Selective Filters ◆Ideal highpass filter(discrete-time system) ( ) 0, 1, jw c hp c w w H e w w = 0 wc − 2 − − wc 2 ( ) jw H e 1 ( ) sin , c hp w n h n n n n = − −
Frequency-Selective Filters Ideal bandpass filter(discrete-time system) ww<w H 0. others H -
9 Frequency-Selective Filters ◆Ideal bandpass filter(discrete-time system) ( ) = others w w w H e j w c c bp 0, 1, 1 2 0 1 wc 1 − − wc ( ) jw H e 1 2 wc 2 − wc
Frequency-Selective Filters Ideal bandstop filter(discrete-time system H,(en) <1 others H -
10 Frequency-Selective Filters ◆Ideal bandstop filter(discrete-time system) ( ) = others w w w H e j w c c bs 1, 0, 1 2 0 1 wc 1 − − wc ( ) jw H e 1 2 wc 2 − wc
tolerance scheme容限图 Figure depicts the typical representation of the tolerance limits associated with approximating an ideal lowpass filter lHer(in)l tolerance scheme discrete-time 1+6 容限图 H(e°) 1-61 continuous-time 1+1 Passband i Transition Stopband Passband i Transition W=QT 6 he/=h 0
11 tolerance scheme 容限图 tolerance scheme 容限图 ◆Figure depicts the typical representation of the tolerance limits associated with approximating an ideal lowpass filter. w T = continuous -time discrete-time ( ) eff jw w H H j T e =