Frequency-Selective Filters Ideal lowpass filter(discrete-time system) l(e") < 0.w<w<兀 sn w n <n<0 2丌 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 Hh(en) <1 1,w<w<丌 m()=-51 0<n<O 丌n 2丌 2丌
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) <w P 0. others
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) < J l1, others 10
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 ler(n)l tolerance scheme discrete-time 1+a1 容限图 IH(ejm) 1-6 continuous-time 1+a1 Passband transition Stopband Passband i Transition W=OT Hle ow 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 =