2. (a) An ideal, zero-phase highpass filter has frequency response {} So, |w| < We Hhp(w) = Derive the corresponding impulse response 1 hhp(n) = Hup(w) = (b) An ideal, zero-phase bandpass filter has frequency response hop(n) = π > س > we ,1 for n = 0 sin(wen), for n>0 πη Derive the corresponding impulse response {{ Hbs (w) = hbs(n) = لما 1 ول > w ,0 1, we ≤|w|≤ W₂ 0, W₁ ≤|w|≤ T sin(wun) TIL (c) An ideal, zero-phase bandstop filter has frequency response 1, |w| 0 7711 Derive the corresponding impulse response wie we 1 π sin(wen) An for n = 0 - wa > س > we ,0 T > س > we ,1 7 " for n= = 0 sin(wun) for n>0 An

Introductory Circuit Analysis (13th Edition)
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2. (a) An ideal, zero-phase highpass filter has frequency response
0₂ |w| < We
Hhp(w)
hhp(n)
Derive the corresponding impulse response
1
=
Hop(w) =
hop(n) =
Wie
u-we
π
(b) An ideal, zero-phase bandpass filter has frequency response
0₁ |w| <we
1, we ≤ |w|≤ w₂
Derive the corresponding impulse response
hbs (n) =
T > س > we ,1
sin(wen)
TN
Hbs (w) =
We
ㅠ
7
sin(wun)
TTL
7
T > س > w ,0
for n =
for In> 0
sin(wen)
7771
Derive the corresponding impulse response
1
Wie we
7T
sin(wen)
πN
= 0
(c) An ideal, zero-phase bandstop filter has frequency response
1, |w| <we
0, we ≤ |w|≤ wie
"
T > س > wa ,1
for n = 0
for n > 0
sin(wun)
пn
for n=
0
for n > 0
Transcribed Image Text:2. (a) An ideal, zero-phase highpass filter has frequency response 0₂ |w| < We Hhp(w) hhp(n) Derive the corresponding impulse response 1 = Hop(w) = hop(n) = Wie u-we π (b) An ideal, zero-phase bandpass filter has frequency response 0₁ |w| <we 1, we ≤ |w|≤ w₂ Derive the corresponding impulse response hbs (n) = T > س > we ,1 sin(wen) TN Hbs (w) = We ㅠ 7 sin(wun) TTL 7 T > س > w ,0 for n = for In> 0 sin(wen) 7771 Derive the corresponding impulse response 1 Wie we 7T sin(wen) πN = 0 (c) An ideal, zero-phase bandstop filter has frequency response 1, |w| <we 0, we ≤ |w|≤ wie " T > س > wa ,1 for n = 0 for n > 0 sin(wun) пn for n= 0 for n > 0
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