Infinite Impulse Response (IIR)

Transcription

1 IIR ILTER DEIGN BY POLE-ZERO PLAEMENT Pof. iipog Potisu Ifiite Impulse Respose IIR ecusive the diffeece equatio is, N o If the system is iitially at est, the impulse espose will have ifiite duatio. M N y a x b a y ] [ ] [ ] [ N N M M a a a b b b X Y H

2 A Naowbad Badpass ilte Also ow as a esoato Pass a sigle fequecy Place a pole at the poit iside the uit cicle that coespods to the esoat feq The coespodig agle is Place eos at the two ed fequecies, i.e., = = ad = - = / H e j j e cos is chose such that the filte is highly selective, i.e., small 3-dB BW of the passbad, D. D,.9 The gai facto is iseted to esue that the passbad gai is, i.e., o amplificatio. e j cos e e j j cos si

3 Example 8.7 Desig a secod-ode badpass filte usig the pole-eo placemet method ad satisfyig the followig specificatios: amplig ate = 8 H 3-dB badwidth = H Passbad cete fequecy = H Zeo gai at eo ad 4 H. A Naowbad Badstop ilte Also ow as a otch filte Remove a sigle fequecy Place eos at the poits o the uit cicle that coespod to the otch feq The coespodig agle is Place poles at the poits iside the uit cicle that coespod to the otch feq 3

4 4 cos cos e e e e H j j j j is chose such that the filte is highly selective, i.e., small 3-dB BW of the stopbad, D. The gai facto is iseted to esue that the passbad gai is, i.e., o amplificatio. cos cos.9, D Example 8.8 Desig a secod-ode otch filte usig the pole-eo placemet method ad satisfyig the followig specificatios: amplig ate = 8 H 3-dB badwidth = H topbad cete fequecy = 5 H

5 5 A ist-ode Lowpass ilte A widebad filte Pass fequecy compoets fom to c, the cutoff fequecy Place a eo o the uit cicle at = - Place a pole o the eal axis ad iside the uit cicle The gai facto is iseted to esue that the passbad gai is, i.e., o amplificatio H LP 4 4

6 Example 8.9 Desig a fist-ode lowpass filte usig the pole-eo placemet method ad satisfyig the followig specificatios: amplig ate = 8 H 3-dB cutoff fequecy = H eo gai at 4 H A ist-ode Highpass ilte A widebad filte uppess fequecy compoets fom to c, the cutoff fequecy Place a eo o the uit cicle at = Place a pole o the eal axis ad iside the uit cicle 6

7 7 The gai facto is iseted to esue that the passbad gai is, i.e., o amplificatio H HP 4 4 Example 8. Desig a fist-ode highpass filte usig the pole-eo placemet method ad satisfyig the followig specificatios: amplig ate = 8 H 3-dB cutoff fequecy = 38 H eo gai at eo H

8 A omb ilte Has seveal equally spaced passbads Passes D,, ad its hamoics fo a total of esoat fequecies, whee is the ode of the filte ad = / Place eos at the oigi Place poles at the poits equally spaced ad iside the uit cicle H is chose such that the filte is highly selective, i.e., small 3-dB BW of the passbad, D. D,.9 The gai facto is iseted to esue that the passbad gai is, i.e., o amplificatio 8

9 Example Desig a comb filte usig the pole-eo placemet method ad satisfyig the followig specificatios: amplig ate = H 3-dB badwidth = H Ode of the filte is A Ivese omb ilte A geealiatio of the otch filte Elimiates D,, ad its hamoics fo a total of esoat fequecies, whee is the ode of the filte ad = / Place eos at the poits equally spaced o the uit cicle Place poles at the poits equally spaced ad iside the uit cicle 9

10 H I is chose such that the filte is highly selective, i.e., small 3-dB BW of the stopsbad, D. D,.9 The gai facto b is iseted to esue that the passbad gai is, i.e., o amplificatio. Example Desig a ivese comb filte usig the pole-eo placemet method ad satisfyig the followig specificatios: amplig ate = H 3-dB badwidth = H Ode of the filte is