Tuyen tap bao cao khoa hgc Hgi nghj Khoa hgc ky thuat Do luflng toan quoc idn thtt IV Hd Ndi, 11 -2005
(THIET KE BO LOC SO BANG PHUONG PHAP DiOLT DIEM KHONG - DIEM CUC VA Q N G DUNG LOC N H l i u NGUON DIEN TRONG TIN HIEU DIEN TIM
Phan Duy Hdng, Phgm Thi Nggc Yen, Eric Castelli Trung Idm nghien cdu qud'c leMICA - Dgi hgc Bdch Khoa Hd Ngi
Tdm tdt:
Mdt vdn di quan Irgng trong viic Ihu tin hieu dien tim (ECG) Id tin hidu do bi nhiiu cdng tit ngudn dien ludi. Mot phuang phdp Id't cd khd ndng logi thdnh phdn nhiiu ndy la ddng bd Igc Notch, bd Igc ndy cd he sdkhuich dgi Id 1 Igi tdl cd tdn sdtrdldn sd notch, Igi ddy he sd khuyech dgi bdng 0. Bdi bdo ndy long kit viec thid't kebd loc bdng phuang phdp ddt diim khdng - diem ctfc, dua ra cdc bieu thiic dinh lugng. Mgt vi dtt cua bg Igc Notch dd thiit ki dugc si dung di Igc nhiiu lin hiiu dien lim. Cdc md phdng dugc Ihuc hien tren phdn mim Matlab cho kit qud tdt.
Abstract:
A major problem in Ihe recording of electrocardiograms (ECG) is that Ihe measurement signal is degraded by additive power line (AC) interference. A well-known method capable of reducing AC inteiference is Ihe use of a notch filler characterized by a unit gain at all frequencies except at notch frequency where gain is zero. This article summarizes the design of the filter by Pole-Zero placement method, gives the quantitative expressions. An example of the Notch filter designed is used lo suppress noise of Ihe signal ECG. The simulations carried out on Matlab software have given good results.
dang:
I. DAT VAN DE
Bifiu thttc ham tmyfin dat H(z) cia mgt bfi Igc stf tflng quat cfl thfi bifiu difin dufli
M-« ( Z - Z | X z - Z 2 ) ( z - Z 3 ) - ( ^ - ^ « )
H(z) = Kz'
(z-p,)(z-p,)(z-p,)...(z-p^)
Uong dfl z„ Z;,..., ZN la cdc difim khflng vd p,, p^,..., p„ Id cdc difim cue cia H(z). Dfi cfl cdc hfi thflng nhdn qua vd fin dinh, cdn thoa man |;7,| < I hay cac difim cue phai nam trong vflng Uon dom vi, khflng cfl rdng bufie nao vfli cdc difim khflng.
Ddp ttng tdn sfi cfl thfi dttgc bifiu difin nhtt sau:
K'")|=l^lt '"-•lk"--= e"'-
(hfi stf khufich dai)
Arg(H(e'°)) = (M-N)n-^arg(e"'-z,) + ...- -arg(e'"-p,)-...-arg(e'"-p„)
' - ' . )
(pha)326
Vdi yfiu edu dang dap dng tan sd-bifin dd, ngudi ta cd the thilt kfi' dfi dang ham truyin dat cua bfl Igc sd vdi phuofng phap dat cac dilm khflng va dilm cue. Bai bdo ndy tong kfi't cac nguyfin tdc chinh cho phucfng phdp nay nhu sau:
- D l tang cudng dap dug bien dfl tai mdt tdn sd co, chdng ta nfin ddt mflt dilm cue gdn vdi dilm e'" (e'" ndm trfin vdng trdn dem vj va bilu difin tdn sd oo).
- Di giam nhd dap dng bifin do tai mflt tdn sd m, chung ta nen ddt mdt dilm khdng gdn voi dilm e'".
- Viec dat cac dilm cue va dilm khflng chdng nhau se tang cudng thfim anh hudng cua chung.
- D l n i n hoan toan ham truyin tin hifiu tai tdn sd bd't ki cd t h i thuc hifin bdng cdch dat mdt dilm khflng trfin vdng trdn don vi tuong utig vdi tdn sd dd. Ddy la nguyfin li cua bfl Igc Notch (hay ehan dai).
II. VI DU THIET KE V i d u I;
D l thilt k l mdt bfl Ige thdng eao, chung ta cdn nen ddp dng bifin dd lai dai tdn sd thdp trong khi tdng cudng nd tai dai tdn cao. Hinh 1 chi ra vi tri eiia cdc dilm cue va dilm khdng trong mat phing z.
Ddy Id bfl Igc thflng cao bdc 3. Vific ddt 3 dilm khflng tai z=l lam giam manh ddp dng bifin dfl tai tdn sd thd'p, trong khi dd cdc dilm cue tai Idn edn z=-l trong vdng trdn don vi tdng cudng he sd dap dng d tdn sd cao.
Su dung phdn m i m Matlab, chung ta cd thi ve cdc dilm khdng vd dilm cue trong mdt phang z vdi lfinh zplane. Lfinh poly cho phep tim ede hfi sd eua ham truyin bd Igc. Cudi e&ng sii dung lfinh freqz ta cd thi ve dugc ddp dng tdn sd vd ddp dng pha eiia bd Igc.
Bdy gid ta di din mflt thilt k l cu t h i hon.
Vidu 2:
Thifi't k l bfl Igc Notch 50 Hz. Bfl loc nay dugc
sir dung d l loai nhifiu ngudn difin trong qud trinh xtt li Hi„h 2. Phan bo cdTdi^m cue va dilm cdc tin hifiu sinh hgc (vi du tin hifiu difin tim), khong trong mat phSng Z
Ta chgn: Vi du vdi cac dilm cue 0,9; 0,9±0.1i Hinh 1. Dat cac dilm khong va
dilm cue trong mat phdng Z
/), =0.9e '«<> , p^=0.9e ham truyin ciia bfl loc la:
{z-Zj)(z-z^) H{z) = -
Ki hifiu o}„ , ta thd'y khi co ra xa {p-Px){p-Pi)
50
^ 8 0 '
dilm (OQ, khoang each iix Z, vd P, dfi'n e-''" se xd'p xi nhau. Tuong tu vdi cdc khoang edeh txtT^vh.
Pj. Vi vdy hfi sd khuyich dai se xdp xi bdng I. Chi khi to tiln tdi gdn co^ thi hfi sd khuyich
Nomiilizeil Frequsncy (n tad/sample)
Hinh 3 Dac tuyfi'n bien dp-tdn sd
dai se thay dfii nhifiu va tai (O. thi he sfl khuyfi'ch ImZ dai bang 0. Dac tuyfi'n tdn sfi bifin do c i a bfl cua bfl igc Notch dugc ve o hinh 3.
cau hoi dat ra la lam sao ta cfl the tinh cdc tdn sfl md tai dfi ddp ttng bifin dfi giam 3 dB hay -7= Idn. Dfi ufle luong cdc tdn so ndy, ta thdy V2
khi (0 rdt gdn (o„ ching ta cfl thfi bo qua anh httflng c i a Pj vd Z;. Vi vay, dfi Ifln ddp ttng bifin dfi = khoang each ttt Z, dfin e^' chia cho khoang cdch ttt P, dfin e'" .Gia s i E rdt gdn voi Z| trfin vfing trfin don vi vd cfi tdn sfi tai difim
suy gidm 3dB. Ta cfl EZ, = a, EPl » -Ja'+0.1' vi tam gidc EZ,?, gdn vuflng tai Z,. (hinh 4)
1
Hinh 4. Bifiu difin dilm suy giam 3 dB
D o d d : > a =0.1 radian.
.la'-t-O.l'
Nhu vdy cdc difim cdn tim la c o ^ . I va - ( O ^ . l radian.
Ttt day ta cfl hfi stf bfl loc Notch IIR:
B= [1 -1.90211303259031 1]
A= [1 -1.87738556316663 0.974169]
Trfin phdn mfim Matlab ta cfl thfi so sdnh tin hifiu ECG mfl phong khi thfim nhifiu SOHz vd kfi't qud sau Igc Notch nhtt hinh 5.
Tin hieu sau
Hinh 5. Ket qua mo phong Igc nhilu nguon dien cua tin hieu ECG
Ttt vific giai phttong ninh dn sfl Id a ta thdy khi P, cdng gdn vfii Z, thi dai nfin SOHz cdng hep. Quay trfl lai vdn dfi thifit kfi bfi loc Notch SO Hz, gia s i cac tdn sfi suy hao 3 dB la 48Hz va 52Hz, tdn sfi ldy mdu la IKHz. Ta cfi:
a=2. =P,Z,= 0.013 = 500
• OP,=0.987.
Ta cfi thfi thdy kfit qua c i a bfl Igc Notch da thifit kfi la rdt tfit, bfi Igc ndy cfl thfi dugc ttng dung vdo qud Uinh loc nhifiu ngufin difin c i a tin hifiu difin tim.
III. KET L U A N
Vific thifi't ke'bfi Igc sfi bdng phucmg phdp difim khfing va difim cue cho phep hifiu ro ban chd't ham truyfin c i a bfi Igc sfi nfli chung va ttong mfit stf trttflng hop phttong phdp nay cho kfit qua tfit dfing thfli cfl kha ndng thay dfii nhanh theo yfiu cdu bdi loan.
Tdi lieu tham khdo:
[1] Gido sa Trdn Dd Trinh: Hudng ddn dgc dien tim: Nhd xudt bdn Y hgc 2003 [2] C.Britton Rorabaugh; Digital Filter Designer s Handbook: Mcgraw-Hili [3] Help of the Matlab
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