CHNG I : TNG QUAN V WEB APPLICATION FIREWALL

I HC QUC GIA TP.H CH MINHTRNG I HC KHOA HC T NHINKHOA VT L-VT L K THUTCHUYN NGNH VT L TIN HC--------------------------------

KHA LUN TT NGHIP I HC

ti:

NG DNG PHP BIN I WAVELET RI RC XC NH NGNG NG KINH DA VO IN NO

SVTH:Nguyn An HaCBHD:ThS. Ha Th Hong Yn

----------------------------------TP H CH MINH 2014

I HC QUC GIA TP.H CH MINHTRNG I HC KHOA HC T NHINKHOA VT L-VT L K THUTCHUYN NGNH VT L TIN HC--------------------------------

KHA LUN TT NGHIP I HC

ti:

NG DNG PHP BIN I WAVELET RI RC XC NH NGNG NG KINH DA VO IN NO

SVTH:Nguyn An HaCBHD:ThS. Ha Th Hong Yn

----------------------------------TP H CH MINH 2014

Li Cm n

Em xin gi li cm n su sc n C Ha Th Hong Yn tn tnh hng dn, ng vin v gip em sut thi gian qua. Em cng chn thnh cm n nh trng v Thy C to iu kin cho em v cng cm n cc bn trong b mn ng vin v gip em trong thi gian qua em thc hin ti.V trn ht l lng bit n ca con i vi cha m, gia nh lun quan tm ng vin v ng h con trong qu trnh hc tp.Mc d rt c gng lm tt ti nhng do trnh l lun cng nh cha kinh nghim nn khng th trnh khi nhng sai st, em rt mong nhn c s gp chn thnh ca Qu Thy C v cc bn.

Tp. H Ch Minh, thng 6 nm 2014Sinh vin thc hin

Nguyn An Ha

Mc lcMc lciBng ch vit ttivDanh sch hnh nhvDanh sch bng biuviiiLi m u1Chng 1. TNG QUAN IN NO 31.1. in no .31.2. Ghi nhn EEG51.3. Cc c tnh ca EEG61.3.1. Tn s c bn:61.3.2. Bin (Amplitude):71.3.3. Hnh thi (Morphology).71.3.4. phn ng (reactivity).91.4. Cc thnh phn sng trong EEG.91.5. Cc dng sng EEG phc hp121.6. Nhiu (artifacts).15Chng 2. BNH NG KINH172.1. Khi nim172.2. Phn loi bnh ng kinh172.3. Sinh l thn kinh (Neurophysiology)192.4. Tn hiu in no trong bnh ng kinh202.5. Bin th dng ng kinh lnh tnh (Benign Epileptiform Variant)222.5.1. Bin th ng vin mnh.232.5.2. Bin th xy ra v kch pht hoc hun luyn.24Chng 3. PHP BIN I WAVELET RI RC263.1. T Fourier n wavelet263.2. Php bin i wavelet293.2.1. Wavelet l g?303.2.2. Php bin i Wavelet lin tc323.2.3. Php bin i Wavelet ri rc343.2.4. Gii thiu c bn cc h wavelet38Chng 4. PHNG PHP THC HIN414.1. t vn 414.2. Phng php thc hin424.2.1. C s d liu424.2.2. S phn tch tn hiu434.2.3. Xy dng s phn tch h s chi tit v xp x434.2.4. Cc c trng ca mi thnh phn sng474.2.5. Hm matlab s dng49Chng 5. KT QU THC NGHIM505.1. Kho st tn hiu ng kinh v tn hiu ca ngi khe mnh505.2. Tnh ton cc h s c trng v xc nh ngng545.3. Xy dng chng trnh565.4. Xy dng giao din57KT LUN V HNG PHT TRIN60Ti liu tham kho62Ph Lc A: Cc c trng ca ngi ng kinh64Ph Lc B: Cc c trng ca ngi khe mnh67

Bng ch vit ttCWTContinuous Wavelet TransformDWTDiscrete Wavelet TransformEEGElectroencephalographyFFTFast Fourier TransformFTFourier TransformIDWTInverse Discrete Wavelet TransformPSDPower Spectral DensitySTFTShort Time Fourier TransformWT Wavelet Transform

Danh sch hnh nhHnh 1.1 Bn phn ca i no3Hnh 1.2 S b tr im cc4Hnh 1.3 S ghi nhn lng cc5Hnh 1.4 Dng sng EEG khng lon nhp6Hnh 1.5 Dng sng EEG b lon nhp6Hnh 1.6 n cu (trn), a cu (di) ca tn hiu EEG7Hnh 1.7 Dng sng tng vt chm (spike slow wave)7Hnh 1.8 phn ng ca dng sng EEG (Reacivity of EEG waveform)8Hnh 1.9 Cc thnh phn sng9Hnh 1.10 Gai v sng (spike and wave)12Hnh 1.11 a gai v sng12Hnh 1.12 Cc phng in dng ng kinh theo chu k13Hnh 1.13 Sng ba pha13Hnh 1.14 Tn hiu bng n, c ch13Hnh 1.15 Nhiu do chuyn ng mt14Hnh 1.16 Nhiu do in p di da15Hnh 1.17 Nhiu dng c v nhiu 60Hz15Hnh 2.1 M phng cho c ch sinh ha19Hnh 2.2 nh v sng nhn20Hnh 2.3 Dng sng ng kinh t bin20Hnh 2.4 Chng Hypsarrhythmia trong ng kinh tr21Hnh 2.5 Tn hiu ng kinh kch pht21Hnh 2.6 ng kinh thy trn21Hnh 2.7 Sng Wicket22Hnh 2.8 Cc nh, gai lnh tnh ca EEG trong gic ng khng su23Hnh 3.1 Joseph Fourier (1768 1830)25Hnh 3.2 Php bin i STFT27Hnh 3.3 Biu th min tn s - thi gian trong STFT28Hnh 3.4 Minh ha cho wavelet29Hnh 3.5 Tnh cht tr30Hnh 3.6 Tnh cht scaling30Hnh 3.7 Ly mu hai ngi thi gian v tn s31Hnh 3.8 Minh ha cho CWT32Hnh 3.9 Lc mc c bn34Hnh 3.10 Thao tc ly mu35Hnh 3.11 Cy wavelet35Hnh 3.12 V d phn tch36Hnh 3.13 Ti to tn hiu t cc h s ca DWT36Hnh 3.14 Tng mu bng cch chn im khng37Hnh 3.15 Haar wavelet37Hnh 3.16 Daubechies (dbN)38Hnh 3.17 Cc dng Biorthogonal wavelets38Hnh 3.18 Cc dng ca wavelet symlets39Hnh 4.1 Daubechies 241Hnh 4.2 C s d liu t website42Hnh 4.3 S phn tch tn hiu42Hnh 4.4 S phn tch h s chi tit v xp x43Hnh 4.5 M hnh tng hp thnh phn sng ca tn hiu45Hnh 5.1 Tch cc thnh phn chi tit v xp x49Hnh 5.2 Tng hp tn hiu thnh phn.49Hnh 5.3 Tn hiu u vo ca ngi khng ng kinh.50Hnh 5.4 Cc thnh phn sng ca ngi bnh thng.50Hnh 5.5 Tn hiu u vo ca ngi ng kinh.51Hnh 5.6 Cc thnh phn sng ca ngi ng kinh.51Hnh 5.7 H s phng sai.52Hnh 5.8 Code tnh PSD.52Hnh 5.9 H s entropy.52Hnh 5.10 S gii thut cho chng trnh54Hnh 5.11 Giao din chng trnh55

Danh sch bng biuBng 4.1 Tng hp cc h s chi tit v xp x44Bng 4.2 Tn s yu cu sau tnh ton mi thnh phn sng45Bng 4.3 t tn cho cc h s c trng47Bng 4.4 Hm matlab c bn48Bng 5.1 Khong gi tr ngng ca tn hiu ng kinh v tn hiu ca ngi khe mnh.53

65

Li m uNo b l trung tm x l mi chuyn giao cm xc, hnh vi, thi . Chnh v th, mt khi no ng bnh ko theo c h ly khng ch cho chnh bn thn m cn gia nh v x hi. Vi sc p nh th, ngi ta pht minh cng c ghi nhn sng no gi l in no .in no (EEG) l cng c quan trng cho vic phn tch sng no, chn on s bt thng, pht hin cc bnh nh: lin quan thn kinh, co git, ung th no, ng kinh.v.v.. Theo thng k ca t chc y t th gii (WHO) th t l ngi mc bnh ng kinh trn th gii khong 0.5% dn s, thay i ty theo a l, Php v M khong 0.85%, Canada khong 0.6% . Vit Nam th khong 2% dn s, trong tr em chim 60% s bnh nhn [11]. Hiu qu pht hin bnh vn cn l thch thc rt ln trong lnh vc ny, c bit l bnh ng kinh, rt phc tp khng th gii thch tt bng lnh vc ha sinh hay vt l, m cn phi c s kho st thc t tm ra nhng c trng cho vic nhn dng hoc chn on. V l do , m c rt nhiu phng php khc nhau cho vic pht hin bnh ng kinh gm: phng php cc c trng tuyn tnh v khng tuyn tnh (linear and non linear features) , php bin i Fourier nhanh,... Mi mt phng php u c nhng u v hn ch, trong kha lun ny th tc gi chn phng php wavelet ri rc tch ra cc thnh phn sng khc nhau[footnoteRef:1], sau tnh ra cc c trng quan trng[footnoteRef:2], kho st s khc bit gia tn hiu ng kinh v tn hiu ca ngi khe mnh, t xy dng ngng d on tn hiu bt k[footnoteRef:3] c ri vo vng ng kinh hay khng. [1: Cc thnh phn sng gm: Alpha, Beta, Delta, Theta.] [2: Bao gm bn h s c trng quan trng: Entropy, nng lng, ph cng sut v h s phng sai.] [3: Tn hiu bt k thuc c s d liu trng i Hc Bonn.]

Kha lun c b tr vi nhng ni dung sau: Phn l thuyt:Chng 1: Tng quan EEG.Chng 2: Bnh ng kinh.Chng 3: Php bin i Wavelet.Phn ng dng:Chng 4: Phng php thc hin.Chng 5: Kt qu thc nghim.Kt lun v hng pht trin.

TNG QUAN IN NO in no .Calo Matteucci (18111868) v Emil Du Bois-Reymond (18181896) l nhng ngi u tin ghi nhn tn hiu in th pht ra t dy thn kinh trn c bp a ra khi nim v thn kinh, nhng gp vn tiu cc din ra khi co c bp, vn ny c Hermann Von Helmholz khng nh.Richard Caton (18421926), mt nh khoa hc ngi anh s dng in k v hai in cc t trn da u ca ngi v l ln u tin ghi nhn tn hiu hot ng ca no di dng tn hiu in vo nm 1875. T , n c tn l EEG (electroencephalogram), t electro ch s ghi nhn tn hiu in ca no, encephalo lin quan n tn hiu pht ra t vng u v gram bn v, kt hp li gi l in no . hiu r tm quan trng ca in no , trong phn ny kha lun s cp n cu trc no ngi. No ngi l c quan phc tp nht trong s tt c h thng trong c th con ngi v cha ng nhiu b n ang c cc nh khoa hc tm hiu. No ngi c chia thnh ba phn nh: i no, tiu no, thn no (gn t sng c). Trong , i no l phn ln nht chu trch nhim cho s khi u di chuyn, s phi hp nhp nhng cho hot ng thng ngy, cm nhn nhit c th, cm gic khi chm cm nm, nhn, nghe thy, s phn on, a ra l do, gii quyt vn , mi cm xc v hc hnh trau di. i no chia lm bn phn nh hnh 1.1 bn di gm c: thy trn (frontal lope), thy chm (occipital lobe), thy nh (parietal lobe) v thy thi dng(temporal lobe).Phn nh hn ca no c gi l tiu no, mc ch chnh ca tiu no l s phi hp c ng ca c bp v duy tr s cn bng cho c th.Cung no hay phn chnh gia ca no, phn ny chu trch nhim v vic iu khin chuyn ng ca mt v ming, a ra nhng thng bo cm gic v nhit cho i no x l, ging ni... N cn chu trch nhim iu khin, kim sot cn i, h hp, chc nng tim vv...

Hnh 1.1: Bn phn ca i noin no (EEG) l cng c rt mnh trong thn kinh hc, bi kh nng ghi nhn chi tit v hot ng ca no b. Phm vi in p cho tn hiu in no trong khong t 3 100 V, tn hiu ny yu hn rt nhiu so vi tn hiu in tim, c th l yu hn gp mt trm ln so vi tn hiu in tim.Trong in no c b tr a in cc ghi nhn thi gian khc nhau ca s bin thin in p do hng triu t bo thn kinh to ra, cc in cc ny c phn b i xng xung quanh da u hnh 1.2, nhm cung cp bng tm tt thi gian v khng gian hot ng b mt no, mi in cc p ng cc tim nng tng hp tn hiu c to ra bi cc t bo thn kinh khu vc bn di n. EEG c gi in no khng xm ln (non invasine). Cn in no xm ln[footnoteRef:4] (EcoGs) c nh ngha l vic ghi nhn tn hiu khng din ra trn b mt da u m cc in cc ny tip xc trc tip vi b mt no. Chnh v th, tn hiu t b suy gim hn so vi EEG, n cung cp phn gii khng gian cao hn, tc l vic thu nhn tn hot ng chnh xc hn. [4: Thng thng c s dng chn on khi tn thng nghim trng no, phng php ny c hn ch ln nht chnh l tip xc trc tip vi b mt no.]

Hnh 1.2: S b tr im ccMt trong nhng ng dng quan trng ca in no l phn tch bnh ng kinh, tn hiu ca bnh nhn ng kinh c nhiu d thng xut hin qu mc so vi hot ng bnh thng ca no. Cng c nhiu ng dng khc nh chn on cc ca hn m hoc nhng ri lon khc nhau do chn thng gy ra trn no b, c bit trong qu trnh gy m ngi ta thng s dng in no theo di tnh trng bnh nhn, nu gy m khng liu lng s gy ra nhng tn thng nht nh i bnh nhn, cn gy m qua su th dn n ngng h hp, da vo mn hnh theo di in no ngi ta c th tng gim cng gy m thch hp.Tn hiu EEG cng ang c s dng trong d n thit k giao din my tnh no (brain computer interface) nhm gip nhng ngi khuyt tt c th giao tip d dng vi cc thit b my tnh bng ngh, bng c ng mt. Ngoi ra, EEG cn c s dng pht hin nhng im cht trong no, khi u, ung th. Ghi nhn EEGGhi nhn lng cc (Bipolar recording) v ghi nhn tham chiu (referential recording) c s dng cho vic vic kho st EEG. i vi ghi nhn tham chiu in p ti mi in cc c ghi nhn lin quan ti mt trong s cc in cc tham chiu A1 v A2. Cc in cc c sp xp nh hnh 1.3. Thng thng, cc in cc bn tri u tham chiu n A2, v bn phi u th tham chiu n in cc A1 tc l tham chiu cho, s hnh 1.3 m bo vic ghi nhn v tham chiu ti cc in cc din ra tt nht m khng lm nh hng ti cc in cc ln cn khc.

Hnh 1.3: S ghi nhn lng cc

Cc c tnh ca EEGHot ng ca in no c th c m t chi tit qua cc c trng nh lng nh tnh nh: tn s c bn, bin , hnh thi, nh v v s phn ng. Ngoi ra hot ng in no cn ph thuc tui tc hay trng thi tnh to ca bnh nhn.Tn s c bnTn s c bn ca dng sng in no c nh ngha mt cch khi qut l tc m dng sng ny lp i lp li trn mt giy, cc dng sng (waveform) ny c hnh dng ty .Mt dng sng in n nh, lin tc th c gi l nhp nhng (rhythmic), cn ngc li th gi l lon nhp (arrhythmic). Hnh 1.4, 1.5 s cho thy s khc nhau gia chng.

Hnh 1.4: Dng sng EEG khng lon nhp

Hnh 1.5: Dng sng EEG b lon nhp

Bin (Amplitude)Bin ca dng sng EEG lin quan ti cc nh in p, thng thng bin ca n vo khong microvolts. V d dng sng hnh 1.4 c bin nh hn 75V, v hnh 1.7 th sng c bin 100V. Mt dng sng EEG cho thy tng hay gim t ngt ca bin chng hn nh hnh 1.8 ta thy r s tng, gim t ngt ny.Hnh thi (Morphology)Hnh thi hay hnh dng ca sng EEG c m t qua hnh dng m ta quan st, n l mt hm ca bin v tn s. Mt dng sng m n ch mt thnh phn th gi l n cu (monomorphic), v bao gm nhiu thnh phn khc nhau th chng ta gi l a cu (polymorphic), nh hnh 1.6.

Hnh 1.6: n cu (trn), a cu (di) ca tn hiu EEGTrong EEG bao gm hai hay nhiu dng sng khc nhau, nhiu hnh thi khc nhau rt phc tp mt v d hnh 1.7 cho ta thy r s phc tp, s tng t bin chm trong mt giy.

Hnh 1.7: Dng sng tng vt chm (spike slow wave)Ni tm li hnh dng sng c chia ra cc loi c bn sau: Monomorphic: l hot ng in no ring bit c to thnh t hot ng no chim u th ca no.Polymorphic: l hot ng in no ring bit bao gm nhiu tn s kt hp to nn mt dng sng phc tp.Sinusoidal: sng ging nh dng sng sin.Transients: l dng sng c lp hoc th, l tn hiu thi gian ngn (short duration signal). phn ng (Reactivity) phn ng ca dng sng EEG lin quan ti mc thay i ca dng sng no trc vn , hay tc nhn kch thch no . Hnh 1.8 l mt trong nhng v d in hnh cho phn ng ny, hnh di biu th dng sng khi nhm v m mt.

Hnh 1.8: phn ng ca dng sng EEG (Reacivity of EEG waveform)Cc thnh phn sng trong EEGTa thu nhn tn hiu t cc my o khong tn s ty thuc vo mi thit b v d nh: Emotiv EPOC EEG tn s khong 128Hz, hoc NeuroSky MindWave EEG khong 512Hz. Sng m ta thu nhn c l tp hp rt nhiu thnh phn sng khc nhau, nhng khong tn s khc nhau. Mi mt thnh phn sng th hin cc hot ng khc nhau ca no b.C nm thnh phn sng chnh delta (), theta (), alpha (), beta (), gamma (). Khong tn s ca mi sng delta 0 4 Hz, theta 4 8 Hz, alpha 8 12 Hz, beta 12 30 Hz v gamma ln hn 30 Hz.

Hnh 1.9: Cc thnh phn sng

Nhp alpha (alpha rhythm):Thnh phn sng alpha c tm thy v trnh by bi Berger 1929. Sng alpha xut hin na sau u v thng c tm thy vng thy chm, khong tn s xc nh vo khong t 8 n 12 Hz, i vi tr em khi mi sinh th nhp alpha rt yu, n s tng dn theo thi gian c th tr mt thng tui th nhp alpha ch khong 7 Hz, v tn s tip tc tng cho n khi trng thnh. Sng alpha c hnh sin to thoi u n bin khong 50 mV, nhp alpha ny xut hin khi nhm mt v thoi mi, n b suy gim hoc mt i khi m mt, s lo lng hay tp trung ch cao (phn ng Berger).Bin i nhp alpha: b kch thch bi nh sng, lao ng tr c, m mt v s tn thng vng mc. ngha nhp alpha: do kch thch t bo thn kinh v no trng thi cn bng thn kinh.Bnh l: da vo sng ny ngi ta c th chn on c cc bnh nh: mt i xng v tn s gia hai bn cu, mt phn ng Berger, mt dng thoi hoc bin dng nhn vv... Nhp beta (beta rhythm):Nhp beta cng c tm thy v trnh by bi Berger, nhp beta thng xut hin vng thy trn, khong tn s xc nh nm trong khong t 12 n 30 Hz, bin vo khong 20 mV.Nhp beta lin quan ti suy ngh tch cc, s ch tch cc, cnh bo, s lo lng, hng gii quyt vn hoc l s cng thng. Nhp beta tng mnh (high - beta) v chim u th khi ta ri vo trng thi hong lon, cng thng qu mc, nhp beta n s b gim i khi c nhng kch thch xc gic, hot ng c bp. Nhp theta (theta rhythm): Khi nim tng quan v nhp theta ny cng c trnh by bi hai nh khoa hc Wolter v Dovey vo nm 1944, v tr thu nhn nhp ny r nht l hai vng thi dng, nh pha bn tri u, khong tn s xc nh vo khong 4 n 8 Hz.Nhp theta c xp vo loi sng chm, n c coi l bt thng i vi nhng ngi ln, nhng hon ton bnh thng i vi tr em di 13 tui v ang ng. Nhp ny xut hin khi chuyn t trng thi tnh to sang trng thi bun ng, s bt tnh, nhng cm hng sng to, i vi nhng hnh gi thin nh su hoc l vng bt thng cc b ni c tn thng v no. Da vo c trng ny ngi ta c th theo di v chn on cc bnh l, tn thng v no nh: bnh l gia ng nm su (deep midline disorders), mt s trng hp no nc (hydrocephalus). Nhp delta (delta rhythm):Nhp delta c Wolter trnh by chi tit vo nm 1936, thng xut hin vng thy trn, khong tn s xc nh vo khong 0 n 4 Hz, bin khong 20 mV. Nhp delta xem l bnh thng i vi tr em di mt thng tui v trng thi ba, bn ca gic ng, n xut hin cc b khi c tn thng di v no v s phn b rng khp khi c tn thng lan trn. Ngoi ra nhp delta cn xut hin khi gy m, hn m v trng thi ng say.Bin i nhp delta, s tng bin v tn s thng l do thiu oxy no v tn thng thc th no nh: u no, t qu, gip no, p xe no. Cn khi nhp delta kch pht xut hin thnh tng nhp, ng b c hai bn cu khi tn thng cu trc li v no. Nhp gama (gama rhythm):Nm 1938, hai nh khoa hc Jasper v Andrews s dng nghin cu dng sng trn 30 Hz, sng gi l gama. Mc d bin ca nhp gama l rt thp v s xut hin rt him gp, nhng khi pht hin nhp ny gip chn on s bnh no nht nh, cc khu vc c tn s cao hoc hot ng mc cao th hin r lu lng mu (s hp thu oxy v glucose). Khong gii hn ca nhp gama cng c chng minh l du hiu tt ca nhng g lin quan ti ng b ha (ERP) ca no, v c th chng minh vng chu trch nhim kim sot di chuyn tri phi ca ngn tay tr, ngn chn phi.Cc dng sng EEG phc hp Sng gai, sc nhnDng sng ny c mi la tui, nhng r nht l tr em. N bao gm mt gai (c th l ngun pht nm v no) v mt sng chm (thng l sng delta) c bin cao. Chng xut hin ng b v cn i hai bn trong cc bnh ng kinh ton th ha (generalized epilepsies) hoc tr ng trong bnh ng kinh cc b.Trong nhng dng gai v sng ton th ha, cn vng thc s (true absense) hay l cn nh (petit mal) c trng bng gai sng 3 Hz, trong khi gai chm sng (slow spike wave) thng thy khi no b tn thng, hi chng Lennox Gastaut. Nhng gai v sng nhanh hn 3 Hz l sng a gai.

Hnh 1.10: Gai v sng (spike and wave)L mt dng ca gai sng, trong mi sng chm km theo hai hoc nhiu gai. Dng ny thng gp l dng gai c tn s nhanh hn 3 Hz, thng l 3.5 ti 4.5. Dng ny i km vi git c (myoclonus) hoc cc cn kch pht git c (myoclonic seizures). ng nhm ln n vi gai sng 6 Hz, vn n c coi l gai sng khng thc (phantom spike and wave) l bin th ca bnh thng.

Hnh 1.11: a gai v sng Cc phng in dng ng kinh lch bn theo chu k (PLEDS Periodic Lateralized Epileptiform Discharges):L mt dng phng in i km vi tn thng hay chn thng no cp tnh. Ta thy dng sng ny r nht khi tn thng no cp tnh c kt hp thm vi ri lon chuyn ha. N khi u bng nhng sng nhn xut hin mt cch u n, trn mt nn tng i bng phng, mt vng hay mt bn ca no. Sau nhp ca n chm dn v xut hin cc sng chm theo chu k, v hot ng in c s nm gia cc phng in dng ng kinh ny cng kh dn ln. Cui cng cc sng dng ng kinh kiu ny cng hon ton bin mt. Kiu PLEDS thng thy khi c triu chng nh khu nng, hoc l trn mt bnh nng ang c xu hng kh dn ln.

Hnh 1.12: Cc phng in dng ng kinh theo chu k Cc sng ba pha (triphasic wave):Sng ba pha l ba sng to vin mu trng c minh ha trn hnh 1.13, chng thng xut hin khi c cc hot ng in gi kch pht (pseudoparoxysmal activity). Cc sng ny tm thy trong bnh no do gan (hepatic enephalopathy), nhng cng c th thy trong cc bnh no do chuyn ha khc.

Hnh 1.13: Sng ba pha Bng n v c ch (burst supression):Bng n v c ch l dng sng chm v hn hp (mixed waves) thng vi bin cao, v xen k lun phin bng nhng ng ng in. Loi sng ny c tm thy khi c nhng tn thng no nng nh: sau khi t qu thiu mu no (postischemia), sau trng thi thiu oxy (postanoxia). trng trc khi EEG tr nn ng in hon ton hnh 1.14.

Hnh 1.14: Tn hiu bng n, c chNhiu (Artifacts)Nhiu l nhng sng hoc nhng nhm cc sng khng mong mun do li k thut hoc do cc li khc gy ra. Nhiu l cc ri lon do khim khuyt k thut, thng l nhng li c tnh tm thi, bao gm do di ng cc in cc lm cho mt tip xc, cc hot ng ca c che khut in no , do c ng u, xc da u, ra m hi... Nhiu do in tm v do mch p(EKG and pulse artifacts):C hai loi nhiu lon ny c th nhn bit nh vo tnh cht c chu k ca chng. Nhiu in tm cho thy r phc QRS theo chu k, v in tm c tn hiu ln hn nhiu so vi tn hiu in no. Nhiu do mch l mch p pha di ca in cc lm cho n chuyn ng theo chu k. C hai loi nhiu trn u d nhn thy nhng gy kh khn cho vic c in no. Do chuyn ng ca mt:Chuyn ng mt gm chp mt, nhm m mt v m mt rung lm pht sinh ngun nhiu gy ra nhng sng chm, hoc nhp. Nhng nhiu ny c ngun gc ni bt nht trong knh pha trc ca c hai lng cc v ghi tham chiu, v c th phn bit vi EEG - hot ng c ngun gc t no pha trc (thy trn) bng cch thm vo nhng in cc xung quanh mi mt. Tuy nhin, cc in cc ny thng khng s dng trong vi thit b, hnh 1.15 th hin nhiu do chuyn ng mt.

Hnh 1.15: Nhiu do chuyn ng mt Nhiu do in p di da:L nhng thay i c bn tn s thp trong cc in no . Cc in p ca da c th thay i do cc hot ng tuyn m hi, hay l thay i tuyn m hi nh hng n nng cht in gia da v cc in cc EEG. Hnh 1.16 cho thy s thay i tn s 1 Hz trong ghi tham chiu ca mt in cc F7 hin th hai giy, bin 50 V.

Hnh 1.16: Nhiu do in p di da Nhiu do dng c truyn tnh mch v nhiu 60 Hz:Nhng nhiu ny thng c thy trong khi ghi in no phng sn sc c bit (ICU) v c hai u l nhng giao thoa v in. Hnh 1.17, nhiu do dng c truyn l nhiu c mu , n c tnh cht chu k, c bin thp v d nhn bit.Nhiu 60 Hz c nhng ni in cc tip xc km, ni t khng tt, v c mt thit b in chuyn dng t gn . N gy ra gai (spikes) c tn s 60 Hz to nn vt ln.

Hnh 1.17: Nhiu dng c v nhiu 60Hz

BNH NG KINH Khi nimng kinh l trng thi thn kinh m c phng in din ra trong no bt thng, mnh. Bnh ny xut hin rt lu hn 3000 nm trc ti thnh Babylon c i bnh ny c t vi tn miqtu . T ng kinh c ngun gc t ting Hy Lp epilambanein c ngha l nm bt hoc tn cng. Y vn c n (4500 trc cng nguyn ) m t trng thi ny l apasmara, apas: ngha l khng c hoc mt, smara: l thc hoc tr nh. N c cho l cuc tn cng ca th lc siu nhin trong thi gian .Ngy nay, khoa hc v cng ngh pht trin vt bc. Chnh v th, m lnh vc y hc ngy cng tin tin nn vic l gii bnh ny rt d dng, bnh ng kinh c bit n l s ri lon ca h thng thn kinh trung ng, do s xo trn, lp i lp li ca mt s n ron trong v no gy ra nhng triu chng: co git c bp, cn li, si bt mp, mt trn ngc, bt tnh, mt kim sot tiu tin, gy cm gic l v.v.. Cn ng kinh bc pht lm bnh nhn kh bit trc v kim sot c.Trong cn ng kinh c nhiu th loi cn, cc triu chng biu hin cc cn co git khc nhau ty thuc vo cc cn phng in trong no, c nhiu l do dn n co git nh: chn thng nng nh hng ti no lc sinh , d dng mch mu no, di chng tn thng vim, nhim k sinh trng no b, u no, chn thng s no, di chng sau tai bin mch mu no, v cc cu trc bt thng khc no b.Phn loi bnh ng kinhGm c 5 loi c bn sau: ng kinh ton th: ng kinh ton th d nhn thy, cn xut hin rt t ngt, ngi bnh ku ln mt ting ri ng ln ra, ngay lp tc mt thc c th chia lm ba giai on sau:Giai on co cng ko di khong mt pht, co cng ton b cc c t chi, c thn, ngc, hai tay co, chn dui. Hu qu c th cn li, ngng th, tm ti.Giai on co git c, git c tng t u n c nhp, hai mt trn trng, nhp nhy, ming si bt mp.Giai on hn m, l ln: sau giai on co git ngi bnh ri vo trng thi hn m, th gp, tiu tin mt kim sot. Sau khi tnh th cm thy mt mi, au u. ng kinh cc b n gin:Khng ri lon thc, biu hin cc triu chng v vn ng cm gic, gic quan, thn kinh thc vt hoc tm thn.ng kinh cc b vn ng l s co cng mt phn c th sau c th gi nguyn v tr hoc lan rng n vng xung quanh.ng kinh cm gic, gic quan: cc ri lon cm gic, gic quan ti khu vc cc b. Triu chng thn kinh thc vt th lin quan ti ri lon ngn ng, tr nh, nhn thc, cm xc, tri gic. ng kinh cc b phc tp:C ri lon thc trong cn, thng bt u t cc b n gin sau dn mt thc, bnh nhn sng s, mt tip xc vi mi trng xung quanh, p ng khng chnh xc vi cc kch thch bn ngoi, c nhng hnh vi mang tnh cht t ng khng mc ch, sau khi dng cn th ngi bnh khng nh nhng g xy ra trc , cn ng kinh c th ko dai t 2 pht n hng gi.. Cn vng thc:c trng bi s t ngt mt thc, ngng mi hot ng trong thi gian rt ngn vi chc giy. Lc h n, mt nhn v hn, nh ri vt dng trn tay hoc bung lng ngi, iu ny rt nguy him cho hot ng cn n s ch nh iu khin phng tin giao thng, bi li, hay lm vic nhng ni c cao ng kinh thi dng:ng kinh ny c gi ng kinh tm thn, rt phc tp v rt ging cc triu chng tm thn, nh trng thi lo u, hong s, hi hp, bt an.Sinh l thn kinh (Neurophysiology)Mc d c ch sinh ha (hnh 1.18) cha gii thch c r rng v no b, nhng mt c s c trng, mt s hin tng c th quan st khi ngi mc bnh ng kinh.i vi ngi bnh ng kinh th bin sng no din ra bt thng km theo qu trnh kh mng v phng in cc khp thn kinh din ra t bin. Hin tng ny gi l s thay i bc pht hay kch pht kh cc.iu ny c m t u tin trong t bo thn kinh bng thc nghim quan trng, ngi ta nhn thy qu trnh kh lu di tng ng vi s lng ng kinh quan st cc in cc b mt.C nhiu c ch khc nhau cho s thc y cng nh kt hp sinh ha din ra bnh ng kinh nh: Gim c ch (khng gama amino butyric acid) Kch thch tng do xo trn trong N methyl D aspartate v glutamate Thay i nng ion Na+, Ca+, K+ Thay i knh ion mng

Hnh 2.1: M phng cho c ch sinh haTn hiu in no trong bnh ng kinhNh cp chng I (mc 1.5 cc dng sng EEG phc hp), do khi cp n mt tn hiu EEG cho vic pht hin bnh no , ta cng u quan tm n cc dng phc hp ca n nh: nh sc, nhn hay dng sng g v.v.. nhn dng bnh ng kinh da vo sng nh v sng nhn (sharp wave): Sng nh: da vo phn tch thi gian ngn (transient) c th phn bit cc hot ng nn vi cc im nh (point peak), trong khong thi gian t 20 70 ms, hu ht u l sng chm hnh 2.2. Sng nhn tng t cng da vo phn tch thi gian ngn, trong khong t 70 200 ms (hnh 2.2)

Hnh 2.2: nh v sng nhnCn c vo cc nh v sng nhn kt hp nhng quan st v mt thc nghim ngi ta a cc nhn tng quan v cc bnh ng kinh cng nh cc tn hiu EEG km theo n, y ch nu ra nhng dng tn hiu EEG c bn ca bnh, nn ch l khi qut khng i m vo c th. Dng ng kinh t bin v tng lin tc nh hnh 2.3.

Hnh 2.3: Dng sng ng kinh t bin Hypsarrhythmia: l chng co tht, co git tr con, c tnh l s ngu nhin trong tn hiu v in p ca n rt cao khong 300V.

Hnh 2.4: Chng Hypsarrhythmia trong ng kinh tr ng kinh kch pht: l chng co git ton thn lp i lp li trong khong t 8 20 Hz, hnh 1.22.

Hnh 2.5: Tn hiu ng kinh kch pht Cc phng in dng ng kinh lch bn theo chu k (PLEDS Periodic Lateralized Epileptiform Discharges) phn cng c cp chng trc (mc 1.5.) ng kinh thy trn: l dng ng kinh phc tp km theo l nhng cn phng in t khu vc ln cn hnh 2.6.

Hnh 2.6: ng kinh thy trnBin th dng ng kinh lnh tnh (Benign Epileptiform Variant)Khi nim: bin th dng ng kinh lnh tnh tc l tn hiu EEG c m hnh tng i ging vi dng sng bnh ng kinh, nhng khng phi bnh ng. Chnh iu gy ra nhng kh rt ln cho vic chun on bnh, c th gy ra nhm ln rt cao.C hai loi chnh ca bin th: bin th ng vin mnh, r(sharply contoured BEV)v bin th xy ra v kch pht hoc hun luyn (burst and trains).Bin th ng vin mnhGm hai loi: sng wicket v Sng Wicket:L sng c dng cung, quan st thy n gn ging k t hy lp , n l sng n hay kt thnh tng cm. Sng ny c ch yu gp cc im cc T3, T4 hoc T3, T4 kt hp vi F7, F8. c im l sng khng n sau sng chm (no after coming slow wave) v khng c bin dng nhp nn [4].

Hnh 2.7: Sng Wicket Cc nh, gai lnh tnh ca EEG trong gic ng khng su (Benign sporadic sleep spikes):L sng c dc tng t ngt, thng c thi gian ngn nh hn 50 ms, l sng n n sau sng chm, khng xut hin trong qu trnh hun luyn. Thng tn hiu ny song phng v vi bin ti a trn mt bn cuPhn ln sng ny xut hin thanh thiu nin, v ngi ln. Sng ny b gim dn khi gic ng su, din ra mnh i vi gic ng theo tng t, chp chn.Sng ny xut hin in cc A1, A2 v T5, T6.

Hnh 2.8: Cc nh, gai lnh tnh ca EEG trong gic ng khng suBin th xy ra v kch pht hoc hun luynPhn ny c trnh by mt cch s lc cc khi nim mi ngi hiu mt cch khi qut, qua bit c vic chn on d nhm ln nh th no. Gai sng (spike - wave) 6Hz: Khong tn s t 5 7 Hz, bin tng t bin tng i thp, xut hin thanh thiu nin, ngi ln v xut hin ba trng thi: tnh to, bun ng v khng ng, thi gian xut hin khong di 1s, ha ln vo cc sng khc gy nn hnh dng rt ging dng bnh ng kinh, rt kh nhn bit, phi l ngi c kinh nghim th mi x l tt c. Gai tch cc 14 v 6 Hz(4 & 6 Hz positive spikes):L thnh phn tch cc dng cung v phn tiu cc c sng mn nh, khong tn s c sng ny 13 17 Hz hoc 6 7 Hz, xut hin khi trng thi bun ng, hay gic ng thong qua. Nhp theta thi dng khi ri vo trng thi bun ng (Rhythmic Temporal Theta of Drowsiness):Khong tn s t 5 7 Hz, thng c hnh ch V, xut hin hai bn thi dng l ch yu. Tn hiu ny gn ging dng tn hiu bnh tm thn.T nhng thnh phn bin th trn cho ta nhn thy c cc khong tn s ca bin th chnh lch rt thp ng thi dng sng ca n rt ging vi dng sng ng kinh nn gy kh khn cho vic phn tch, chn on. Chnh iu ny, ngi ta da vo cc phng php tnh ton, phn tch cc thnh phn sng bng cc phng php khc nhau nh: wavelet, fourier v.v.. kt vi phn mm my tnh nhm a ra kt qu chn on tt nht.

PHP BIN I WAVELET RI RCCc chng trc kha lun trnh by v EEG l g, tm quan trng ca n nh th no i vi phn tch, tnh ton v chn on cng nh tm hiu khi qut v bnh ng kinh, cc dng sng EEG thng gp. chng 3 ny, kha lun tip tc trnh by php bin i wavelet m c th l wavelet ri rc, ta c c s kin thc nn tng cho vic phn tch cc c trng ca thnh phn sng v d on tn hiu c ri vo vng ng kinh khng.T Fourier n wavelet

Hnh 3.1: Joseph Fourier (1768 1830)Trc nm 1930, l thuyt phn tch tn hiu c bt u vi l thuyt phn tch ca Joseph Fourier (1807), thng gi l phn tch Fourier. ng pht biu rng mi hm f(x) tun hon vi chu k 2 u c th biu din bng tng [2].

(3.1)Cc h s a0, ak, bk c tnh bi cc tch phn sau

(3.2)Php bin i Fourier (FT) l bin i tch phn dng khai trin mt hm s theo cc hm s sin c s, c ngha l di dng tng hay mt tch phn ca cc hm s sin c nhn vi cc hng s khc nhau hay cn gi l bin , bn di l php bin i Fourier thun nghch:

(3.3)Bin i Fourier ngc:

(3.4)Trong : j l s o j2 = -1, . x(t) l tn hiu thi gian v X(f) l tn hiu tn s tng ng.FT l cng c hu ch trong vic tnh ton biu din tn hiu trong min tn s. Tuy nhin FT khng cp ti thi gian ca tn s trong mi ln xut hin, n ch thch hp vi cho nhng tn hiu tun hon, khng cha nhng t bin, hay l nhng thay i khng c d bo trc (stationary tn hiu dng ), i vi tn hiu khng dng (non stationary) nh: tn hiu ging ni, hnh nh, m thanh, in no .v.v.. Th nhng thng tin v thi gian xut hin ca tn s n din ra trong khong thi gian ngn, khng r. Chnh v th, FT khng p ng yu cu ny. Vy ti sao FT li khng p ng thi gian v tn s cng mt lc? L v trong phn tch tn hiu th vic yu cu ng thi c c thng tin min thi gian v tn s l vn phc tp v rt kh t n s hon ho c, v min thi gian v min tn s tun theo nguyn l bt nh Heisenberg [4], cng thc (3.5) cho ta thy c iu ny.

(3.5)Trong : l h s bt nh ca tn hiu trong min thi gian, l h s bt nh ca tn hiu trong min tn s. Nu mt trong hai h s tin v khng th h s cn li s tin n v cng [4]. V th, ch c php bin i mang tnh tt hn ch khng c php bin i no mang tnh hon ho, FT ch p ng tt min tn s nn khng p ng tt v min thi gian, v khng c nh gi cao i vic x l tn hiu khng dng. Hng nghin cu dn c pht trin cc nh khoa hc ngh ra tng mi gii quyt vn min tn s v min thi gian bng cch dng STFT (Short Time Fourier Transform) chia tn hiu thnh tng khong nh theo thi gian ri dng FT Hnh 3.2, hay c th hn l hi sinh mt t thng tin v cc tn s thp trong min tn s c thm nhng thng tin trong min thi gian, STFT c biu din bng hm G(, t) theo hai bin tn s v thi gian t. Nh vy khi nhn vo kt qu ta c th bit c tn s xut hin thi im no trong min thi gian.

Hnh 3.2: Php bin i STFTCng thc:

(3.6)Hm G(, t):

(3.7)STFT ph bin nht l Garbor transform, c trng bi hai tham s l v tr v rng. T a ra vn l chn v tr v rng nh th no t c kt qu mong mun, nu chn v tr v rng ca s cng ln th c thm thng tin v tn s (thp) nhng mt thng tin v min thi gian v ngc li hnh 3.3, vic chn la ny khng c quy lut no thng nht c m ch yu da vo xc nh th cng, chnh v th c trng hp b sai lch v kt qu c khi cn km hn so vi FT.

Hnh 3.3: Biu th min tn s - thi gian trong STFTNhng nm 1930 nhiu nhm cc nh khoa hc nghin cu cch biu din cc hm dng cc hm c s c t l thay i (scale varying basic function). H nhn thy Haar c nhiu u im hn so vi FT v STFT. Nhng nm 1960, Guido Weiss v Ranald.R Coifman nghin cu cc phn t c bn nht ca mt khng gian hm, c gi l cc atom, nhm mc ch tm cc atom cho mt hm chung v tm cc lut kt hp cho php xy dng tt c cc phn t ca khng gian hm dng cc atom ny. Nm 1980, Grossman v Morlet nh ngha wavelet trong vt l lng t. n nm 1985, Stephene Mallat p dng wavelet trong x l tn hiu s , cc thut ton hnh thp, hm c s trc giao wavelet v Meyer wavelet c cng b, Ingrid Daubechies s dng nghin cu Meyer xy dng nn cc hm c s cho cc ng dng [2], t wavelet gii quyt vn rng ca s khc nhau ng vi tn s khc nhau v tr thnh cng c tt nht cho vic phn tch tn hiu khng dng.Php bin i wavelet Phn trn ta gii thiu khi qut i t Fourier n wavelet, qua ta cng hiu s c nhng im u v hn ch ca FT v cng gii thch c ti sao wavelet c s dng ph bin cho tn hiu khng dng. Tip theo ta s tm hiu mt cch c th v wavelet.Wavelet l g? Khi nim:Trong ton hc chui wavelet l mt i din gm cc hnh vung kh tch (square-integrable) c gi tr thc v phc tp [14].

Hnh 3.4: Minh ha cho waveletPhp bin i wavelet (WT) l nh x ca mt hm thi gian thnh mt hm hai chiu ca s v (thay v v trong STFT). Tham s s c gi l t l, n chia t l hm bng cch nn hoc dn n, v l tnh tin ca hm wavelet dc theo trc thi gian. Bn di l hm wavelet m:

(3.8)Trong :

: l hm wavelet c s, hay wavelet m.

: nhn t t l.

: nhn t dch chuyn.

: l mc nng lng tiu chun gia hai thnh phn khc nhau.Tnh cht: Tnh cht tr hay dch (shift):Bin i Fourier c tnh cht tr, nu mt tn hiu f(t) v tn hiu bin i F() th tn hiu tr f(t ) l e-j F(). Cn i vi wavelet th sao? Tng t ta gi s hm v h s bin i l f(t) v F(m,n) th lc ny tn hiu tr f(t k) s l F(m,n).

Hnh 3.5: Tnh cht tr Tnh cht t l (scaling):nh t l wavelet l ko gin hoc nn tn hiu, thng c k hiu bng ch a. H s a cng nh, wavelet cng c nn mnh hn, do c kh nng biu din cc tn hiu c thnh phn tn s cao

Hnh 3.6: Tnh cht scaling Ly mu hai ngi thi gian v tn s:Khi xt mt m rng wavelet th nh v cc hm c s trong mt phng thi gian tn s l rt quan trng. Vic ly mu theo thi gian, t l m, c thc hin vi chu k 2m. V tn s th ngc li vi t l nn ta tm c nu wavelet tp trung quanh 0. iu ny dn n vic ly mu dyadic ca mt phng thi gian tn s nh minh ha trong hnh 3.7.

Hnh 3.7: Ly mu hai ngi thi gian v tn s

Tnh cht nh v (localization):Mt trong l do khin wavelet tr nn ph bin l kh nng nh v tt. nh v bao gm nh v tn s v nh v thi gian. nh v v thi gian, xt mt tn hiu ti thi im t = t0 khi ta s bit F(m,n) gi tr ca php bin i wavelet mang nhng thng tin no ca tn hiu f(t) thi im t0, Cn nh v tn s cho bit thnh phn tn s 0 s nh hng nh th no n wavelet t l m no .Php bin i Wavelet lin tc Php bin i thun:Php bin i wavelet lin tc l tng trn ton khong thi gian ca tn hiu nhn theo t l, dch mc ca hm wavelet [1], cng c th nh ngha nh sau:

Gi f(x) l tn hiu 1 D (mt chiu), php bin i wavelet lin tc ca f(x) s dng hm wavelet c biu din bi:

(3.9)Trong :

l h s bin i wavelet lin tc ca f(x), vi s l t l v l dch chuyn c trng v tr.

l hm lin hip phc ca wavelet c gi l hm wavelet phn tch. Phng trnh (3.9) cho thy php bin i wavelet l mt nh x chuyn t hm mt bin th f(x) thnh hm ph thuc vo hai bin s t l s v bin dch chuyn . H s chun ha trong (3.9) m bo cho s chun ha sng wavelet vi cc t l phn tch s khc nhau.

Hnh 3.8: Minh ha cho CWT Php bin i nghch:Nu php bin i wavelet thun c dng (3.9) th php bin i wavelet nghch c dng nh sau:

(3.10)Trong :

l hng s ph thuc vo hm wavelet c s dng.Cng thc (3.10) cho php khi phc li tn hiu nguyn thy t cc h s bin i wavelet bng php tch phn theo ton b cc tham s t l s v dch chuyn .Php bin i Wavelet ri rcMc d php bin i wavelet lin tc cho php s tnh ton ca bin i wavelet lin tc bi my tnh nhng vic tnh ton cc h s wavelet mi t l l cng vic nng nhc v pht sinh nhiu d liu, cc d liu ny yu cu mt s lng ln thi gian tnh ton v ti nguyn lu tr. V th, thng ngi ta ch chn mt tp con cc t l v v tr thc hin tnh ton [1].Trong trng hp ny php bin i wavelet c thc hin bng cch da trn li ri rc (discrete grid) ca h s t l v h s dch. Vi mi khung (framework c th hiu l vung kh tch biu th cho h s t l v dch), mt tn hiu bt k x(t) c nng lng hu hn (finite energy) c th c vit bi cng thc wavelet trc giao c bn sau:

(3.11)

c tnh nh sau:

(3.12)

l hm trc giao c bn, bao gm tt c h s t l v h s dch ca hm phn tch wavelet , c th hin bn di:

(3.13)Vi m v n ln lt l h s t l v dch tng ng th cng thc biu th cho php bin i wavelet ri rc mc m c cng thc sau:

(3.14)i vi tn hiu, ni dung tn s thp l thnh phn quan trng nht, n cung cp nhng thng tin quan trng lin quan ti vic nhn dng chnh n. Cn i vi tn s cao n cung cp sc thi ca m thanh. V d xem xt ging ni ca con ngi, nu chng ta loi b thnh phn tn s cao th ging ni s khc i nhng vn c th nghe h ni g, tuy nhin nu loi b cc thnh phn tn s thp chng ta khng nghe r c m thanh , n b sai lch. Chnh v th trong php bin i wavelet ri rc chia tn hiu thnh hai thnh phn quan tm l h s chi tit (details D) v h s xp x (approximation A).Cng thc xc nh hai h s ny c biu hin bn di:

(3.15)

(3.16)Trong : h[l 2n], g[l-2n] tng ng lc thng cao, thng thp. M hnh cho DWT ny c th hin l mt lc (filter) hai thnh phn thng thp (lowpass) v thng cao (highpass). Trong h s chi tit (D) tng ng vi thng thp v tn s cao, cn h s xp x (A) tng ng thng cao v tn s thp. hnh 3.9 th hin r iu ny:

Hnh 3.9: Lc mc c bnTn hiu gc s i qua hai b lc thng thp, thng cao vi hai c khc nhau hay b nhau. Nu tn hiu s c 1000 mu d liu th kt qu d liu ra mi u s l 1000 mu v tng l 2000 mu. iu chnh li, ta gim mu to ra hai chui cA v cD. Khi lm vic ny s dn n hin tng bit danh[footnoteRef:5] trong thnh phn tn hiu. [5: Tn hiu s b thay i, c th mt i mt s tnh cht hay c trng ca tn hiu]

Tuy nhin, khng c hin tng bit danh trong trng hp ny v mi b lc c rng bng na chiu di ca tn hiu, do khi cc d liu nhp b ly mu xung th khong cch gia hai mu vn tha mn tn s Nyquist. r hn ta xem hnh 3.10 cc thao tc ly mu ca DWT [1].

Hnh 3.10 Thao tc ly mu Phn tch a mcQu trnh tch c th c lp li trn h s xp x, do tn hiu c tch thnh nhiu thnh phn phn gii thp hn. N gi l cy phn tch wavelet

Hnh 3.11 Cy waveletV d mt tn hiu gc c phn tch thnh cc mc vi nhiu h s chi tit, xp x bn di:

Hnh 3.12: V d phn tch Ti to wavelet (Recontruction)Ti to hay tng hp tn hiu ngha l ta s lm cch no nhng thnh phn tn hiu m chng ta phn tch kt hp li vi nhau to thnh tn hiu nguyn thy m khng lm mt i nhng thng tin. Cch lm nh th ny ta gi l bin i ngc wavelet ri rc (IDWT). tng hp tn hiu, ti to tn hiu t cc h s chi tit v xp x th ngi ta thc hin cc bc bao gm hm lc v tng mu (up sample). Tng mu ta hiu mt cch n gin l tng chiu di thnh phn tn hiu bng cch chn s khng vo [1].

Hnh 3.13: Ti to tn hiu t cc h s ca DWT

Hnh 3.14: Tng mu bng cch chn im khngGii thiu c bn cc h wavelet Haar wavelet: y l nhng l dng wavelet u tin n gin nht, l mt wavelet ri rc(x) = 1 nu 0 x (3.17)(x) = -1 nu x 1(3.18)(x) = 0 nu x [0,1](3.19)

Hnh 3.15: Haar wavelet Wavelet Daubechies: y l nhng wavelet khng c biu hin r rng, ngoi tr h wavelet db1, l wavelet Haar. Wavelet Dauberchies l mt wavelet trc giao.Tn vit tt l dbN, N l th t, db l tn h ca wavelet. Hu ht dbN thng khng i xng

(3.20)

Vi v Hnh 3.16 th cc dng Daubechies khc nhau.

Hnh 3.16: Daubechies (dbN) Biorthogonal wavelets: Cc Biorthogonal wavelets th hin thuc tnh ca pha tuyn tnh, iu ny rt cn thit cho vic phn tch tn hiu c bit l hnh nh.

Hnh 3.17: Cc dng Biorthogonal wavelets Wavelet SymletsCc h wavelet symlets a s i xng, gn ging vi h wavelet Daubechies. H ny c k hiu l symN, vi N (N=2,8) l bc ca wavelet.

Hnh 3.18: Cc dng ca wavelet symlets

PHNG PHP THC HINNgy nay, c rt nhiu phng php phn tch tn hiu EEG khc nhau nh: Fourier, phng php tuyn tnh hoc khng tuyn tnh, php bin i wavlet kt hp mng n ron, phn tch trong min tn s.v.v..Kha lun ca tc gi dng wavelet ri rc (DWT) xc nh cc thnh phn sng, sau trch ra cc h s c trng c bn nhm xc nh ngng ng kinh v ngng ca ngi khe mnh.t vn v chn h wavelet qu trnh thc hin phn tch tn hiu EEG t hiu qu cao, trc ht cn chn ra loi wavelet thch hp, khi cho ra h s chi tit v h s xp x tt cho qu trnh x l. Do tnh nng ca php bin i wavelet ri rc cho phn gii tn s ti u trong tt c cc phm vi tn s, nhanh v mang tnh n nh cao, nn tc gi chn DWT cho kha lun ny. Nhc li khi qut v DWT: cung cp biu din di dng nn trong min thi gian tn s gip cho vic tnh ton din ra nhanh chng, t hiu qu hn.Cng thc:

(4.1)H s xp x v chi tit:

(4.2)

(4.3)Sau khi chn c wavelet, ta tin hnh chn h wavelet. H biorthogonal wavelets (bior) ch thch hp cho x l nh v h ny th hin thuc tnh pha tuyn tnh, mt trong nhng c tnh quan trng trong x l nh. H sym v db th c dng gn ging nhau nn c th chn mt trong hai h ny, y tc gi chn h db (Daubechies). b)a)

Hnh 4.1: Daubechies 2(a) v Haar(b)Trong h Daubechies c rt nhiu loi khc nhau (db1 ... dbN), db1 (Haar) khng tt v hnh dng nh hnh 4.1.b. B lc db1 ging ca s lc (window filter), chnh v hnh dng ca b lc ny nn cc gi tr ca tn hiu nm cc bin hai bn (vng nh du hnh 4.2) khng c x l tt khi dng b lc db1, c th nh hng n phn tch cc thnh phn.

Hnh 4.2 nh hng ca db1 vi cc tn hiu nm vng bin.Cn i vi db2 th c dng nh hnh 4.3, cc gi tr ca tn hiu nm vng bin (vng nh du) s c x l tt hn db1, v c dng gn ging nh tn hiu EEG tng t bin to nh v gim mnh hai bin.

Hnh 4.3 db2 v tn hiu EEG h wavelet Daubechies c nhiu loi tr db1 kho st, tc gi ch chn db2 v c nhng l do nh hng n tng hp tn hiu (recontruction). L do nh hng l s mu khng trng khp, xt v d.V d: Dng db2 cho phn tch mt tn hiu EEG, yu cu cn tng hp tn hiu s t hai h s cA9 (130 mu), cD11 (66 mu), vn khi ta nng s mu cD11 ln hai (66x2) tng hp tn hiu s, kt qu hai h s cA9 v cD11 khng tng thch s mu v gy li khi tng hp tn hiu nh hnh 4.4. Cch khc phc: tc gi loi b hai gi tr hai bin ca h s cD11(sau khi dng lnh upsample)

Hnh 4.4 S sai khc s mu khi dng db2 cho phn tch.Quay li vn ti sao chn db2 m khng chn loi Daubechy khc, Gi s nu ta tip tc dng db3, db4.... dbN th hai s mu ca hai h s cA9, CD11 chnh lch rt ln hnh 4.5 (phi loi b 6 gi tr), iu ny dn n cch khc phc ca tc gi s loi b nhiu hn hai gi tr hai bin. Cch lm ny s dn n tn hiu tng hp b lch, sai khc so vi tn hiu ban u, nh hng n kt qu tnh ton.

Hnh 4.5 db4 cho phn tch tn hiu EEG T nhng nh ngha, c trng v nhng nguyn nhn trn, tc gi kt lun i vi phn tch ny th chn db2 l ti u nht.Phng php thc hinC s d liu c th phn tch tn hiu th trc ht phi c ngun tn hiu, l iu khng th thiu, ngun tn hiu phi uy tn ng thi tha mn cc yu cu thit cho vic phn tch, nu ngun tn hiu khng thch hp th kt qu phn tch s hon ton sai.Trong ti ny tc gi chn c s d liu t khoa nghin cu ng kinh thuc trng i hc Bonn. Trong c nm b d liu t set A n set E mi mt th mc trong mi b c tn hiu cha 4096 mu (sample), vi tn s ly mu l 173.61 Hz c ghi nhn t h thng chun t 10 n 20 im cc. Mi b tn hiu EEG c trng ring cho mi tnh nguyn vin, ta ch quan tm n hai b mu cn cho kha lun l set A v set E. set A l tn hiu c ghi nhn t nhng ngi khe mnh, cn set E l ca nhng ngi ng kinh, co git hoc c triu chng bnh ng kinh.

Hnh 4.6: C s d liu t websiteS phn tch tn hiu Tn hiu EEGBin i waveletCc thnh phn sng Cc h s c trngKt lun Xy dng ngngHnh 4.7: S phn tch tn hiu

Hnh trn l s cc bc thc hin, i t d liu ban u khi qua php bin i wavelet th thu c cc thnh phn sng nh alpha, beta, delta, theta. Sau da vo cng thc tnh ton ta s thu c cc c trng cho mi thnh phn sng, da vo cc c trng tc gi xy dng ngng v kt qu l d on tn hiu bt k c ri vo vng ngng hay khng.Xy dng s phn tch h s chi tit v xp xNh cp chng mt, mt tn hiu EEG cha nhiu thnh phn sng khc nhau cc khong tn s khc nhau, c c thnh phn sng mong mun th vic xy dng v kt hp cc h s chi tit v h s xp x rt quan trng.

Hnh 4.8: S phn tch h s chi tit v xp x c c s hnh 4.4 l nh vo chng 3 mc 3.2, tn s v s mu gim i mt na sau mi ln dng DWT cho h s chi tit hoc l h s xp x. Tn s ly mu l 173.6 Hz nhng phi tha mn iu kin Nyquist Shannon l fs fm/2. Trong fs/2 l tn s Nyquist v khong Nyquist (-fs/2; fs/2), l l do ti sao tc gi li chn tn s phn tch t hnh 4.4 l 86.8 Hz.Cn c vo s hnh 4.4 ta s chn ra h s ph hp nht tng hp tn hiu mong mun, Nn lu n cc h s c nh du nh: CA7, CA8, CD8, CA9, CD9, CA11, CD11, CD10, CD6 v CA4. Da vo khong tn s ca tng thnh phn sng alpha (8 12 Hz), beta (12 30 Hz), theta (4 8 Hz), delta (0 4 Hz), m ta tng hp cc h s chi tit sao cho ph hp nht.Bng 4.1: Tng hp cc h s chi tit v xp xThnh phn sngKhong tn s (Hz)H sS mu sau khi tng hp tn hiu

Delta0 - 4CA7, CA8256

Theta4 - 8CD8, CD9256

Alpha8 - 12CD9, CA11256

Beta12 - 30CD11, CD10, CD6, CA41024

Vn : s mu ca CA7 (64 mu), CA8 (128 mu) khng ging nhau gy kh khn cho vic tng hp tn hiu (recontruction), gii quyt ta nng s mu CA7 ln bng cch dng hm upsample trong matlab. Tng t i vi CD8, CA11 v CD11.c)b)a)

d)

Hnh 4.9: M hnh tng hp thnh phn sng ca tn hiuCc thnh phn sng alpha, beta, theta, delta c tng hp bngcch kt hp nhng h s chi tit v xp x nh hnh 4.5 sao cho ph hp nht, sau khi tng hp ta c bng 4.2 sau:Bng 4.2: Tn s yu cu sau tnh ton mi thnh phn sngThnh phn sngKhong tn s yu cu (Hz)khong tn s sau khi tnh (Hz)

Delta0 - 40 - 4.05

Theta4 - 8 4.05 - 8.1

Alpha8 - 128.1 - 12.15

Beta12 - 3012.15 - 32.5

Cn c vo Bng 4.2, kt qu sau khi tng hp cc h s chi tit v h xp x cho kt qu tng i chnh xc.Cc c trng ca mi thnh phn sngSau khi tch ra c cc thnh phn sng, bc tip theo l bc quan trng nht chnh l trch ra cc h s c trng cho mi thnh phn sng, cc c trng nh cha kha gip chng ta phn bit c nhng tn hiu no l ng kinh, nhng tn hiu no ca ngi khe mnhGm bn c trng sau: H s phng sai (Variance)H s phng sai l tham s rt tt o lng s bin thin hay phn tn ca d liu trong mu v quan tm n lch ca mi quan st so vi s trung bnh, loi b nhng nh hng ca kch thc mu. Gi s c bin ngu nhin X c gi tr mu cho mi thnh phn sng nh sau: Xi = {X1, X2, X3 ... Xn, Xi chnh l cc thnh phn sng delta, theta, alpha, beta. Phng sai ca chng c nh ngha nh cng thc 4.4.

(4.4) l gi tr trung bnh ca ca X, n l s mu ca d liu EEG, phng sai ca mi thnh phn c th c biu din bng cc vector c trng. Thng thng ngi bnh ng kinh c phng sai rt ln so vi ngi khng ng kinh. Nng lng (Energy):Nng lng ca tn hiu c nh ngha l tng ca bnh phng m un ca mu gi tr ca tn hiu bt k. Nng lng ca tng thnh phn sng c tnh bi cng thc sau:

(4.5) Mt ph cng sut (Power Spectral Density):Mt ph cng sut (PSD) l i lng ca cng sut trn n v tn s ging nh hm tn s. Tch phn ca PSD trn mi khong tn s chn c tnh l trung bnh cng sut ca tn hiu trn khong tn s . C rt nhiu thut ton khc nhau xc nh PSD.Mc d FFT c s dng ph bin phn tch tn hiu nhng li khng p ng tt i tn hiu khng dng, loi b nhng nhc im ngi dng phng php Periodogram cho phn tch PSD xc nh nhng thay i trong min thi gian ca tn hiu EEG. Cng thc 4.6 th hin r iu ny.

(4.6) Entropy:Entropy m t s thng k s thay i ca tn hiu in no , l s o ty chn ca tn hiu, l cng c tt nht phn tch cc c trng ca chui tn hiu thi gian. Entropy l mt trong nhng c trng quan trng cho phn tch v pht hin bnh ng kinh, c tnh bi cng thc 4.7.

(4.7)Trn l bn c trng c cho l quan trng, nhng thng thng khi xc nh bnh ng kinh ngi ta ch quan tm n ba c trng ln l: h s phng sai, mt ph cng sut v entropy. Bng 4.3 l cch t tn ngn gn cho tng c trng ca mi thnh phn tn hiu EEG.Bng 4.3: t tn cho cc h s c trngCc c trngDeltaThetaAlphaBeta

H s phng saiv1v2 v3v4

Nng lngE1E2E3E4

PSD maxmax1max2max3max4

PSD minmin1min2min3min4

Entropyen1en2en3en4

Hm matlab s dngBng 4.4: Hm matlab c bnHm c bnnh nghaC php

1dwtPhp bin i ri rc thun dng phn tch cc thnh phn sng[CA1, CA2] = dwt(s,'db2')

2idwtPhp bin i ri rc nghch nhm tng hp tn hiua = idwt(CA1, CD2, 'db2')

3upsampleNng s mu thch hp tng hp tn hiuca8 = upsample(cA8,2)

4wentropyEntropye1 = wentropy(DELTA,'shannon')

5varH s phng saiy1= var(DELTA)

6wenergyNng lng[Ea1,Ed1] = wenergy(C1,L1)

7periodogramMt ph cng sut[Pxx1,w1] = periodogram(DELTA)

KT QU THC NGHIMChng bn kha lun trnh by v cch phn tch thnh phn tn hiu nh th no? Tnh cc c trng ra lm sao? Ni tm li chng bn trang b kin thc cn thit v phng php thc hin, chng nm ta i vo vit code xy dng chng trnh, kho st gia tn hiu ng kinh v tn hiu ca ngi khe mnh c s khc bit nh th no? ng thi xc nh ngng tn hiu xt mt tn hiu bt k xem th chng c ri vo vng ng kinh hay khng.Kho st tn hiu ng kinh v tn hiu ca ngi khe mnh Phn tch cc thnh phn:

Hnh 5.1: Tch cc thnh phn chi tit v xp x Trong matlab c rt nhiu hm matlab dnh cho php bin i wavelet ri rc, nhng ti sao tc gi chn hm dwt m khng chn nhng hm khc, l do nh sau: Hm dwt tha mn cc iu kin, th nht khng hn ch l vic phn tch t cc h s chi tit v xp x, th hai l ngn gn d hiu.Xt hm wavedec[footnoteRef:6], i vi hm ny ch phn tch t cc h s xp x m khng phn tch c h s chi tit. Chnh v th, nu dng hm ny ta khng th tng hp tn hiu mong mun mt cch tng i chnh xc c khi chng ri vo vng chi tit. hiu r hn xt v d 5.1. [6: L mt trong nhng hm dnh cho php bin i wavelet ri rc ]

V d 5.1: Cn tch thnh phn sng t 10 32.5 Hz t sng c tn s 43.4 HzHm wavedecHm dwt

Khng th tng hpTng hp (recontruction) t hai h s CD3 v CA4

Khng th phn tch h s chi titLinh ng c th phn tch h s chi tit v xp x

Tng hp tn hiu:

Hnh 5.2: Tng hp tn hiu thnh phnDa vo bng 4.1 ta tin hnh vit code nh hnh 5.2. a8 = ca8(2:131) hoc cc dng tng t nh vy c ngha g? Mc ch ca tc gi cc dng ny l ly 130 s liu v b i hai bin ca h s, l do tc gi lm vic ny l v cA7 v ca8 khng cng s mu gy li khi tng hp tn hiu.Sau khi tc gi phn tch cc thnh phn tn hiu tin hnh v xem hnh dng ca tng sng v tnh cc h s c trng. Tn hiu ca ngi khe mnh:

Hnh 5.3: Tn hiu u vo ca ngi khng ng kinh

Hnh 5.4: Cc thnh phn sng ca ngi bnh thng Tn hiu ca ngi bnh ng kinh

Hnh 5.5: Tn hiu u vo ca ngi ng kinh

Hnh 5.6: Cc thnh phn sng ca ngi ng kinhKt qu: i vi hnh 5.6 th quan st ta thy tn hiu bnh ng kinh xut hin nhiu gai nhn, t bin din ra lin tc. thy r lp bng so snh gia l thuyt v kho st.L thuytKho st bng matlab

Tn hiu ng kinh nh gai theo l thuyt trnh by chng 2 Mu S008 tn hiu ng kinh git lin tc

Phng in dng ng kinh theo chu k

Mu s007 ca tn hiu ng kinh

Dng a gai Mu s005, 007, 022, 036 v.v..

Kt qu kho st bng matlab tng i ging vi l thuyt trnh by, qua ta c th nhn bit cc dng ng kinh bng quan st da trn cc th ca tn hiu[footnoteRef:7] [7: Lu : vic nhn dng bng quan st tn hiu bnh ng kinh ny ch mang tnh tng i v rt ging vi cc bin th dng ng kinh ( c cp chng 2).]

Tnh ton cc h s c trng v xc nh ngngXc nh h s phng sai:

Hnh 5.7: H s phng sai.Xc nh mt ph cng sut (PSD):

Hnh 5.8: Code tnh PSD.Xc nh h s entropy:

Hnh 5.9: H s entropy.T h s xy dng da trn hnh 5.7, 5.8, 5.9 tc gi dng chng x l cho 100 b d liu gm 50 b tn hiu ng kinh v 50 b tn hiu bnh thng, sau xc nh ngng bng cch tm ra cc gi tr ln nht v gi tr nh nht ca tng h s c trng. Trong bng 5.1 t max dng ch nhng gi tr ln nht, t min ch gi tr nh nht cho cc h s .Bng 5.1 bn di l khong (ngng) xt mt tn hiu bt k c ri vo vng ng kinh hay khng, bng ny c tnh ton da vo bng trong phn Ph lc A, B.Bng 5.1: Khong gi tr ngng ca tn hiu ng kinh v tn hiu ca ngi khe mnh.

v1v2v3v4

Khng ng kinhmax32735.98474.285414.7062622.793

min2652.121317.551059.917439.901

ng kinhmax175296211998551373797640599.521

min47532.722529.57326.0491965.273

max2max3en2en3

Khng ng kinhmax16808.316706.3-1726050.71-993906.076

min1422.06928.756-11202956.1-81116678

ng kinhmax31942004128871-30965288.4-12529097.2

min42276.19872.44-2151666141-2868389579

Xy dng chng trnhCc bc xy dng chng trnh nh sau: Bc 1: a d liu EEG vo.Bc 2: dng php bin i wavelet tch ra cc thnh phn da vo tn s tng ng.Bc 3: tng hp tn hiu sau khi tch.Bc 4: Tnh ra cc c trng c mi thnh phn tn hiu v xy dng khong xc nh hay ta gi l ngng.Bc 5: da vo ngng c th d on tn hiu c ri vo khong ng kinh hay khng. hiu r hn v cc bc thc hin ta xem lu gii thut sau hnh 5.10:

Nh hn ngngBt u uD liu vo EEGPhp bin waveletTnh cc c trng v xc nh ngngLn hn ngngVng khng ng kinhVng ng kinhVng tim n ng kinhKt thcHnh 5.10: S gii thut cho chng trnh

Xy dng giao dinDa trn s thut ton v yu cu kha lun, di y l giao din chng trnh s dng php bin i wavelet ri rc kho st cc c trng v d on tn hiu c ri vo vng ng kinh hay khng, giao din c thit k bng Matlab GUIDE.

Hnh 5.11: Giao din chng trnh Chng trnh c b tr 6 khung:Khung Raw signal dng v tn hiu cha phn tch bng wavelet. Khung Input Data a d liu vo, hin tn file khi dng button Browse tm th mc d liu. Khung Processed signal v tn hiu x l khi ta n button DWT analysis.Khung Result hin th cc c trng ca mi thnh phn tn hiu khi ta nhn button Caculate. Khung Detection, khung ny ta s d on tn hiu bt k thuc setA hoc setE xem chng c ri vo vng ng kinh hay khng. Khung Output file xut ra th mc vi nh dng .txt khi dng button Write, button Earse xa d liu trong th mc Output.txt.Bng 5.2: Kt qu d on vi 100 b d liu cn li thuc setA, setEMu Tn hiu mu chnh xc ca d on

SetA50 b d liu cn li (t Z051 Z100)90%

SetE50 b d liu cn li (t S051 S100)90%

Kt qu: sau khi dng chng trnh ny phn tch thm 100 b d liu cn li khng thuc b d m ta em phn tch kt qu thu c rt tt, chng trnh xc nh tng i chnh xc cc tn hiu no ri vo vng ngng ng kinh, chnh xc khong 90%.

KT LUN V HNG PHT TRINNgy nay, vic phn tch cc tn hiu EEG chn on ra cc cn bnh tim n nh bnh ng kinh, nhm c bin php thch hp v can thip kp thi cha tr, l vn c quan tm rt nhiu trong nghin cu y sinh. Kha lun trnh by khi nim c bn v in no , l thuyt v bnh ng kinh v nhng bin th gy nhm ln, l thuyt v php bin i wavelet (bin i wavelet lin tc v wavelet ri rc), ng thi phn tch cc c trng quan trng khng ch d on ng kinh hay khng m nhng c trng ny cn ng dng phn tch cc hot ng khc, bt thng ca no nh: ung th no, co git, cc bnh lin quan khc. KT LUN Kt qu t c: Phn l thuyt, trong ti ny tc gi tip cn l thuyt in no v php bin i wavelet. L thuyt bnh ng kinh, cc dng bt thng, bin th dng ng kinh. Phn thc nghim: Tc gi xy dng thnh cng s phn tch cc thnh phn tn hiu: alpha, beta, delta, theta. Tnh c cc c trng nh: h s phng sai, mt ph cng sut, entropy, nng lng nh vo vic dng php bin i wavelet ri rc vi h dng tt nht l db2 (v h db2 cho s mu tng i ph hp khng gy kh khn nhiu khi tng hp tn hiu). Xc nh khong hay ngng tn hiu ri vo vng ng kinh hay vng khe mnh Xy dng chng trnh giao din thn thin v n gin d s dng cho ngi dng. Gii hn ti: Do hn ch thi gian, kha lun ch dng vic xc nh khong hay ngng tn hiu, cha th xc nh mt cch chnh xc l tn hiu ang xt c ng kinh hay khng. Cha tm hiu cch hun luyn tn hiu EEG thng qua cc c trng bng mng n ron chun on bnh. HNG PHT TRINNu c iu kin, tc gi mun tip tc tm hiu thm v mng n ron, cch a cc c trng vo mng n ron, cch chn cc nt n ph hp hun luyn tn hiu bt k nhm xc nh mt cch chnh xc bnh ng kinh, ch khng ch dng li vic kho tn hiu EEG.

Ti liu tham khoTing Vit [1]Nguyn Thy Uyn Phng (2013), ng dng php bin i Wavelet pht hin bnh thiu mu da trn tn hiu in tm , trang 20.Ting Anh [2]Amara Graps (1995), An Introduction to Wavelets, IEEE Computational Science and Engineering, Vol. 2, No. 2.[3]Dumitru Baleanu (2012), Waveler Transform and Their Recent Application in Biology and Geoscience, Cankaya University, Faculty of Art and Sciences.[4]Pao Yen, An introduction to Wavelet Transform, Lin Digital Image and Signal Processing Lab Graduate Institute of Communication Engineering National Taiwan University, pp. 16 17.[5]Saeid Sanei and J.A. Chambers (2007), EEG processing, Centre of Digital Signal Processing.[6]Laxman Tawade (2011), Detection of Epilepsy Disorder Using Discrete Wavelet Transforms Using MATLABs, Vidya Pratishthans College of Engineering, Baramati, India.[7]Mandeep Singh and Sunpreet Kaur (2012), Feature Selection for Epilepsy Detection Using EEG, International Journal of Information Technology and Knowledge Management.[8]Shah Aqueel Ahmad (2013), Wavelet Based Epilepsy Detection in EEG Using Neural Network, Royal Institute of Tech. & Science, pp.73 77.[9]Juuso Olkkonen (2011), Discrete Wavelet Transforms Theory and Applications, India.[10]Yves Misiti Michel Misiti, Georges Oppenheim, and Jean-Michel Poggi (1997), Wavlet Toolbox Users Guide, University of Marne La Valle and Paris10 University Sciences at Paris 11 University.T trang web[11]http://www.tamgiaan.com/dong-kinh-cuc-bo_p1_1-1_2-1_3-598_4-39.html.[12]http://www.bvtt-tphcm.org.vn/n-vn-1195-0.[13]http://phvu.net/2014/01/25.[14]http://en.wikipedia.org/wiki/Wavelet_transform

Ph Lc A: Cc c trng ca ngi ng kinhBng d liu cc h s c trng ca ngi bnh ng kinhSTTv1v2v3v4

1852486.735982718.94461265.921264882.666

21340920.229500075.75580663.124309890.227

3320156.062429684.01262487.471233766.284

497557.90452102.371165526.3219738.31

583676.89440045.12481822.3979535.468

6430797.712115257.4669838.01857309.061

7575951.186272286.931261816.803128186.163

8482668.869275847.98594818.13489577.451

9326028.046512188.08601494.018574226.873

10412055.907429896.55401096.14158120.322

111106356.622665903.781357860.94131068.282

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21145387.604121374.2287814.6245969.632

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50142724.71398483.88675609.65520351.419

STTmax2max3en2en3

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50171680.36785769.375-155270191.3-139974336.7

Ph Lc B: Cc c trng ca ngi khe mnhBng d liu cc c trng ca ngi khng ng kinhSTTv1v2v3v4

15681.5192808.963498.6531508.637

29922.8562570.3711626.854827.863

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467329.3732221.0991836.697509.453

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485601.8613935.7532234.3111287.974

4923150.295268.2362917.2941983.498

5024409.587043.6235414.7061963.988

STTmax2max3en2en3

12848.5755299.296-3072908-3300910

22850.9622566.764-2637425-1038188

38901.3623521.349-3985950-4542902

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2411263.294559.323-6905510-4586432

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3015810.72879.888-6269429-3265986

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496413.1353687.868-6077074-3990590

5010498.987241.829-7981667-6692116