Determination of Optimum Length of Frames and Number of Vectors to Compress ECG Signals

Transcription

1 World Acadmy of Scnc, Engnrng and Tchnology Vol:, No:, 7 Dtrmnaton of Optmum ngth of rams and Numbr of Vctors to Comprss ECG Sgnals aft Adnz, Pınar Tüfç, and B.Sıddı Yarman Intrnatonal Scnc Ind, Elctroncs and Communcaton Engnrng Vol:, No:, 7 wast.org/publcaton/654 Abstract In ths study, to comprss ECG sgnals, KT (Karhunn- ov Transform) mthod has bn usd. Th purpos of ths mthod s to prform ffctv ECG codng by a corrlaton btwn th lngth of frams and th numbr of vctors of ECG sgnals. Kywords ECG Comprsson, EKG Comprsson. I. INTODUCTION ODAY, th basc struggl of sgnal procssng groups s T to ncras th spd of data transmsson for dffrnt transmsson nvronmnts whch hav lmtd bandwdth. Th othr struggl n dffrnt data storag nvronmnts s to wor on how th data s stord n th lss spac as much as possbl. Th mdcal sgnal procssng, th spch codng, th spch rcognaton, th spch classfcaton, th nformaton scurty tc. for dffrnt ams l mthods frquncy doman, tm doman, transform doman, fuzzy logc and nural ntwors ar usd [,,3,4,5,6,7]. Th rason of why bomdcal data procssng, storng and transmttng mportant s to us n mdcal dagnoss and tratmnt. Bcaus of th ndd vry larg capacty, data storng, transmttng and rconstructng may caus spd and mmory problms partcularly n bomdcal sgnals (ECG, EEG, EMG tc). Th mntond problms ar sortd out by comprssng th sgnals n approprat ratos by png th mportant parts of th sgnals [8]. Th lctrocardogram (abbrvatd ECG or EKG) s a graphc rprsntaton of th hart's lctrcal actvty. If w wsh to stor an ECG rcordng that spans mor than a fw mnuts, som form of data comprsson s hghly dsrabl. aft Adnz s wth th Elctroncs and Communcaton Engnrng Dpartmnt, Çorlu aculty of Engnrng, Traya Unvrsty, Trdağ, Tury ( phon: ; fa: ; -mal: adnz@corlu.du.tr ). Pınar Tüfç s wth th Elctroncs and Communcaton Engnrng Dpartmnt, Çorlu aculty of Engnrng, Traya Unvrsty, Trdağ, Tury (-mal: pnart@corlu.du.tr ). B.Sıddı Yarman s wth th Elctrcal and Elctroncs Engnrng Dpartmnt, aculty of Engnrng, Istanbul Unvrsty, Istanbul, Tury (mal: yarman@stanbul.du.tr ). cordngs ovr qut long prods, as much as 4 hours, mayb ndd whn a patnt has compland of rrgular hart rhythms. Doctors may wsh to bult a databas of ECG rcordngs for thr patnts so that two ECG tracs tan on dffrnt dats may b compard. Comprsson s also dsrabl f a doctor wshs to transmt ECG ovr a tlphon ln to a cardac spcalst for an prt opnon [9]. Many stng comprsson algorthms hav shown som succss n lctrocardogram comprsson; howvr, algorthms that produc bttr comprsson ratos and lss loss of data n th rconstructd data ar ndd. Th Karhunn- ov Transform (KT) appars to b partcularly sutabl and s oftn usd for ECG comprsson. A comparson btwn th ECG comprsson mthods mntond abov. It ncluds Tabl, that collcts rportd rsults from many dffrnt sourcs [9]. II. METHOD (n) dscrt sgnal whch has N lngth can b dfnd as follows; N ( n) =. δ ( n ) () = In hr, δ (n) s unt sampl squnc and s ampltud of th sgnal. By dvdng th sgnal nto qual parts; ( ) + ( ) + = M followng th rsult s tan. = =, KN [ ] N T =,,...N T () s th sgnal of th fram, N T s th sum of th frams. or ach fram, topltz matr s calculatd as shown T Intrnatonal Scholarly and Scntfc sarch & Innovaton () scholar.wast.org/37-689/654

2 World Acadmy of Scnc, Engnrng and Tchnology Vol:, No:, 7 Intrnatonal Scnc Ind, Elctroncs and Communcaton Engnrng Vol:, No:, 7 wast.org/publcaton/654 blow. ( ) [( ) l ] ( + ) = r l l j= l =,,, K, as ndcatd, r () r () = r (3) M r ( ) r ( r () r () r () M ) j+ [( ) + ] r (3) r () r ( r () M ) O j+ + l r ( ) r ( ) r ( ) M r () (3) (4) s th slctd fram numbr. Th calculatd topltz matr for th th fram s a ral symmtrc and postv matr as blow dmnsons. V = λ V (5) λ and V dfn gnvalu and gnvctor for topltz matr. Th rlaton btwn th topltz matr of th srs and ts gnvctors can b shown as blow; By = = C V (6) C = ( ) T V (7) puttng λ,..., λ, λ, V V,..., V gnvalus n th dscndng ordrs, ar found wth th λ λ,..., λ gnvctors matchng. As a rsult of usng th gnvctors ndcatng th sgnal wth th mamum nrgy for ach fram can b calculatd wth th quaton (6). III. ECONSTUCTION O ECG SIGNA Accordng to (6) and (7) quatons, can b found asly from th gnvctors for ach N fram. Startng from th frst fram of sampl ECG sgnal, th stps blow can b prformd squntually. g.5 llustrats th flow chart of KT for ECG sgnal. Comprsson rato changs n ln wth th lngth of fram..stp:.stp: To dvd th ECG sgnal to aproprat lngth of fram (4-48). To dtrmn th Topltz matr for ach fram. 3.Stp: 4.Stp: 5.Stp: 6.Stp: 7.Stp: To dtrmn th gnvalus and gnvctors for ach Topltz matr. To dtrmn th C I coffcnt whch shows th lnar rlaton btwn th ECG sgnal and gnvctors. To arrang n dcayng squnc th gnvalus wth usng KT mthod. To spcfy th mamum gnvctors (havng th mamum nrgy) qual to mamum gnvalus. To rconstruct th ECG sgnal by multplyng th gnvctors whch ar havng th mamum nrgy and th coffcnt. = C V (8) IV. ESUTS In ordr to cod ECG sgnal n ffctv way optmum lngth of fram and numbr of vctors ar found. :3 rato whch s th numbr of vctors pr lngth of fram may b suffcnt for mdcal dagnoss and tratmnt. In ths mthod, frstly for any slctd ECG sgnal topltz matr s found for ach fram. And thn, th gnvctors ar slctd whch hav mamum nrgy. nally, th codng of th ECG sgnal s prformd by usng ths slctd gnvctors. Tabl shows th man squar rrors accordng to th dffrnt lngth of fram and numbr of vctors. MSE = C = (, C, ) (9) = gurs -4 show that th ratos of :, :, :3, :4 whch ar btwn th lngth of fram and numbr of vctors. Th rsults of fgurs and tabls sarch ar that to hav optmum ECG codng, th lngth of fram should b as much as mnmsd, th numbr of vctors should b as much as mamsd. EEENCES [] Adnz., Karaş A.M., Yarman B.S., Tursh spch codng by Sgnatur Bas Squncs, ICSPAT- Intrnatonal Confrnc on Sgnal Procssng Applcatons & Tchnology, p.9-94, Toronto, Canada, Sptmbr 998. [] Adnz., Yarman B. S., Gnraton of optmum Sgnatur Bas Squncs for spch sgnals, IEEE- ICASSP, Istanbul, Tury, Jun. [3] Adnz., Yarman B.S., Tml Tanım Dzlr İl onuşma odlama, SIU'98-6. Snyal İşlm V Uygulamaları Kurultayı, p.78-83, Anara, 998. [4] Bg, B., Mor., El-Bz M., Sprt T., A uzzy dcson stratgy for topc dntfcaton and dynamc slcton of languag modls, Sgnal Procssng (EUASIP), Volum:8, No.6, Jun. [5] Bourlard H., Kong Y., Morgan N., A tranng algorthm for statscal squnc rcognaton wth applcatons to transton-basd spch rcognaton, IEEE Sgnal Procssng ttrs, vol.3 No.7, July 996. [6] Kalouptsds N., Sgnal Procssng Systms-Thory And Dsgn, John Wly & Sons Inc. Nw Yor, 997. [7] Karaş A., Yarman B.S., A nw approach for rprsntng dscrt sgnal wavforms va prvat Sgnatur Bas Squancs", ECCTD'95 Procdngs, p , Istanbul, Tury, 995. Intrnatonal Scholarly and Scntfc sarch & Innovaton () 7 98 scholar.wast.org/37-689/654

3 World Acadmy of Scnc, Engnrng and Tchnology Vol:, No:, 7 [8] Güran H.,Güz Ü, Yarman B.S., EKG İşartlrnn Özgün Tml Tanım onsyonları l Modllnms, SİU- IEEE Snyal İşlm v Uygulamaları Kurultayı,c., s , 5-7 Nsan, Gazmağusa, T..N.C. [9] Horspool.N., Wndls W.J., An Z Approach to ECG Comprsson, /ECGComprsson/ TABE I SUMMAY O ECG DATA COMPESSION SCHEMES Mthod Comprsson ato Samplng at (No.of bts) Prcnt MS Dffrnc AZTEC, 5() %8, TP, () %5,3 Intrnatonal Scnc Ind, Elctroncs and Communcaton Engnrng Vol:, No:, 7 wast.org/publcaton/654 COTES 4,8 () %7, an/sapa 3, 5 %4, Entropy Codng of nd Dffrncs,8 5() - Pa Pcng (Spln) wth Entropy Codng, 5(8) %4, DPCM-Dlta Codng wth Thrshold 4, 3(8) - DPCM-nar Prdcton,5 5() - DPCM-nar Prd, Intrpl..Entropy Codng 7,8 5(8) %3,5 Orthogonal Transforms-CT, KT, HT 3, 5 - Dual Applcaton of KT, 5() - ourr Dscrptors 7,4 5() %7, T h N u m b r o f V c t o r s TABE II MEAN SQUAE EOS ACCODING TO THE DIEENT ENGTH O AMES AND THE NUMBE O VECTOS Th ngth of rams ,495E-8 3,43E-8 4,665E-8 3,3545E-8 4,375E-8 5,647E-8 8,4943E-8 8,33E-8 9,57E-8,657E-7,947E-7,38E-7 7,598E-9,849E-8,476E-8,765E-8,373E-8 3,9E-8 5,3E-8 3,53E-8 7,38E-8 7,659E-8 7,95E-8 8,85E-8 3,83E-,786E-9 4,5845E-9 7,84E-9 7,6E-9,76E-8,8348E-8,5356E-8 4,89E-8 6,68E-8 6,569E-8 6,435E-8 4 3,487E-37,5E-9,9958E-9 5,7E-9 6,577E-9,893E-8,634E-8,353E-8 3,973E-8 3,647E-8 4,654E-8 6,9E-8 6,345E- 7,976E-,538E-9,65E-9 4,6459E-9 3,3559E-9 8,8358E-9,66E-8 9,6664E-9 3,37E-8,63E-8 8 6,36E-37,99E- 6,48E-,36E-9,5468E-9,588E-9 3,699E-9 4,647E-9 4,58E-9,9E-8,3E-8 5,99E-,694E- 5,5E- 7,99E-,997E-9,444E-9,934E-9 3,375E-9 4,9E-9 4,666E-9 7,3395E-37,97E-,5988E- 5,493E- 7,73E- 8,77E-,93E-9,379E-9,694E-9 3,35E-9 6 8,578E-37 8,947E-,78E- 3,54E- 4,398E- 6,95E- 8,45E- 7,474E- 9,368E- 9,9E-37 9,554E-,333E-,49E- 3,448E- 4,457E- 5,8E- 5,89E- 4,E-36 4,97E-,367E-,386E-,5559E- 3,6898E- 4,67E- 8,898E-36 6,8994E-,4458E-,56E-,34E-,868E- 3,47E-36 6,7435E-,63E-,536E-,974E- 36,5666E-36 3,9795E- 6,5899E-,674E- 4,5985E-36 3,7875E-,347E- 44,43E-36 6,78E- 48,8765E-36 Intrnatonal Scholarly and Scntfc sarch & Innovaton () 7 98 scholar.wast.org/37-689/654

4 6,36E-37 World Acadmy of Scnc, Engnrng and Tchnology Vol:, No:, 7 3,E-36,5E-36,5985E-36,E-36,8765E-36,5666E-36,5E-36,43E-36,E-36,898E-36,47E-36,E-36 7,3395E-37 8,578E-37 9,9E-37 5,E-37 3,487E-37,E Intrnatonal Scnc Ind, Elctroncs and Communcaton Engnrng Vol:, No:, 7 wast.org/publcaton/654 Çrçv Uzunluğu Vtör Sayısı 4 Vtör Sayısı 8 Vtör Sayısı Vtör Sayısı 6 Vtör Sayısı Vtör Sayısı 4 Vtör Sayısı 8 Vtör Sayısı 3 Vtör Sayısı 36 Vtör Sayısı 4 Vtör Sayısı 44 Vtör Sayısı 48 g. Man squar rrors to th numbr of vctors / th lngth of frams = / 6,48E- 8,E-9 7,598E-9 7,E-9 6,E-9 5,E-9 4,E-9 3,E-9,E-9,5E-9,E-9 7,976E- 5,5E- 5,493E- 4,9794E- 4,398E- 4,676E- 4,457E- 4,39E- 4,67E-,E Çrçv Sayısı Vtör Sayısı Vtör Sayısı 4 Vtör Sayısı 6 Vtör Sayısı 8 Vtör Sayısı Vtör Sayısı Vtör Sayısı 4 Vtör Sayısı 6 Vtör Sayısı 8 Vtör Sayısı Vtör Sayısı Vtör Sayısı 4 g. Man squar rrors to th numbr of vctors / th lngth of frams = /,5E-9,9958E-9,E-9,5468E-9,5E-9,93E-9,E-9 9,368E- 5,E-,E Çrçv Uzunluğu Vtör Sayısı 4 Vtör Sayısı 8 Vtör Sayısı Vtör Sayısı 6 g. 3 Man squar rrors to th numbr of vctors / th lngth of frams = / 3 8,E-9 7,598E-9 7,E-9 6,E-9 5,E-9 4,E-9 3,E-9,E-9,5E-9,E-9 7,976E- 6,48E- 5,5E- 5,493E- 4,9794E- 4,398E- 4,676E- 4,457E- 4,39E- 4,67E-,E Çrçv Sayısı Vtör Sayısı Vtör Sayısı 4 Vtör Sayısı 6 Vtör Sayısı 8 Vtör Sayısı Vtör Sayısı Vtör Sayısı 4 Vtör Sayısı 6 Vtör Sayısı 8 Vtör Sayısı Vtör Sayısı Vtör Sayısı 4 g. 4 Man squar rrors to th numbr of vctors / th lngth of frams = / 4 Intrnatonal Scholarly and Scntfc sarch & Innovaton () 7 98 scholar.wast.org/37-689/654

5 World Acadmy of Scnc, Engnrng and Tchnology Vol:, No:, 7 Orgnal ECG Sgnal Sgmnt Choos ram ngth Intrnatonal Scnc Ind, Elctroncs and Communcaton Engnrng Vol:, No:, 7 wast.org/publcaton/654 construct Th ECG ram ngth ato=/4 8 construct Th ECG ram ngth ato=/4 Dtrmn Topltz Matr Dtrmn Egn Valus & Egn Vctors Dtrmn C Cofcnts Arranc dcayng ordr Egn Valus & Egn Vctors Spcfy ma. Egn Vctors construct Th ECG ram ngth ato=3/4 construct Th ECG ram ngth ato=4/ Numbr of Vctors/ngth of rams=/ Numbr of Vctors/ngth of rams=/ Numbr of Vctors/ngth of rams=3/ Numbr of Vctors/ngth of rams=4/4 g. 5 low chart of KT for ECG sgnal Intrnatonal Scholarly and Scntfc sarch & Innovaton () scholar.wast.org/37-689/654