Optimal Design of DPCM Scheme for ECG Signal Handling

Transcription

1 Proceedgs of the 6th WSEAS Iteratoal Coferece o Sgal, Speech ad Image Processg, Lsbo, Portugal, September 22-24, Optmal Desg of DPCM Scheme for ECG Sgal Hadlg BAHAR H. B. ad KHIABANI Y.S. Departmet of Electrocs, Tabrz Uversty, Faculty of Electrcal ad Computer Egeerg I.R. IRAN Abstract: - Dfferetal pulse code modulato (DPCM) plays a mportat role commucato systems. I ths paper, a theoretcal work has bee sgfcatly carred out to desg a optmal DPCM system. At DPCM structure, stead of drect codg of sgal, dfferece betwee two sgals, put to DPCM ad output of predctor s ecoded. The dfferece of two sgals s so small value that ca be quatzed by fewer bts. I ths study, Levso-Durb algorthm s utlzed to desg the optmum predctor. Furthermore, classcal ad Lloyd methods are used to determe quatzer levels. The desged predctor should be coordated wth desged quatzer ut whch s used to mplemet a optmum DPCM scheme. Fally, some smulatos have bee mplemeted to evaluate performace of dfferet structures for DPCM system ad to choose the best structure wth least complexty ad dstorto. These smulatos show the effectveess of Desged scheme for ECG sgal trasmsso. Key words: DPCM - Predctor - Quatzer - ECG Sgal - MSE - Lloyd algorthm 1 Itroducto Electrocardogram (ECG) s a objectve sample of the electrcal actvty of heart, whch s reflected the form of electrc potetal chages o the surface of sk ad ca appear o the tape or osclloscope motor. Electrocardogram s a complex sgal ad has bee formed by a umber of segmets. Due to the amout of devato of ay segmet out of ts ormal state, physcas ca dagose the effects whch costrat ormal actvty of heart [1]. Thus t s ecessary to have the sgal of electrocardogram for dagosg heart dseases. Electrocardogram s prmarly aalog sgal, ths study; t would be dgtzed usg the advatages of DPCM scheme. A broad spectrum of techques for electrocardogram (ECG) data compresso has bee proposed durg the last three decades [2, 3, 4]. Oe of effcet methods for compresso ad trasmsso of ECG s DPCM method [2, 4]. However, the objectve am represetato of ths work s to vestgate how to use the advatages of DPCM system to trasmt ECG sgal ad to utlze sutable methods for reducg the rate of error trasmttg ECG sgal. I the structure of DPCM system, predctor ad quatzer are fudametal uts [5, 6, ad 7], ad ther effcet desg has a large effect o DPCM performace. Ths study provdes ths mportace by employg the best structure for predctor ad quatzer uts that are coordated wth each other DPCM system. Classcal method ad Lloyd algorthm have bee employed for determg levels quatzer ut, ad Levso- Durb algorthm has bee used for desgg the optmum predctor [8]. DPCM uses a kd of dfferetal ecodg for reducg the umber of trasmsso bts, whch ecodes the dfferece betwee sgals ad the predcted output values [6]. Therefore varous parts of DPCM system have bee desged such a way that result of smulato would be a optmum stuato. I ths work, programmg MATLAB evromet has bee used for all smulatos. It should be metoed that each complete perod of ECG sgal s formed approxmately from 365 samples ad the rate of samplg s 512 samples per secod. I vestgated perods, backgroud ose effect to ECG sgals has bee observed. Amog varous IIR flters, for elmatg the backgroud ose low-pass Butterworth flter, wth 40 Hz cut-off frequecy, has bee selected sce t provdes a flat frequecy respose at pass-bad rego. I dscusso of sgal processg, the approach of desgg flters ad ther fuctos o sgal have bee explaed detal refereces [7, 8]. A typcal perod of ose free ECG sgal ready to trasmt through DPCM system has bee show Fg.1. 2 Costructo of DPCM System Dfferetal ecodg techques of DPCM are employed extesvely varous felds such as

2 Proceedgs of the 6th WSEAS Iteratoal Coferece o Sgal, Speech ad Image Processg, Lsbo, Portugal, September 22-24, soud, pcture ad speech processg. DPCM s a kd of closed-loop dfferetal ecodg that at ts feed-back path there s a typcal dgtal flter, called predctor. DPCM scheme uses a kd of dfferetal ecodg, stead of drect ecodg, whch ecodes the dfferece betwee the sgal tself ad ts predcted value. Fg.2 shows a overall structure of DPCM system where predctors are used at trasmtter ad recever dagrams. A predctor s usually assembled at feed-back path ad behaves as a lear predcto to estmate the magtude of put sample at DPCM system. At DPCM system, dfferece sgal e, betwee put data sample x, ad estmated data ˆx s appled as put sample to quatzer ut, show Fg.2(a). Based o the error sgal e, quatzer produces a equvalet teger bary umber at ts output y to trasmt towards the recever ut. The magtude of error sgal e, comparso wth x ad ˆx s very small thus the error sgal e ca be quatzed wth fewer umber of bary bts ad trasmtter ut trasmts fewer umber of bts per data sample; ad cosequetly, a cosderable amout of rase at rate of data trasmttg, ca be acheved [5, 6]. But desg of a optmal DPCM system for ECG sgal hadlg wth mmum recostructo error eeds to desg optmal predctor ad quatzer uts that are coordated together DPCM structure to reach the best performace. The rest of the paper s focused o ths problem ad the best structure wll be chose based o the smulato results. 2.1 Desg of Lear Predctor Predctg output of a dyamc system, by observg prevous values of output, has always bee oe of the mportat mathematcal problems. Here, for sampled data sgal, lear predcto algorthm has bee used to desg a optmum predctor [8, 9]. A typcal, lear predctor s a lowpass dscrete-tme flter wth fte mpulse respose (FIR). A desged lear predctor model produces estmated sample ˆx, as show Fg.2(a). I geeral, kth order lear predctor cotag p coeffcets, p 1, p2,..., p k, ad tme delay, z -1, betwee successve data samples are show Fg.3. I geeral, predctor at feed-back path of DPCM system receves the sum of quatzed error sample ad ts prevous out-put data samples (see Fg.2). The output data sample of predctor s usually affected by quatzed error sample. Therefore, addtoal error creasg would be expected at output data sample of predctor. The frst step to reduce overall error at DPCM, s to desg a optmum quatzer ut. Ths ca be acheved wth mmzg the quatzato error for put error dfferece e. the quatzato error wll be dscussed later secto 4. Further reducto ca be acheved by desg of a optmum lear predctor; hece, mea square error (MSE) of predcto has to be mmzed. MSE ca be computed as follows: 2 2 E p = E[( x( ) xˆ( )) ] = E[ d( ) ] (1) Ad to mmze MSE, Weer-Hopf equato ca be obtaed as follows r = Ra (2) R p p s correlato matrx, p s the order of the predctor, r s autocorrelato vector ad a = [ a 1 La p ] s predctor coeffcets vector whch ca be obtaed by vertg Matrx R as follows : a = R 1 r (3) So desg of optmal lear predctor cludes followg 3 steps: 1. Determe the order of the predctor, p 2. Estmate the correlato Matrx, for a k R p p put sgal. 3. Solve equato (3) accordg to equato (3) to obta coeffcets,, t s evtable to compute the verse of the matrx R. R s a Toepltz matrx, so we ca effcetly use algorthms such as Levso Durb to vert t. Levso-Durb algorthm computes recursvely the predcto coeffcets of order 1 to P ad reduces error utl the defed threshold value. Steps of the algorthm are as fallows [5,6,8] : 1. E 0 = r[0] = 0 2. = a k = aj r[ j] E + r[] 1 = 1 = k 5. For j = 1, 2,, a j 6. ed = a k a 1 1 j + j 2 7. E = (1 k )E 1 8. f < p go to (2) 9. [ a a...a ] = [a a...a ] p p p 1 2 p 1 2 p

3 Proceedgs of the 6th WSEAS Iteratoal Coferece o Sgal, Speech ad Image Processg, Lsbo, Portugal, September 22-24, For defed ECG sgal, MSE (Mea Square Error) should be as small as eeded ad the lowest possble order for the predctor must be chose. The amout of MSE of predcto s computed for predctor orders p = 1 to p = 15, oce for ufltered ECG sgal ad oce for ECG sgal whch has bee passed through low-pass flter wth 40Hz cut-off frequecy, ad obtaed results are llustrated Fg.4 ad Fg.5, respectvely. Fg.4 ad Fg.5 shows that resulted MSE for ufltered sgal s approxmately 6 tmes greater tha resulted MSE for fltered sgal. Thus flterg of sgal, reduces the sharp sgal varatos resulted by ose, ad leads to reducto of predcto error, ad cosequetly reducto of predctor order. Fally, secod order predctor s foud to be optmum ad lowest degree to process fltered ECG sgal at DPCM system. 2.2 Ivestgato of Quatzer Ut Quatzg process s carred out by covertg cotuous put sgal to quatzer ut to umerous dscrete quattes at output stage. I smulato of DPCM, two types of quatzers have bee used. Oe kd of the quatzer s classcal mult-level quatzer ad the other s optmum quatzer based o L1oyd algorthm. I ths study, oe, two ad three bt quatzers are used. I addto, caocal sged dgt (SCD) ecodg s also utlzed [2]. To eable the quatzato ut to perform correctly ad to lmt quatzato error wth acceptable boudary, mult-level quatzato, put of the quatzer must be located a specfc rego by ga adjustmet. Icrease the umber of quatzer bts ad employg L1oyd method wll mprove quatzer performace. RMS crtero s used to aalyze quatzato error. Employg L1oyd algorthm ca be effectve overall performace of DPCM system. I ths algorthm tal quatzato levels ad spaces are determed ad a successve process based o the PDF of put sgal s performed o these quatzer parameters to reduce RMS error whch fally cocludes optmal levels ad spaces wth mmum RMS for quatzer ut. L1oyd algorthm comparso wth others provdes some advatages, e.g. t does t eed ay ga adjustmet to lmt quatzer put a specfc boudary,ad ts resulted RMS s less tha others. 3 DPCM Desg Techques I ths secto proposed method to desg the optmal DPCM system s llustrated. Dscusso o dfferet approaches clarfes the characterstcs of each cocered method ad ther flueces o hadlg ECG sgal by DPCM system. The followg subsectos expla the desg techques of DPCM system detal. 3.1 DPCM wth Classcal Multlevel Quatzer I ths study, we have used oe bt quatzer ut that based o the put sample, produces threelevels at output. Here, CSD ecodg for each put sample s used to produce three levels, -1, 0, or +1 at the output of the quatzer. The ga factor Fg.2, s adjusted such a way that error samples are lmted wth rego of -1.5 ad 1.5, hece recostructed sgal would be a desrable state. The recostructed sgal usg 1 bt quatzer ad 2 order predctor Fg.6, s smlar to the orgal sgal Fg.1, but t mght ot have eough precso. The RMS errors for DPCM system wth 1 bt quatzer ad 1, 2, 3 order predctors are gve Table 1. As show table 1 there s ot eough decrease RMS by crease at the order of predctor. To acheve a adequate precso CSD ecodg for 2 bt quatzer wth 7 levels, [ ], s utlzed. Smulato results of DPCM wth 2 bt quatzer for oe, two ad three order predctors are gve Table 1, that shows a cosderable reducto RMS error, compared wth the results of 1 bt quatzer. By comparg orgal ECG

4 Proceedgs of the 6th WSEAS Iteratoal Coferece o Sgal, Speech ad Image Processg, Lsbo, Portugal, September 22-24, sgal fg. 1 ad recostructed oe Fg. 7 t ca be ducted that 2 bt quatzer wth oe order predctor results hgh dstorto. Therefore, let us go back to Fg.5, whch MSE of predcto s plotted versus the orders of predctor. Fg.5 shows a sharp decrease MSE error whe the order of predctor rses from order oe to two, ad t shows a slght decrease whe t rses to 3 or hgher orders. I cocluso, optmum DPCM system could be desged by meas of 2 order predctor ad 2 bt quatzer. For verfcato, let us cosder the results o orgal fltered ECG sgal as llustrated Fg.8 whch recostructed sgal s determed by +. The recostructed ECG sgal Fg.8 s qute acceptable from research pot of vew, where there s ot ay dstorto ad lost formato at output ECG sgal. Icreasg the order of predctor wll ot have a sgfcat effect o overall error. It could be ducted from RMS results of 2 bt quatzer table 1. Results for 3 bt quatzer are also gve table 1, but these results do t show a cosderable mprovemet for 3 bt quatzer. Hece, the optmum ad proper DPCM system wth least complexty ad cost pot of vew s oe that cossts of 2 bt quatzer wth secod order predctor. quatzer wth 1 order predctor has bee chose to have the least complexty ad RMS error. I geeral, the resultat errors by L1oyd method, compared wth errors classcal method gve at Table 1, are very small ad eglgble. Hece, to hadle ECG sgal at DPCM scheme, L1oyd method s a optmum method to be appled at desgg DPCM parameters. 4 Cocluso I ths work, advatages of DPCM systems are effectvely used for trasmttg ad recevg of electrocardogram (ECG). Three types of dfferet approaches to realze a optmum DPCM system have bee dscussed detal. Here, betwee classcal methods whch have bee studed, the optmum DPCM system cossts of 2 bt quatzer ad 2-order predctor has the least complexty ad the best performace. A alteratve approach called L1oyd method has also bee vestgated. The resultat errors by L1oyd method, compared wth RMS errors classcal method, are very small ad eglgble. Hece, to hadle ECG sgal at DPCM, L1oyd method wth 3 bt quatzer ad 1 order predctor, s the best structure for DPCM system. 3.2 DPCM Desg Usg L1oyd Method Lloyd algorthm uses a teratve process to mmze the mea square quatzato error quatzer ut [10, 11]. L1oyds algorthm optmzes quatzato parameters to reduce the overall system error. For gve put samples of quatzer ut, both the levels ad spaces of quatzer are optmally computed [9]. Smulato results of trasmttg ECG sgal usg L1oyd method are show Fg.9. For 1, 2 ad 3 bt quatzers, the RMS error varatos are tabulated Table 2. It shows that the best results are obtaed by 3 bt quatzer. The, 3 bt Refereces: [1] Kasper D. L., Brauwald E., etal, Harrso's Prcples of Iteral Medce, 16 th Edto, [2] WU S.C., BAI Y.P., Study o Dyamc Electrocardogram System wth Fucto of ECG Tele-trasmsso, Procs of Rado Scece Coferece, Asa Pacfc; 2004, pp [3] Slom M.A., Lev M., Yaro D., Ovsyshcher E.A., COMPUTER FILTEIUNG OF AN ECG SIGNAL BASED ON THE PRIOR KNOWLEDGE PRINCIPLE - GENERAL CONCEPT, Procs of Computers Cardology Coferece; 1989, pp [4] Madhukar B., Patakt L.M., Murthy I.S.N., Improved Parametrc Models ad DPCM

5 Proceedgs of the 6th WSEAS Iteratoal Coferece o Sgal, Speech ad Image Processg, Lsbo, Portugal, September 22-24, Techques for ECG Data Compresso, Procs of the Aual teratoal Coferece of the IEEE Volume 2; 1992, pp [5] Bahar H. B, Dgtal flterg techques havg mproved computatoal effcecy, CARDIFF, U.K., [6] Shamuga K.S. Dgtal ad aalog commucato system, Joh Wley ad Sos Ic, [7] Ala V O., Schafer R. W., Dscrete tme sgal processg, Pretce-Hall, [8] Smo S. H., Adaptve flter theory, Eglewood clffs, N.J., Pretce-Hall, [9] Adreas S., MATLAB Adaptve Flterg ad predcato, March [10] Jalaledde S.M.S.,Hutches C.G., Staratta R.D., Coberly W.A., ECG data Compresso techques - a ufed approach, IEEE trasactos o Bomedcal Egeerg, Volume 37, Issue 4, 1990, pp [11] Bavlle I., Armstrog S., QUANTIFICATION OF REAL-TIME ECG DATA COMPRESSION ALGORITHMS, Proceedgs of the Frst Jot BMES/EMBS Coferece Servg Humaty, Advacg Techology, 1999, pp264. e x() ˆ = x x y = e + q ~$ h x xˆ y Flter e LPF - Quatzer Predctor (a) Ga + Flter Predctor x x + y = x xˆ (b) Fg.2: Complete DPCM structure, (a) Trasmtter (b) Recever. + p k p p 2 1 LPF Z Z -1 Z -1 y output ~ h Fg.3: Typcal kth order lear predctor. xˆ Fg.4: MSE versus predcto order for ufltered ECG sgal. Fg.1: Orgal ECG sgal, output of flter. Fg.5: MSE versus predctor order for fltered ECG sgal.

6 Proceedgs of the 6th WSEAS Iteratoal Coferece o Sgal, Speech ad Image Processg, Lsbo, Portugal, September 22-24, Fg.6: Recostructed ECG sgal usg oe bt quatzer ad secod order predctor. Fg.8: Comparso of recostructed sgal ad put sgal usg 2 bt quatzer ad secod order predctor. Fg.7: Recostructed ECG sgal usg 2 bt quatzer ad frst order predctor. Fg.9: Comparso of orgal sgal ad recostructed sgal after flterg ad usg optmum L1oyd quatzer. Table 1: Smulato results of DPCM system usg ormal quatzer Quatzer ut oe Bt quatzer two Bt quatzer three Bt quatzer Ga (G) Order of predctor RMS error Table 2: Smulato results of DPCM system usg Lloyd quatzer Quatzer ut Order of predctor RMS error oe Bt quatzer two Bt quatzer three Bt quatzer