SEMG Signal Processing and Analysis Using Wavelet Transform and Higher Order Statistics to Characterize Muscle Force

Transcription

1 SEMG Signal Procssing and Analysis Using Wavlt Transform and Highr Ordr Statistics to Charactriz Muscl Forc M. S. HUSSAIN, M. B. I. REAZ, M. I. IBRAHIMY Dpartmnt of Elctrical and Computr Enginring Intrnational Islamic Univrsity Malaysia Gombak, Kuala Lumpur MALAYSIA Abstract: - An algorithm is proposd for procssing and analyzing surfac lctromyography (SEMG) signals using wavlt transform and Highr Ordr Statistics (HOS). EMG signal acquirs nois whil travlling though diffrnt mdia. Wavlt dnoising is prformd in this rsarch for initial EMG signal procssing. With th appropriat choic of th Wavlt Function (WF), it is possibl to rmov intrfrnc nois ffctivly. Root Man Squar (RMS) diffrnc and Signal to Nois Ratio (SNR) valus ar calculatd to dtrmin th most suitabl WF. Rsults show that WF db2 prforms dnoising bst among th othr wavlts. Powr spctrum analysis is prformd to th dnoisd SEMG to indicat changs in muscl contraction. Furthrmor, HOS mthod is applid for furthr fficint procssing du to th uniqu proprtis of HOS applid to random tim sris. Gaussianity and linarity tsts ar conductd as part of HOS which shows that SEMG signal bcoms lss gaussian and mor linar with incrasd forc. Ky-Words: -SEMG, wavlt transform, dnoising, man powr frquncy, HOS, bispctrum. 1 Introduction Th lctromyography (EMG) signal givs an lctrical rprsntation of nuromuscular activation associatd with a contracting muscl. A muscl is composd of many Motor Units (MUs). Th tchniqu of studying muscl function by using a surfac lctrod is normally known as Surfac Elctromyography (SEMG). EMG signals dtctd dirctly from th muscl or from th skin by using surfac lctrods show a train of motor unit action potntials (MUAP) and noiss. Wavlt-basd basd nois rmoval is prformd in this rsarch prior to signal procssing and analysis. Wavlt dnoising (nois rmova has bn found ffctiv in dnoising a numbr of physiological signals [1, 2, 3, 4]. It is prfrrd ovr notch filtrs and signal frquncy domain filtring bcaus it tnds to prsrv signal charactristics vn whil minimizing nois. In this rsarch, daubchis, symmlt and orthogonal Myr Wavlt Functions (WFs) ar usd for th Wavlt transform (WT). Th bst suitabl WF is dtrmind by finding th Root Man Squar (RMS) diffrnc and Signal to Nois Ratio (SNR) valus. SEMG signals can b charactrizd by a powr spctrum dnsity function bcaus th signal is stochastically modlld as a zro man colourd nois. Th amplitud of th signal incrass du to rcruitmnt of MUs with incrasd muscl forc [4, 5]. SEMG signal analysis can also provid th masurmnt from a muscl through out a sustaind fatiguing contraction. In this rsarch, man powr frquncy is considrd for th SEMG powr spctrum analysis during load tst to undrstand muscl contraction and dtrmin fatigu. Furthrmor, this study xploits th us of Highr Ordr Statistics (HOS) in furthr fficint SEMG signal procssing and analysis. HOS mthod is also applid for supprssing gaussian whit nois within th signal. A fundamntal mans by which th probability thory can dscrib a random procss is by mans of th diffrnt ordr momnts and cumulants. Th first ordr momnt or cumulant of any procss indicats th man of that procss. Th scond ordr momnt of that procss indicats th autocorrlation, whil its scond ordr cumulant indicats th varianc of that procss. HOS starts from th 3 rd ordr to n th ordr momnt [6]. Along with othr HOS masurs, th bispctrum, a frquncy-domain masur of third-ordr cumulants has bn usd in this rsarch for th signal analysis to provid information about th signals gaussianity and linarity. Th Gaussianity tst and linarity tst of th normalizd bispctrum shows changs in muscl contraction. Th analysis also dtrmins th ffctivnss of th wavlt basd dnoising mthod. ISBN: ISSN:

2 Rsults in this study show that, wavlt basd nois rmoval tchniqu using WF db2 works bst to rmov intrfrnc nois from SEMG signals. Th ffctivnss was obsrvd mor clarly whil analyzing th powr spctrum proprtis of th SEMG signals. Th bispctrum analysis also shows that SEMG bcoms lss gaussian and mor linar with incrasd walking spd/forc (incras in man voluntary contraction). Morovr, this rsarch provs that th powr spctrum of EMG shows a shift to lowr frquncis during fatigu. rspctivly. For this rsarch WFs Daubchis (db2, db4, db5, db6, db8), Symmlt (sym4, sym5), and orthogonal Myr (dmy) ar usd for th dcomposition. Four lvls of dcomposition is considrd for th SEMG signals in this xprimnt Thrshold mthod: A thrshold is dtrmind for th raw EMG signal which is applid on th wavlt dcomposition. Th thrsholding procss of th wavlt cofficints is illustratd in Fig Mthodology 2.1 Exprimntal Stup Two sts of diffrnt SEMG data fils wr considrd for th xprimnt. Th first st of SEMG signal was rcordd from th lft bicps brachii and th scond st was rcordd from th right rctus fmoris muscl. Th sampl raw SEMG signals wr collctd from thr normal subjcts agd 22 to 40 at Univrsity Kbangsaan Malaysia (UKM). All analog channls wr rcordd at 1000 sampls pr scond without any filtr. 2.2 Algorithm Dsign Th two main algorithms applid in this rsarch for th EMG signal procssing and charactrization ar th WT and HOS Wavlt Dnoising Wavlts gnrally usd for dnoising biomdical signals includ th Daubchis db2, db4 db5 db6 and db8 wavlts and orthogonal Myr wavlt. In th cas of SEMG, th wavlts ar gnrally chosn whos shaps ar similar to thos of th MUAP [3, 7, 8]. Wavlt dcomposition: Th DWT is computd by succssiv low-pass and high-pass filtring in th discrt-tim domain. Th DWT of a signal x[n] is calculatd by passing it through a sris of filtrs. Th outputs giv th dtail cofficints (from th high-pass filtr, yhigh[n]) and th approximation cofficints (from th low-pass, ylow[n]). Th filtr outputs ar thn down-sampld as givn by k = y [ n] = x[ k]. g[2n k] (1) low k = y [ n] = x[ k]. h[2n k] (2) high Fig. 1: Thrsholding procss on wavlt cofficints Considring that th contaminatd signal f quals th raw SEMG signal s plus th nois signal n, i.. f=s+n. Th thrsholding is prformd in following stps, whr T s is th signal thrshold and T n is th nois thrshold [9]: 1. Th nrgy of th original signal s is ffctivly capturd, to a high prcntag, by transform valus whos magnitud ar all gratr than som thrshold T s >0. 2. Th nois signal s transform valus all hav th magnituds which li blow som nois thrshold T n satisfying T n < T s. Thn th nois in f can b rmovd by thrsholding its transform whr all valus of th transform whos magnitud lis blow th nois thrshold T n ar st qual to 0. This way of thrsholding is calld hard thrsholding. Wavlt rconstruction: An invrs transform is prformd on th cofficints aftr thrsholding, providing a good approximation of th EMG signal. Th rconstruction is th rvrs procss of wavlt dcomposition. For this rsarch, four lvls of wavlt dcomposition/rconstruction is applid as mntiond arlir RMS Diffrnc Calculation Th RMS diffrnc, R of th contaminatd signal f[n] compard with th dnoisd signal s[n] is dfind by 2 2 ( f[ 1] s[1] ) ( f[ N ] s[ N ] ) R = (3) N whr f is th raw SEMG signal and s is th signal aftr dnoising. N is th total numbr of sampls (lngth of data). According to quation 3, th highr th RMS diffrnc, th bttr th dnoising prformanc of th WF. ISBN: ISSN:

3 2.1.3 SNR Calculation Th SNR is calculatd by quation 4. SNR = 10log10 (Xn/Xs) (4) whr, X n is th varianc for th noisy signal, and X s is th varianc for th dnoisd signal. According to quation 4, highr th valu of ( db), th bttr th prformanc of th WF Highr Ordr Statistics Bispctrum is obtaind by th two-dimnsional discrt Fourir transform of th 3 rd ordr cumulant. Knowing th frquncy componnts X(k) and X( of th output signal x(k), th bispctrum B x (k, can b stimatd by B x ( k, = E{ X ( k) X ( X *( k + } (5) whr E{.} donats th statistical xprssion, k,l ar th discrt frquncy componnts and * dnots th complx conjugat. Bispctrum Estimation Procss: Givn a st of ral obsrvations (hr th SEMG signa {x(n)} for n = 0, 1, 2,.,N-1, whr it is assumd that th data st is stationary [10,11, 12]. Th algorithm for th bispctrum stimation is givn in dtails in fig. 2. Fig. 2: Flow chart of bispctrum stimation A common problm in signal procssing is that th obsrvd signal consists of a non-gaussian stationary signal in additiv gaussian nois. Lt us considr a mixtur procss which is th sum of two procsss (gaussian and non-gaussian), as quation 6, x ( n) = ( n) + w( n) (6) whr, (n) is non-gaussian zro man and w(n) is th gaussian whit nois. Equation 6 can b rprsntd in trms of powr spctrum, P x (k) and bispctrum, B x (k) through quation 7 and 8 rspctivly. x w P ( k) = P ( k) + P ( k) (7) x w B ( k, B ( k, + B ( k, = B ( k, = γ 3 = (8) whr k and l ar th frquncy componnts. It is notd that bispctrum of a gaussian signal is zro and th rsulting bispctrum of th modld mixr signal givs th skwnss ( γ ) valu only. Thrfor, additiv nois has bn supprssd in th output signal. Thrfor, th bispctrum offrs robustnss to additiv gaussian whit nois. Gaussianity and Linarity Tsts: Th normalizd bispctrum givs th bicohrnc. Bicohrnc is th mixd function of th scond and third ordr statistics and it is usd to quantify th non- Gaussianity of a random procss. Bicohrnc, B n (k, is stimatd by Bx ( k, Bn ( k, = (9) P( k) P( P( k + whr B x (k, is th bispctrum and P( ) is th powr spctrum. Th tst of Gaussianity, S g is basd on th man bicohrnc powr dfind by S g = Bn ( k, (10) Th Gaussianity tst is mainly th zro-skwnss tst which dtrmins whthr or not th stimatd bicohrnc is zro. Th linarity tst dtrmins whthr or not th stimatd bicohrnc is constant in th bi- frquncy (k, domain. It is th masurmnt of th diffrnc (dr) btwn a thortical and an stimatd intr-quartil rang R [13]. Powr Spctrum Analysis: Th powr spctrum is obtaind by fast Fourir transform (FFT) givn in quation 12 during th bispctrum stimation procss. Hanning window is usd with a 256 point FFT. Th man powr frquncy pf is obtaind by quation 11. fps( f ) df pf man = (11) PS( f ) df whr f is th dnoisd signal and PS is th powr spctrum. 3 Rsult and Discussion Wavlt dnoising mthod is applid to SEMG signal at various muscl contraction/forc stags (rst, light contraction, strong contraction and contraction with load for bicps brachii muscl) and at various walk styls/forc (slow walking styl, mdium walking styl, fast walking styl, and vry 3 ISBN: ISSN:

4 fast walking styl for rctus fmoris muscl). Th man powr frquncy and bispctrum was usd to analyz th EMG signal to undrstand th muscl forc and fatigu. Kumar t. al [14] dmonstratd that using wavlts, th diffrncs btwn th EMG corrsponding to fatigu muscl and non-fatigu muscls is highlightd in th powr of th wavlt cofficints whn using WFs symmlt4 (sym4) and symmlt5 (sym5). Rn t. al [8] usd WF db5 to dnois EMG signal in thir rsarch. In this xprimnt th appropriat WF for EMG is chosn basd on th calculatd RMS diffrnc and SNR valus. Th raw EMG signals wr takn to calculat th RMS diffrnc and SNR for th all WFs suitabl for biomdical signal procssing (db2, db4, db5, db6, db8, and dmy) including sym4, sym5, and db45 with four lvls of dcomposition. Tabl 1 and tabl 2 givs th rsults of th avrag RMS diffrnc of th chosn WFs for th thr subjcts from th rctus fmoris muscl at various contraction lvls. Tabl 1 : Avrag RMS diffrncs of various WFs WF/ Forc Slow Mdium Fast V. Fast Avg db db db db db sym sym dmy Tabl 2 Avrag SNR valus of various WFs WF/ Forc Slow Mdium Fast V. Fast Avg db db db db db sym sym dmy According to th rsults in Tabl 1, th considrd WFs show similar kind of prformanc; howvr th daubchis WFs hav highr RMS diffrnc compard to WF sym4, sym5, and dmy. This mans that daubchis (spcially db2 from th avrag column in Tabl 1) WF s ar capabl of dnoising SEMG signals bttr than othr wavlt familis; symmlt and orthogonal myr. According to Tabl 2, th SNR valus show a similar kind of rsults whr th Daubchis WFs show bttr prformanc compard to th othr WFs. But from th SNR valus it is also obsrvabl that WFs db2 givs th bst rsult. Sinc WF db2 shows bttr prformanc from th rsults, thrfor, it is considrd for th SEMG signal dnoising procss. Fig. 3 givs th sampl raw SEMG signal and its dnoisd signal. Figur 3 Raw SEMG signal and dnoisd SEMG signal at WF db2 at four lvl of dcomposition According to th study by Hagbrg and Ericson, man powr frquncy is lowr at low contraction lvls whn compard with high contraction lvls [15]. Moritani t al. also obtaind similar rsults whr significant incras in SEMG amplitud and man powr frquncy wr found with incrasing forc [16]. It is also shown that during muscl fatigu, th powr spctrum of SEMG shows a shift to lowr frquncis [3, 17]. Man/mdian frquncy is usd to quantify this shift. Fig. 4 shows th man powr frquncy of SEMG signal for th thr subjcts at th various muscl contraction stags using WF db2. Rsults obtaind by this rsarch that thr was significant incras in th man powr frquncy with incras of muscl forc as in [15, 16]. Fatigu was also noticd by obsrving a shift to lowr frquncis in th powr spctrum as in [17]. For this xprimnt, SEMG signal was capturd from rctus fmoris muscl at th following forc lvls/walking styls: slow walk, mdium walk, fast walk, and vry fast walk. Rsults for a subjct at th mntiond forc lvl ar prsntd in this papr using bispctrum analysis for two cass; a. SEMG signal with wavlt dnoising, b. without wavlt ISBN: ISSN:

5 dnoising. Th rsults ar obtaind from th Gaussianity tsts of th raw signal using only bispctrum, and th signal using bispctrum aftr th nois rmoval tchniqu. Th rsults for th Gaussianity tsts ar givn in Fig. 5 for a subjct during th walking trial. mpf (Hz) MPF from SEMG Powr Spctrum Rst Light Strong Load (Start Point) Muslc Contraction Load (Mid Point) Load (End Point) Subjct 1 Subjct 2 Subjct 3 Figur 4 Man powr frquncy of SEMG signal for th thr subjcts at th various muscl contraction stags using WF db2 (bicps brachii) Gaussianity Subjct 1 HOS Only WT+HOS th chang of gaussianity for th raw signals applying HOS only and th solid lins dmonstratd th gaussianity for th signal aftr nois rmoval applying WT and HOS. Th raw signal and dnoisd signal show similar charactristics whr both SEMG signals bcom lss gaussian from slow walking styl to vry fast walking styl. Th important thing to notic from th Fig. 5 is that, th signals aftr dnoising is lss gaussian compard to th othr signal using only HOS. This indicats that th wavlt basd dnoising mthod using WF db2 ffctivly filtrd intrfrnc nois. Furthrmor, additiv nois (Gaussian whit nois) prsnt in th EMG signal is supprssd in th bispctrum of th output signal. MUAPs hav bn stimatd in Fig. 7 for rctus fmoris muscl for a subjct. Linarity Slow Mdium Fast Vry fast Waking spd (forc lv Subjct1 Subjct 2 Subjct 3 Figur 6 Linarity tsts for thr subjcts during walking trail using WT and HOS 0 Slow Mdium Fast Vry fast Walk Spd (forc lv Figur 5 Gaussianity tsts of a subjct during walking trail using HOS only and WT plus HOS Bispctrum analysis was also usd by Kaplanis and Pattichis [13] for analyzing th Bicps Brachii muscl. It is rportd that SEMG bcoms lss Gaussian and mor linar on incrasing man voluntary contraction (MVC). Othr rsarch using HOS also showd similar rsults whr SEMG bcoms lss gaussian with incrasd muscl contraction du to load [4, 11, 12]. Th rsults for th linarity tst for th thr subjcts ar givn in Fig. 10. According to Fig. 6, it is dmonstratd that th signals bcom mor linar with incrasd walk spd/muscl forc. Th linarity tsts show sam pattrn as th Gaussianity tsts which is th rvrs pattrn for th trial. Rsults obtaind by this rsarch xplain that th signal bcoms lss gaussian as in [11, 12, 13] and mor linar as in [12, 13] with incrasd forc. Th dottd lins in Fig. 5 rprsnts Figur 7 Output signal of rctus fmoris during walk for a subjct using bispctrum 4 Conclusion In this rsarch, WT is succssfully applid for dnoising SEMG signal and HOS is also abl to supprss Gaussian whit nois. So, both th tchniqus wr suitabl for SEMG signal ISBN: ISSN:

6 procssing, which filtrd rcording nois (dnois) and rmov Gaussian nois ffctivly. Rsults show that WF db2 can dnois EMG signal most ffctivly among th othr WFs. Th study also shows that incras in th muscl contraction lvl (from low contraction lvl to high contraction lv provids significant incras in SEMG man powr frquncy dmonstrating changs in th MUs rcruitmnt. Morovr, powr spctrum of SEMG shows a shift to lowr frquncis during fatigu. Bispctrum analysis shows that th signal bcoms lss Gaussian and mor linar with incrasing muscl forc. Rfrncs: [1] T. David Mwtt, N. Homr, J. R. Karn, Rmoving Powr Lin Nois from Rcordd EMG, Procdings of th 23rd annual intrnational confrnc, pp , Oct 25-28, 2001, Istanbul, Turky [2] P. Carr, H. Lman, C. Frnandz, C. Marqu, Dnoising of th utrin EHG by an undcimatd wavlt transform, IEEE Trans. on Biomdical Enginring, vol 45, issu 9, pp , 1998 [3] M. S. Hussain, M. B. I. Raz, F. Mohd-Yasin, M. I. Ibrahimy, EMG Signal Analysis Using WT and HOS to Dtrmin Muscl Contraction, Exprt Systms, Spcial issu Advancs in Mdical Dcision Support Systms (Accptd, April 2008), ISSN: [4] M. S. Hussain, M. B. I. Raz, M. I. Ibrahimy, A. F. Ismail, F. Mohd-Yasin, Wavlt Basd Nois Rmoval from EMG Signals, Informacij MIDEM-Journal of Microlctronics, Elctronic Componnts and Matrials, vol. 37, issu 2, pp , Jun ISSN: [5] H. S. Milnr Brown, R. B. Stin, Th rlationship btwn th surfac lctromyogram and muscular forc, Journal of Physiology, vol. 246; pp ; 1975 [6] C. L. Nikias, and J. M. Mndl, Signal Procssing with Highr-Ordr Spctra, IEEE Signal Procssing Magazin, vol. 10, pp 10-37; 1993 [7] P. W. Mark, Wavlt-basd nois rmoval for biomchanical signals: A comparativ study, IEEE Trans. on biomdical nginring, vol 47, no. 2, pp [8] X. Rn, X. Hu, Z. Wang, MUAP xtraction and classification basd on wavlt transform and ICA for EMG dcomposition, Md Biol Eng Comput, (44), pp , 2006 [9] J. S. Walkr, A prmir on wavlts and thir scintific applications, Champman & Hall/CRC, 1999, USA [10] C. L. Nikias, and M. R. Raghuvr, Bispctrum Estimation: A Digital Signal Procssing Framwork, Procdings of th IEEE, Vol. 75, No. 7, pp , [11] S. Shahid, J. Walkr, G. M. Lyons, C. A. Byrn; A.V. Nn, Application of highr ordr statistics tchniqus to EMG signals to charactriz th motor unit action potntial, IEEE Transactions on Biomdical Enginring, vol. 52, issu 7, pp , July 2005 [12] M. B. I. Raz, M. S. Hussain, F. Mohd-Yasin, Kinsiological Surfac EMG Analysis using Highr Ordr Statistics, Procdings of th 4th APT Tlmdicin Workshop 2006, pp , 25-26, Rawalpindi, Pakistan January, 2006 [13] P. A. Kaplanis; C. S. Pattichis, L. J. Hadjilontiadis, S. M. Panas, Bispctral analysis of surfac EMG, 10th Mditrranan Elctrotchnical Confrnc, vol.2, pp , 2000, Cyprus [14] D. K. Kumar, N. D. Pah, A. Bradly, Wavlt analysis of surfac lctromyography to dtrmin muscl fatigu, IEEE Trans Nural Syst Rhabil Eng., vol. 11, No. 4, Dc 2003 [15] M. Hagbrg and B. E. Ericson, Myolctric powr spctrum dpndnc of muscular contraction lvl of lbow flxors, Europan Journal of Applid Physiology, vol. 48; issu 2, pp , 1982 [16] T. Moritani, A. Nagata, M. Muro, Elctromyographic manifstations of muscular fatigu, Md Sci Sport Exrc, vol. 14, pp , 1982 [17] C. J. D Luca, Myolctrical manifstations of localizd muscular fatigu in humans, CRC critical rviws in Biomdical Enginring, vol. 11, issu 4, pp , ISBN: ISSN: