SUBTRACTION METHOD FOR REMOVING POWERLINE INTERFERENCE

Transcription

1 SUBTRACTION METHOD OR REMOVING POWERLINE INTERERENCE ROM ECG IN CASE O REQUENCY DEVIATION Georgy Slavtchev Mhov, Ratcho Marnov Ivanov, Chavdar Lev Levkov aculty of Electronc Engneerng and Technologe (ETT), Techncal Unverty Sofa, Kl. Ohrdky tr. No 8, bl., 797 Sofa, Bulgara, phone: , e-mal: gm@tu-ofa.bg Extenon of the ubtracton method for power-lne nterference removng from ECG gnal propoed n cae of power-lne frequency varaton. The extng veron utable for non-multplcty between amplng rate and nterference frequency mproved and adapted to dynamc devaton around the rated power-lne frequency. The ongong nterference value, whch are tored n temporary buffer, are ued for recalculaton of the flter coeffcent. A mplfed algorthm elaborated and expermented n cae of odd ample number n one perod of the nterference. The correpondng formulae for even ample number are alo derved. The propoed procedure uccefully compenate abrupt and gradual change of the power-lne frequency allowed by the tandard. Keyword: Dgtal flterng, ECG flterng, Interference reecton.. INTRODUCTION The ubtracton method for removng the power-lne (PL) nterference from ECG gnal [, 8] how hgh effcency when the amplng ate (SR) Φ and the PL frequency are ynchronzed,.e. when Φ / = n nteger. The method nclude three man phae (the followng nterpretaton for odd value of n):. Each current ample checked whether t belong to a lnear egment of the ECG gnal, normally contamnated by PL nterference. The ntroduced crteron of lnearty D M, where D = ( X n X) ( X X+ n), () whch called further D-flter, repreent a econd dfference between gnal ample, located each other at dtance of one or more perod of the PL frequency, thu elmnatng the nterference nfluence. M a practcally choen value of contant or varable threhold. Theoretcally, the acceleraton of the lnear part of the gnal hould be zero, but deal traght lne can not be found n a phyologcal gnal. 2. The PL nterference removed by a low-pa flter type movng average, whch called K-flter. The free of nterference ample Y obtaned by ( n )/2 ( n )/2 Y = X+ = X+ + X + X +. (2) n = ( n )/2 n = ( n )/2 = Smultaneouly, a mple ubtracton of fltered from non-fltered ample gve the value of the current nterference BB, whch tored n a temporary buffer. 04

2 ( n )/2 B = X Y = X+ + ( n ) X X+ (3) n = ( n )/2 n = 3. If the current ample doe not belong to lnear egment, a precedng value that correpond to the ame nterference phae taken from the buffer B, B 2, K, B n B = B n. (4) It ubtracted from the contamnated ample Y = X B (5) and tored back at the current poton n the buffer. A more ophtcated approach to the ubtracton method [4] nclude the cae of non-multplcty between Φ and,.e. when Φ/ a real number. The ample to be ubtracted determned by a larger number of addtonally fltered value of the temporary buffer. If movng average appled n cae of multplcty on n conecutve ample and the mddle value calculated by B ( n )/2 0 = B ( n )/2 + + = n+ = ( n )/2+ the computaton (extrapolaton) of ( n )/2 B B by + ( n )/2 + = n+ = ( n )/2+ = n+, the obtaned flter, called B-flter, allow B = B B B = B +. (6) Equaton (6) propoed to be ued ntead of equaton (4). In a frt veron of the ubtracton method, the PL frequency varaton are compenated by hardware ynchronzaton of the analog-to-dgtal converter (ADC) to a gven nterference phae. A the PL frequency n tme lower than the SR, ynchronzaton appled at every n-th ample only, whle the tme-nterval between the other ample are generated by an nternal tmer. The error of uch type of ynchronzaton are analyzed n [6]. The author report for error elmnaton by contnuou meaurement of the perod of the PL frequency, whch dvded by n to determne nter-ample nterval correpondng to the PL varaton. Hardware meaurement of the PL perod practcally mpoble n battery powered devce. A oftware oluton for meaurng the nterference frequency throughout the ECG gnal ubected to band-pa flterng from 49 tо 5 Hz propoed n [9]. The PL perod calculated ung ampltude of two conecutve ample located bellow and above the zero lne. Both hardware and oftware determnaton of the PL perod requre an embarrang to ome extent hardware ADC ynchronzaton. Bede, the tmedepended parameter have to be recalculated to meet the tandard for accuracy [2] epecally n large devaton of PL frequency [3]. Another dadvantage of the hardware ynchronzaton that t cannot be appled on already recorded gnal. The theoretc bae of applyng the ubtracton method to the general cae of no multplcty between SR and Φ conecutvely developed n [4, 5 and 0]. The 05

3 expreon of the K- and B-flter are modfed ung auxlary hgh-pa flter. The K-flter preented by equaton (2) tranformed n a hgh-pa flter, called (-K)- flter. 2. THEORETIC STUDY O THE PL REQUENCY DEVIATIONS AROUND ITS RATED VALUE The varaton of the PL frequency repreent a pecfc cae of non-multplcty. Therefore, we appled modfed flter obtaned by ung the low-pa K-flter from equaton (2) a an auxlary flter. The new flter are gven by: D D = D ( X Y) ; (7) K K X Y Y = Y ( X Y) = X ; (8) K K Where D and K are tranfer coeffcent of the correpondng flter for the PL frequency. The adapted B-flter become B /( ) ( n )/2 = B ( n )/2 K. The modfed algorthm of the ubtracton method ue D and Y, whch are frt computed from () and (2) and then recomputed by mean of (7) and (8). Takng n conderaton the adapted B-flter, the extrapolaton equaton (6) for nonlnear ecton tranformed n: ( n+ )/2 = + [ ] ( n )/2 B +. (9) = n+ = ( n 3)/2 B B nk B The coeffcent D and K are dynamcally recalculated to compenate the PL frequency varaton durng the nterference removal procedure. Let the power-lne frequency change wth d. Then, accordng to equaton (9), the coeffcent K + d ha to be computed by ( n+ )/2 B+ + B+ + B = n+ = ( n 3)/2 K+ d= + B ( n )/2 n. (0) The coeffcent D + d calculated ung etablhed relaton for D+ d= f( K+ d). The new value of D + dand K + d are ubttuted for D and K n equaton (7), (8) and (9) for proceng the next ample. urther, K + d ued for calculatng the dveron of the PL frequency. nπ ( + d) n Aumng ome tranformaton over equaton K+ d= Φ n π ( + d), we may n Φ derve 06

4 g.. low chart of the ubtracton method wth compenaton of the PL frequency devaton. Φ π d K + d n π Φ. () The relaton D+ d= f( K+ d) become π D+ d 4n K+ dn Φ. (2) The flow chart of the procedure for compenatng the PL frequency varaton hown n fg.. Some retrcton Intal value of: are ntroduced when the program, D, K ha been wrtten:. The K + d calculaton D-flter D protected agant dvon by zero. The dvon not performed f D <M Ye B ( n )/2 le than one bt; 2. The coeffcent K + d Non-lonear egment No Lnear egment retrcted wthn the allowed range B-flter K-flter B Y of PL frequency varaton; 3. The maxmum peed of Y =X -B B =X -Y K + dalteraton lmted; Determnng 4. Snce the PL frequency K +d compenaton organzed a a typcal feedback control, the Recalculatng of: ntablty avoded by a D,K proportonally ntegral rule of adutment. =+ 2n K = K + K. +d 2n 2n 3. EXPERIMENTAL RESULTS The reult of tetng a real ECG gnal wth amplng rate Ф = 250 Hz and emulated PL frequency = 50 Hz (n=5) hown n fgure 3. The ntal value of the coeffcent are D = 0 and K = 0. An abrupt change n PL frequency from 52 to 48 Hz mulated n the mddle of the epoch. The lat trace n fg. 2a how the PL frequency (curve a), the etmated accordng to equaton () dveron of the PL frequency (curve b) and the crteron for lnearty (curve c). Correcton n the D-flter not ntroduced, becaue of the mall nfluence of the PL frequency devaton. The tme neceary to be reached the tatonary value of the changed PL frequency (fg. 2a) about 0.5. The error commtted le than 20 μv. The reult wthout PL frequency compenaton hown for comparon n fg. 2b. The error more than ten tme hgher, epecally wthn the QRS complexe. g. 2c preent the cae of a gradually frequency change wthn. It can be 07

5 een that the compenaton proce fall behnd, becaue of erroneouly detected nonlnear egment. Obvouly, a dynamc crteron for lnearty [7] utable to be ued n uch cae. The tme for overtakng the new tatonary frequency reman the ame, but the tranent between the two tatonary frequence accompanyng by a lot of non-lnear egment detected. Th due to the pecfc of the algorthm, whch compenate frequency change durng lnear egment only. It poble to peed up the algorthm, f a compenaton tep can be extrapolated n non-lnear egment. Orgnal gnal - 0 Sgnal+Interference - 0 ltered gnal Zoomed error PL devaton, Compenated devaton, Threhold b c Hz 0 a a) ltered gnal Zoomed error b) Hz 2 0 PL devaton, Compenated devaton, Threhold g.2. Experment wth automatc compenaton of the PL frequency varaton n real ECG gnal. In cae of even multplcty (n=2m), equaton (2) hould be changed to a b c c) 08

6 /2 n X Y = X+ + n = n/2+ + X 2 n/2 + n/2 that wll ntroduce modfcaton of equaton (9), n /2 = n 2 + 2( ) -n/2 2 + = n+ = n/ 2+ (0), () and (2) a B B B nk B B for (9), n /2 B n B + B+ + B+ + 2 = n+ = n/2+ 2 K+ d= + Φ π B -n/2 n for (0), d K + d tg π Φ π for () and D+ d 4n B+ dtg for (2). The other equaton a well a the Φ algorthm reman the ame. 4. CONCLUSIONS A modfcaton of the ubtracton method for nterference removng from ECG gnal elaborated to compenate the PL frequency varaton, whch are condered a dynamcally appearance of non-multplcty between amplng rate and PL frequency. Approprate formulae for correcton of bac flter coeffcent are derved. Experment wth odd multplcty (n=2m+) how that the method uccefully compenate the PL frequency varaton, except for the tranent of gradually change. The formulae for even multplcty (n=2m) are derved too. 5. REERENCES [] Levkov, C., G. Mchov, R. Ivanov, I. Dakalov. Subtracton of 50 Hz Interference from the Electrocardogram. Medcal & Bologcal Engneerng & Computng 22, pp , 984. [2] Standard ANSI/AAMI EC-99. Dagnotc electrocardographc devce. 99. [3] Ovcharov, S., N. Tulev, P. Yakmov. Man frequency montorng ytem. 3-rd Internatonal Scentfc and Appled Scence Conference Electronc ET 94, b., pp , Sozopol, Bulgara, 994 (n Bulgaran). [4] Mhov G., Reecton of Non-Synchronou Man Interference from ECG Sgnal. In: Phlpov, Ph. (Ed.) Annual School Lecture, 8-th Internatonal Sprng Semnar on Semconductor and Hybrd Technologe. vol.8, No, pp , 996. [5] Levkov C., G. Mhov. Reecton - Subtracton lter of Man Interference from the ECG. BIOSIGNAL 96, vol. 3, pp , Brno, Czech Republc, 996. [6] Dotnky, I., I. Dakalov. Accuracy of the 50 Hz Interference Subtracton from the Electrocardogram. Med. Bol. Eng. Comput., 34, pp , 996. [7] Chrtov, I. Dynamc powerlne nterference ubtracton from bognal. Journal of Med. Eng. & Tech., 24, 69-72, [8] Levkov, C., G. Mhov, R. Ivanov, Ivan K. Dakalov, I. Chrtov, I. Dotnky. Subtracton Method for Powerlne Interference Removng from ECG. 3-th Internatonal Scentfc and Appled Scence Conference Electronc ET 2004, b., pp. 3-4, Sozopol, [9] Dotnky, I., T. Stoyanov. Power-lne nterference cancellaton n ECG gnal. Bomed. Intr. Techn., 39, pp , [0] Mhov, G., I. Dotnky, T. Georgeva. Subtracton Procedure for Power-Lne Interference Removng from ECG: Improvement for Non-Multple Samplng. Journal of Medcal Engneerng & 09

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