Locally-adaptive Myriad Filters for Processing ECG Signals in Real Time

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1 Locally-adaptve Myrad Flters or Processng ECG Sgnals n Real Tme Natalya Tulyakova Research Center o Equpment or Educaton and Research Insttute o Appled Physcs Natonal Academy o Scences o Ukrane 58 Petropavlvska Str., Sumy, Ukrane E-mal: natalyatulyakova@gmal.com Receved: December 01, 2016 Accepted: February 16, 2017 Publshed: March 31, 2017 Abstract: The locally adaptve myrad lters to suppress nose n electrocardographc (ECG) sgnals n almost n real tme are proposed. Statstcal estmates o ecency accordng to ntegral values o such crtera as mean square error (MSE) and sgnal-tonose rato (SNR) or the test ECG sgnals sampled at 400 Hz embedded n addtve Gaussan nose wth derent values o varance are obtaned. Comparatve analyss o adaptve lters s carred out. Hgh ecency o ECG lterng and hgh qualty o sgnal preservaton are demonstrated. It s shown that locally adaptve myrad lters provde hgher degree o suppressng addtve Gaussan nose wth possblty o real tme mplementaton. Keywords: Electrocardogram lterng n real tme, Locally adaptve myrad lters, Statstcal estmates o ecency. Introducton Several noses are always accompanyng the electrocardographc (ECG) recordngs: mans ntererence, electromyographc (EMG) nose, and baselne wander (drt) o the sgnal. The EMG nose s due to muscle stran and ts domnant energy s located n the Hz range. The EMG spectra s totally overlappng the ECG spectra thus makng mpossble the automatc analyss o the ECG. Flterng o the EMG nose causes dstortons o the hgh-requency components o the ECG, volatng ther dagnostcally sgncant morphologcal parameters. In a study o the sources o varaton n the QT readngs [19] the authors argue that most o the low-pass lterng procedures eect on shtng outward the Q and T marks. For that reason, the recommendatons rom 1967 o the Amercan Heart Assocaton [20] or low-pass lterng o not less than 35 Hz cuto were changed to 150 Hz or adolescents and adults and to 250 Hz or chldren [12]. Two hghly eectve methods or nose suppresson have been suggested [11, 15,], based on orthogonal dscrete cosne and wavelet transorm, but at a hgh computaton cost. Smple and hghly eectve algorthm or dynamc approxmaton have been descrbed [4-6, 8] but ths lters were not mplemented n real tme. The approxmaton s based on the [18] smpled last square procedure, appled dynamcally n respect o the requency spectra o the ECG waves. Despte the act that the modern computer technology s allowng mplementaton o complex dgtal sgnal processng algorthms, some portable devces and ECG montors are o lmted resources and requre lterng algorthms o hgh-speed perormance and real tme applcablty. 5

2 A well-reasoned selecton, among the dgtal lters or hgh requency nose suppresson n bomedcal sgnals, s lterng wth nonlnear stablty, not only because o the non-gaussan nature o the nose, but also due to the hgh dynamc propertes (preservaton o the sgnal waveorm) o the nonlnear lters [3]. There are lexble algorthms, whch at a certan parameter s settngs, provde sgncant non-lnearty propertes to preserve dscontnutes and abrupt changes o the sgnal and to remove outlers. One example o such lter s based on a sample myrad estmator. Dependng on a value o the lnearty parameter K, the myrad estmator n one margnal case has more robustness than a medan lter and s optmal or Cauchy dstrbuton whch descrbes mpulsve nose. In the other margnal case, the myrad estmator tends to a sample average and has lnear propertes, not worse than those o the averagng lter accordng to the degree o suppresson o the Gaussan nose [9, 10]. The ablty to change the myrad estmator propertes, dependng on the parameter K, was the bass or the development o adaptve myrad lterng algorthms, n partcular or ECG processng [16]. In work [2], a locally-adaptve myrad lter that changes the lnearty parameter K dependng on the local adaptaton parameters calculated n current -th poston o sldng wndow has been suggested. However, length o the sldng wndow o the adaptve lter should be selected based on a balance between ecent nose suppresson and reducton o dstortons ntroduced by the processng. For not a large wndow, the adaptve myrad lter s mplemented n real tme [2], but the use o a wndow o xed sze or ECG s not avourable, snce hgh-requency QRS complex requres processng wth small wndows appled; and the wndow length should be enlarged n order to suppress nose enough n the low-requency P-, T-waves. In ths connecton, locally-adaptve myrad lters wth dynamcally varyng wndow length and estmatng o myrad lnearty parameter K are proposed and ther ecency wth respect to other adaptve algorthms s presented. Locally-adaptve myrad lters A sample myrad s a robust M-estmator o locaton o the Cauchy dstrbuton wth scalng actor K > 0 [9, 10], whch s dened as: ˆ ˆ {,,..., ; } arg mn log [ 2 ( ) 2 myrad x x x K N K x ] N, (1) where x denotes the data samples wthn the sldng wndow; N s sldng wndow length; K s lnearty parameter o myrad estmator, K > 0. In order to adjust the lnearty parameter K o myrad lter or each -th poston o the sldng wndow, drectly proportonal dependency can be used: K, K max N xk x j k, j 1, (2) a bk k j where b s a xed coecent. The output sgnal o the adaptve myrad lter, denoted as AMF, can be descrbed as ollows: y myrad { x, x,..., x,..., x, K }, (3) AMF 1 2 N a where Ka s the lnearty parameter calculated or the -th sldng wndow. The locally adaptve lter (LAF) s suggested or processng the neghbourhood o the current -th sample o nput sgnal. In one case the LAF apples AMF wth a small wndow length and wth nonlnear propertes, and n another t uses AMF wth a large wndow length and settng the propertes to lnearty mode by ncreasng the coecent b (2). Thus, the local adaptaton s controlled by choosng the more approprate AMF sldng wndow length and by adaptaton 6

3 o the lnearty parameter Ka or an -th poston o AMF sldng wndow by choosng the approprate coecent b and calculatng parameter K that estmates sgnal scale (2). For adaptve hard swtchng o the outputs between two AMF, prelmnary smoothed adaptaton parameters smlar to threshold parameters o Hampel lter [17] can be used. The output o the proposed myrad LAF, denoted as AMH, s dened as: y y, r th ; AMF ( N1, b 1) AMH AMF ( N2, b 2) y, otherwse, AMF ( N1, b1) AMF ( N2, b2) where y, y are the outputs o AMF (3) wth tunng parameters: wndow lengths N1 < N2 and coecents b1 < b2; 1 2 N 2 (4) r mean { r, r,..., r,..., r } are values o the r x m smoothed by averagng lter, where x s a central sample o the nput set o the 2 samples { x } N j j N wthn the sldng wndow wth length N2, m s the sample medan; th mean { th, th,..., th,..., th } are the smoothed values o the threshold parameters th t S Mad, where 2 S medan { x m, x m,, x m } are the local Mad 1 2 N estmates o the sgnal scale, where s the coecent or the Gaussan dstrbuton, { } N 2 xj j 1 s the set o nput samples, m s the set s medan; t s a xed threshold. It s expected that LAF AMH (4) can preserve ECG sgnal on ragments o ts rapd changng due to hgh dynamc propertes o AMF n the nonlnear mode and small length o the sldng wndow and can eectvely suppress nose whle processng ragments o the slow sgnal behavour by adjustng the parameter Ka to a lnear mode and ncreasng the wndow length. The more approprate algorthm or calculaton a sample myrad or the LAF (4) s the algorthm o mnmzaton o myrad cost uncton based on a numercal Newton technque [1, 22] because n order to determne the accuracy o teratons can be use calculated MAD-estmates o data scale. The myrad LAF whch adaptvely swtches the output sgnals between three AMF components by comparng local actvty ndcators reerred as Z-parameters [13, 14] to the gven thresholds s consdered [21-24]. The output o ths LAF denoted as AMZ s dened as: AMF ( N3, b 3) t y, Z Z1 ; AMZ AMF ( N2, b 2) t t y y, ( Z Z1) ( Z Z2); (5) AMF ( N1, b 1) t t y, ( Z Z2) ( QZ Z2); where y AMF ( N j, bj), j = 1, 2, 3, s output o j-th AMF (3) wth the wndow length Nj and the tunng coecent bj, N3 > N2 > N1, b3 > b2 > b1; values o local actvty ndcators j Z, Z 2 Q are pre-ltered by medan lter ( N1)/2 ( N1)/2 j j j j j( N 1)/2 j( N 1)/2, where Z ( y x ) / y x x are pre-ltered and nput samples or calculaton o the Z-parameter, respectvely (N = N2); ( q) ( p) Z y, Q Z Z s quasrange o Z-parameter calculated as the derence between the q-th and p-th order statstcs o the sorted set (1) (2) ( N) { Z, Z,, Z } j, q p ( N 1) / 2; t t Z1 0.2, Z2 0.4 are the thresholds. The prelmnary lter wth the mddle sldng wndow length N and ntermedate dynamc and statstcal propertes s used to calculate the 7

4 Z-parameter. Ths lter s usually an ntermedate component o LAFs based on Z-parameter [13, 14, 21, 23, 24]. For myrad LAF (5) n contrast to LAF (4), not two but three component lters are used. The use o an ntermedate component can mprove the dynamc propertes o lterng. However, applcaton o three-component s LAF requres more calculatons whch can essentally aect the processng tme as the samplng rate and length o the wndow ncreases. Crtera o eectveness The statstcal estmates o lterng ecency are evaluated usng crtera o mean square error (MSE) and sgnal-to-nose rato (SNR) averaged or a large number o nput sgnal realzatons [3]:, (6) NR I 2 [ ( ) / ]/ 1 1 j R MSE y s I N N SNR R 10lg( p ) / j 1 s pn N R, (7) where y s the output o the evaluated lter; s s the true sgnal value o the -th sample; I 2 I s the sgnal s length; ( ) / I ps s 1 s I s the sgnal power; s / s 1 I s the mean I 2 value o the sgnal; ( p ) / n y 1 s I s the nose power; NR s number o nput sgnal realzatons or statstcal averagng. State o the art Eectveness o nonlnear robust lters s usually evaluated by numercal smulatons snce analytcal descrpton o ther propertes s too complex [3]. Parameters o these lters can also be selected or speced by numercal smulatons. In ths case, or myrad LAF AMH (4) parameters or the test ECG are chosen n presence o medum level o the Gaussan nose (nput SNR s db): N1 = 5, b1 = 1, N2 = 17, b2 = 10, t = 0.5. Smlarly, or myrad LAF AMZ (5) the parameters are as ollows: N1 = 5, b1 = 1, N2 =13, b2 = 5, N3 = 17, b3 = 10. The ntermedate component o LAF AMZ as a prelmnary lter or calculatng the Z-parameters has the parameters N2 = 13, b2 = 5. Due to the nosness o Z-parameter [13, 14, 24] ts values are processed by the medan lter wth wndow length N = 5. Note that or the other test sgnals sutable parameters o adaptve algorthms AMH and AMZ may der. Myrad LAF AMH and AMZ process the nput sgnal wthn sldng wndows wth lttle delay o the current -th sample o output sgnal n relaton to the reerence sample o the nput sgnal,.e. n almost n real tme. The proposed myrad LAF processes the nput sgnal by two or three component lters n parallel and n parallel calculates the parameters o local adaptaton r, th (4), Z (5), whch dene the selecton o the output sgnal o the more approprate lter. Thus, or myrad LAF AMH, output delay n relaton to the nput sample can be N2 samples where N2 s the length o the sldng wndow used or calculaton o the local adaptaton parameters and the wndow length o the second LAF component (4). Snce (1) (2) ( N) the sorted set { Z, Z,..., Z } s requred or calculaton o quasrange o the Z-parameter, the processng delay or AMZ s hgher than that o AMH. Myrad LAFs (4-5) were compared to the dynamc approxmaton algorthms [4, 6] that suppress sucently the nose n ECG wth mnmal dstorton o hgh requency content o the sgnal. These lters apply the optmal Savtzky and Golay (S&G) procedure wthn the 8

5 approxmaton nterval, whch length s adaptvely changed dependng on the ast (QRS complex) or slow (P-, T-waves) behavour o the ECG sgnal. For dynamc approxmaton presented n works [6, 7], Wng-uncton wth extremes nsde hgh-requency QRS complex was ntroduced to estmate the slope o the ECG sgnal. Smoothed Wng-uncton, ts mnmum and maxmum values were used n the analytcal expresson whch dene the length n o approxmaton ntervals or the applcaton o the S&G algorthm, so that the processng nterval was mnmal nsde the QRS complex and the maxmal outsde t. For processng o ECG regstered wth samplng rate 400 Hz, the length o approxmaton nterval ranged rom nmn = 1 to nmax = 15 [6]. The advantages o the dynamc approxmaton algorthm [6], denoted as DAW, are the smplcty and hgh ecency o nose suppresson, but ths algorthm s not mplemented n real tme, because t s necessary to use the sgnal realzaton along ECG perod n order to calculate the Wng-uncton, to smooth t, to search ts mnmum and maxmum values. For dynamc approxmaton algorthm descrbed n work [4], the rato o standard devatons o the resdual nose outsde and nsde QRS was used or adaptve settng o the mnmum length o approxmaton nterval appled nsde the QRS complex, and the constant maxmum length o approxmaton nterval nmax was appled outsde QRS. In case o ECG sgnals sampled at 400 Hz, the mnmum length o the approxmaton nterval or processng the QRS complex was automatcally adjusted between nmn = 6 to nmn = 2, dependng on the nose level. To process the low requency segments o the ECG sgnal the maxmum length o approxmaton nterval equals to nmax = 15 [4]. Ths dynamc approxmaton algorthm, denoted as DARN, has hgh dynamc and statstcal propertes [4, 24], but ts mplementaton requres the segmentaton o the ECG sgnal and adjustng the parameter nmn. Results and dscussons A clean ECG sgnal recorded wth the samplng rate 400 Hz (Fg. 1) s used as a model sgnal. Condtons or the addtve Gaussan nose wth zero mean and derent varances a 2 are smulated. The ecency o the suggested myrad LAF AMH (4), AMZ (5) and dynamc approxmaton algorthms DAW [6] and DARN [4] are analyzed on the bass o the statstcal estmates o the MSE (6) and SNR (7) (Table 1). A number o realzatons or the statstcal averagng operaton s NR = 200. As can be seen rom Table 1 (case 1-3) or low level o the addtve Gaussan nose, the DARN dynamc approxmaton algorthm has the best eectveness, provdng hgh dynamc propertes (mnmal dstortons o a sgnal). In case o low level o nose (the nput SNR varyng rom 21.2 to 12 db) DARN algorthm provdes a reducton o MSE n tmes and ncrease o SNR by 9-10 db. The advantage o DARN s observable at very low level o nose (Table 1, case 1-2) and s lost as the nose varance ncreases. In cases o ncreasng nose varance, the best ecency or the consdered adaptve lters s provded by AMH (Table 1). In case o mddle level o nose (Table 1, case 4-7, the nput SNR belongs to the nterval db), AMH MSE s decreased n tmes and AMH SNR ncreases by db. In case o hgh level o nose (Table 1, case 8-10, the nput SNR varyng rom 8.2 to 3.5 db), the ndcators o the ecency o AMH are as ollows: the AMH MSE decreases n tmes, AMH SNR ncreases by db. The llustratons o the output sgnals (Fgs. 1-5) o the consdered adaptve lters conrm the numercal smulaton results (Table. 1). I a nose-ree sgnal s processed (Fg. 1), the smallest dstortons n QRS-complex area are produced by the algorthm DARN [4] due to 9

6 nmn tunng to mnmal value. Snce or LAF (4-5) the sldng wndow lengths o component lters are xed, QRS-complex processng by the myrad LAF leads to more dstortons wth some smoothng o Q, R, and S peaks. The algorthm DAW preserves ampltude o R-peak but dstorts Q and S-waves. In the case o low level o nose (Fg. 2), the consdered adaptve lters demonstrate hgh qualty o preservng sgnal component. In the cases o mddle (Fg. 3) and hgh (Fg. 4) levels o Gaussan nose, the LAFs provde better qualty o lterng. A) B) C) D) E) F) G) H) I) Fg. 1 Sgnal dstortons: A) clean ECG sgnal; B) output o AMH; C) output o AMZ; D) output o DAW; E) output o DARN; F) sgnal dstortons o AMH; G) sgnal dstortons o AMZ; H) sgnal dstortons o DAW; I) sgnal dstortons o DARN. 10

7 Table 1. Statstcal estmates o the ecency accordng to MSE (ppm) and SNR (db) crtera Flter MSE SNR MSE SNR MSE SNR MSE SNR MSE SNR 1) a 2 = ; NR = 200 2) a 2 = ) a 2 = ) a 2 = ) a 2 = None AMH AMZ 21 28, DAW DARN ) a 2 = ) a 2 = ) a 2 = ) a 2 = ) a 2 = None AMH AMZ DAW DARN A) B) C) D) E) Fg. 2 Processng o the test ECG sgnal wth low level o the addtve Gaussan nose: A) nosy sgnal (a 2 = ); B) output o AMH; C) output o AMZ; D) output o DAW; E) output o DARN. The resdual nose retaned ater applcaton o the myrad LAF AMH s less than or the lters AMZ, DAW (Fgs. 3-4). It s more observable on the hgh-requency QRS-complex. 11

8 A) B) C) D) E) F) G) H) I) J) Fg. 3 Processng o the test ECG wth mddle level o the addtve Gaussan nose: A) nosy sgnal (a 2 = ); B) output o AMH; C) output o AMZ; D) output o DAW; E) output o DARN; F) nose; F) resdual nose ater AMH; G) resdual nose ater AMZ; I) resdual nose ater DAW; J) resdual nose ater DARN. Mnmal dstortons o the sgnal ampltudes and hgh eectve suppresson o EMG nose n ECG by the consdered lters are can be seen (Fg. 5). The algorthm DARN and the LAFs (4-5) better preserve QRS-complex snce the algorthm DAW slghtly expands the Q-wave. 12

9 A) B) C) D) E) F) G) H) I) J) Fg. 4 Processng o the test ECG wth hgh level o the addtve Gaussan nose: A) nosy sgnal (a 2 = 0.004); B) output o AMH; C) output o AMZ; D) output o DAW; E) output o DARN; F) nose; F) resdual nose ater AMH; G) resdual nose ater AMZ; I) resdual nose ater DAW; J) resdual nose ater DARN. The behavor o the local adaptaton parameters o the myrad LAFs (4-5) n Fgs. 6-7 shows manly correct hard-swtchng. The use o ncorrect component lters due to nosness o local adaptaton parameters does not lead to essental decrease o processng qualty (Fgs. 2-4). 13

10 A) B) C) D) E) F) G) H) I) J) Fg. 5 Processng o the test ECG: A) ECG wth power lne ntererence; B) ECG corrupted by EMG nose; C, D) outputs o AMH n case o absence and presence o EMG nose, respectvely; E, F) outputs o AMZ n case o absence and presence o EMG nose; G, H) outputs o DAW n case o absence and presence o EMG nose; I, J) outputs o DARN n case o absence and presence o EMG nose. As can be seen rom Fg. 6, small values o lnearty parameter Ka (2) that determne nonlnear mode o myrad operaton and small values o scannng wndow sze or LAFs correspond correctly to hgh-requency ragment o QRS complex and neghborhoods o T-wave start and end where one needs to use a processng algorthm wth hgh dynamc propertes. 14

11 A) B) C) D) E) F) G) H) I) J) Fg. 6 Illustraton o the local adaptaton n case o low level o Gaussan nose: A) test sgnal; B) local adaptaton parameters r, th o LAF AMH; C) smoothed r, th; D) adaptable parameters o wndow length and o coecent b o LAF AMH; E) adaptable lnearty parameter Ka o AMH; F) local actvty ndcators Z, QZ o LAF AMZ; G) adaptable parameters o wndow length and o coecent b o LAF AMZ; H) adaptable lnearty parameter Ka o AMZ; I) Wng-uncton; J) approxmaton ntervals o DAW and o DARN. I the nose s level hgh, the probablty o ncorrect swtchng or AMH s less than or AMZ (Fg. 7). However, the algorthm AMZ (5) correctly swtches wndow sze to N1 = 5 and 15

12 N2 = 13 or processng parabolc wave. Ths provdes smaller dstortons due to lterng or ths ragment o ECG. Besdes, the thresholds or LAF AMZ are obtaned by analytcal way [19, 20] whereas the threshold parameter t or LAF AMH s tuned or the sgnal heurstcally. A) B) C) D) E) F) G) H) I) J) Fg. 7 Illustraton o the local adaptaton n case o hgh level o Gaussan nose: A) test sgnal; B) local adaptaton parameters r, th o LAF AMH; C) smoothed r, th; D) adaptable parameters o wndow length and o coecent b o LAF AMH; E) adaptable lnearty parameter Ka o AMH; F) local actvty ndcators Z, QZ o LAF AMZ; G) adaptable parameters o wndow length and o coecent b o LAF AMZ; H) adaptable lnearty parameter Ka o AMZ; I) Wng-uncton; J) approxmaton ntervals o DAW and o DARN. 16

13 Conclusons The locally adaptve myrad lters wth varable wndow length and coecent used or adaptve calculaton o myrad lnearty parameter K dependng upon local estmates o sgnal propertes are proposed. Hgh ecency o locally-adaptve myrad lters s demonstrated wth the statstcal estmates o lters ecency accordng to MSE and SNR crtera or the test ECG sampled wth 400 Hz or derent levels o the addtve Gaussan nose. Locally adaptve myrad lters are more ecent n suppresson o nose as compared to hghly eectve dynamc approxmaton algorthms whch are not mplemented n real-tme. Locally adaptve myrad lters do not requre any prelmnary procedures or estmatng nose varance, detecton o the QRS complexes, do not requre adjustng the lter parameters and have ast algorthm mplementatons whch allow process the sgnal n a real tme mode. Acknowledgements My warmest thanks to Pro. D.Sc. Ivaylo Chrstov rom the Insttute o Bophyscs and Bomedcal Engneerng, Bulgaran Academy o Scences, who helped me a lot. Reerences 1. Abramov S. K. (2000). Myrad Flterng Realzaton Algorthm, Aerospace Engneerng and Technology, Kharkov, NAU, 21, (n Russan). 2. Abramov S. K., V. V. Lukn, J. Astola (2001). Adaptve Myrad Flter, СD-ROM Proc. o the NSIP 2001, Baltmore (USA). 3. Astola J., P. Kuosmanen (1997). Fundamentals o Nonlnear Dgtal Flterng, New York, CRC Press. 4. Bortolan G., I. Chrstov (2014). Dynamc Fltraton o Hgh-requency Nose n ECG Sgnal, Computng n Cardology, 41, Bortolan G., I. Chrstov, I. Smova, I. Dotsnsky (2015). Nose Processng n Exercse ECG Stress Test or the Analyss and the Clncal Characterzaton o QRS and T Wave Alternans, Bomedcal Sgnal Processng and Control, 18, Chrstov I., I. Daskalov (1999). Flterng o Electrocardogram Artacts rom the Electrocardogram, Medcal Engneerng & Physcs, 21, Chrstov I., T. Neycheva, R. Schmd, T. Stoyanov, R. Abächerl (2017). Pseudo Real-tme Low-pass Flter n ECG, Sel-adjustable to the Frequency Spectra o the Waves, Medcal & Bologcal Engneerng & Computng, Dotsnsky I., G. Mhov (2010). Smple Approach or Tremor Suppresson n Electrocardograms, Internatonal Journal Boautomaton, 14(2), Gonzalez J. G., G. R. Arce (2001). Optmalty o the Myrad Flter n Practcal Impulsvenose Envronments, Proc. o the IEEE Tran on Sgnal Processng, 49(2), Gonzalez J. G., G. R. Arce (2002). Statstcally-ecent Flterng n Impulsve Envronments: Weghted Myrad Flters, EURASIP Journal on Appled Sgnal Processng, 1, Gotchev A., I. Chrstov, K. Egazaran (2002). Denosng o Electrocardogram rom Electromyogram Artacts by Combned Transorm-doman and Dynamc Approxmaton Method, Proc. o the IEEE Internatonal Conerence on Acoustcs, Speech and Sgnal Processng, Klgeld P., L. S. Gettes, J. J. Baley et al. (2007). Recommendatons or the Standardzaton and Interpretaton o the Electrocardogram: Part I: The Electrocardogram and ts Technology. A Scentc Statement rom the Amercan Heart Assocaton Electrocardography and Arrhythmas Commttee, Councl on Clncal Cardology; the Amercan College o Cardology Foundaton; and the Heart Rhythm 17

14 Socety Endorsed by the Internatonal Socety or Computerzed Electrocardology, Journal o the Amercan College o Cardology, 49(10), Lukn V. V., A. A. Zelensky, N. O. Tulyakova, V. P. Melnk. (1999). Adaptve Method or 1-D Sgnal Processng Based on Nonlnear Flter Bank and Z-parameter, Proc. o the IEEE/EURASIP Workshop on Nonlnear Sgnal and Image Processng, Antalya, Turkey, 1, Lukn V., A. Zelensky, N. Tulyakova, V. Melnk, S. Peltonen, P. Kuosmanen (2000). Locally-adaptve Processng o 1-D Sgnals Usng Z-parameters and Flter Banks, Proc. o the Nordc Sgn. Proc. Symp., Kolmarden, Sweden, Nkolaev N., A. Gotchev (2000). ECG Sgnal Denosng Usng Wavelet Doman Wener Flterng, Proc. o the European Sgnal Processng Conerence, Pander T. (2010). Impulsve Nose Flterng In Bomedcal Sgnals wth Applcaton o New Myrad Flter, Proc. o the Internatonal Conerence o Bosgnal, 20, Pearson R. K., Y. Neuvo, J. Astola (2015). The Class o Generalzed Hampel Flters, EUSIPCO-2015: Proc. o the 23rd European Sgnal Processng Conerence, Savtzky A., M. Golay (1964). Smoothng and Derentaton o Data by Smpled Least Squares Procedures, Analytcal Chemstry, 36, Smova I., I. Chrstov (2007). Sources o Varaton n the QT Readngs: What Should You be Aware o?, Internatonal Journal Boautomaton, 6, Subcommttee on Instrumentaton Commttee on Electrocardography Amercan Heart Assocaton (1967). Recommendaton or Instruments n Electrocardography and Vectorcardography, IEEE Transactons on Bomedcal Engneerng, 14, Tulyakova N. O. (2015). Locally-adaptve Myrad Flterng o Electrocardogram Sgnal, Radotekhnka: All-Ukr. Sc. Interdep. Mag., 180, (n Russan). 22. Tulyakova N. O., O. M. Troymchuk, O. Ye. Stryzhak (2014). Algorthms o Myrad Flterng, Radoelectronc and Computer System, 4(68), (n Russan). 23. Tulyakova N. O., O. M. Troymchuk, O. Ye. Stryzhak (2016). Adaptve Myrad Flters or Processng Sgnals o Electrocardogram Regstered wth Hgh Samplng Frequency, Radoelectronc and Computer System, 4(78), (n Russan). 24. Tulyakova N. O., O. M. Troymchuk, O. Ye. Stryzhak (2016). Algorthms o ECG Flterng wth Dynamcally Varable Wndow Sze, Radoelectronc and Computer System, 2(76), 4-14 (n Russan). Natalya Tulyakova, Ph.D. E-mal: natalyatulyakova@gmal.com Natalya Tulyakova graduated rom Kharkv Avaton Insttute named ater M. Ye. Zhukovsky, Faculty o Radoelectronc Systems o Flyng Vehcles, wth a M.Sc. degree n Botechncal and Medcal Devces and Systems (wth hghest honors). She receved her Ph.D. degree n Bologcal and Medcal Devces and Systems n Kharkv Natonal Unversty o Radoelectroncs. Her research work deals wth bomedcal sgnal processng by the authors. Lcensee Insttute o Bophyscs and Bomedcal Engneerng, Bulgaran Academy o Scences. Ths artcle s an open access artcle dstrbuted under the terms and condtons o the Creatve Commons Attrbuton (CC BY) lcense ( 18