REPORT Submitted: 25.02.2020; Accepted: 23.03.2020; Published online: 21.05.2020
Polynomial filtering of low- and 2020; р.85-96; DOI: 10.12710/cardiometry.2020.16.8596; Avail- high- frequency noise for able from: http://www.cardiometry.net/issues/no16-may-2020/ accuracy-of-ecg-signal-processing improving the accuracy of ECG signal processing: Introduction Nowadays, in solving the electrocardiographic data new advancements processing issues widely used are processing methods Yeldos A. Altay1*, Artem S. Kremlev1 based on polynomial ECG signal filtering methods [1- 9]. The topicality of the polynomial filtering methods 1 St Petersburg National Research University of consists in the fact that they allow us to largely adjust Information Technologies, Mechanics and Optics their parameters according to the processed ECG sig- Russia, 197101, St. Petersburg, Kronverksky av. 49 nal parameters, as well as improve the efficiency of processing and selecting informative ECG signal com- * Corresponding author: ponents from an additive mixture of noises. e-mail: [email protected] To improve the efficiency of processing of the elec- phone: +7 (952) 278-52-53 trocardiographic data, at present there is a necessity to jointly consider the measuring electrodes to evaluate Abstract their quality, which determines the efficiency and re- The article describes a solution of the ECG signal processing liability of the ECG signal processing analysis, in par- problem in the presence of low- and high- frequency noises, ticular the means of noise filtering [10,11]. The need which reduce the accuracy of selection of the signal informative for such consideration is as follows. First, characteris- parameters during their processing. To increase the accuracy tics of contact conductive agents make their effect on of the signal informative parameters selection, developed is a the accuracy of reproduction (formation) of the sig- new method for noise filtering based on a polynomial approx- nal parameters, i.e. the minimization of losses of the imation of high frequency filters and wide-band reject filters obtained ECG signal informative segments during the using Newton polynomials. Applying the developed method of signal recording. Second, it is required to increase ac- processing, analyzed is its functionality and efficiency with the curacy of the ECG signal processing means against the use of full-scale reference ECG signal samples, and on the basis background of affecting noises. In case of low quali- of quantitative indices, the comparison of the efficiency of the ty of the ECG signal recording due to the character- offered method in relation to the known approaches is carried istics of the electrodes themselves, errors may occur, out. To evaluate the noise characteristics by means of the pres- which are associated with the formation of the ECG ent method some fragments of low- and high- frequency nois- signal informative parameters and which may be rec- es are selected from noise-laden ECG signal recording. It has ognized in the process of noise filtering as distortions been found that the application of the Newton polynomials to introduced by filter algorithms. All this is particularly approximations of the transfer characteristics in high frequency important in the development of methods for noise filters and wide-band reject filters greatly increases the accuracy filtering, as well as in the analysis and processing of of the ECG signal processing analysis and attenuates noises. long-term monitograms. Noises, appearing in recording an ECG signal, Keywords namely the low- and high-frequency ones, are among ECG signal processing, Filtering, High-frequency filter, Reject filter, the main factors that reduce the accuracy of ECG sig- Cascade of filters, Low-frequency noise, High-frequency noise, nal processing. When recording ECG signals, the low Newton polynomial, Noise attenuation, Measuring electrodes frequency noises occur due to a poor physical contact between a measuring electrode conductive agent and Imprint a bioobject, due to human breathing, etc. [1-3,5-8,12]. Yeldos A. Altay, Artem S. Kremlev. Polynomial filtering of low- and High-frequency electrical noises are generated main- high- frequency noise for improving the accuracy of ECG sig- ly by networked external electrical devices, including nal processing: new advancements. Cardiometry; Issue 16; May such as physiotherapy and surgical equipment [1-
Issue 16. May 2020 | Cardiometry | 85 9,12]. Besides, high-frequency noise can also include ular, the type of wave patterns of the signal RR-inter- some muscle noises appearing as a result of bioobject vals. However, the identified wide-band noise differs skeletal muscular motion activity [3,5-7,12,13]. from the narrowband network noise in frequency Effects produced by the above types of noises characteristics. greatly reduce the accuracy of the ECG signal analysis, Reference research literature suggests that the most in particular the measurements of signal amplitudes commonly used are filters approximated by the But- and the time parameters, carried out automatically or terworth polynomials, and as to other polynomials, for manually by a physician [14]. example, by the Chebyshev (I and II type), Bessel and The low frequency noise analysis has been treated Cauer, they are employed less common for elimination by a number of works [2-8,12,15], from which it can of the above analyzed noises, namely for removal of be noted that the ECG signal low-frequency noise is the low- and high-frequency ones. In papers [1-7,19] a sum of deterministic components with a frequency the experimental evidence shows that the Chebyshev from 0.1 Hz to 0.3 Hz, but not more than 1 Hz, having polynomials (I, II), the Bessel and Cauer polynomials a random amplitude. for filtering the ECG signal noises are less effective. The analysis of the high-frequency noise parame- This is due to low accuracy of the obtained ECG sig- ters is also the subject of several studies [2-8,12,13], nal processing output results that can be attributed to from which it can be understood that the electrical generation of the greatest values of the filter’s own er- noise is a narrowband deterministic signal, having ror based on the filter frequency characteristics. At the slowly varying harmonics of different phases with same time, filters based on the Butterworth polynomi- a frequency of 50 Hz. Hence, the muscle noise is a al are characterized by flatness and smoothness of the wide-band noise with the zero mean value, overlap- frequency response characteristics as compared with ping with the ECG signal frequency spectrum [13,16]. the other types of filters [2-8]. The Butterworth poly- The muscle noise is the most dangerous, difficultly re- nomials are a generally accepted form of placing the movable noise due to high muscle activity during the transfer function into the circular quadratics [20,21]. signal recording. Taking into account these features of Also known is the application of the Newton polyno- the myographic noise, in the ECG signal processing mials for approximation of the transfer characteristics used is the so-called “rejection” approach, i.e. highly of the reject filters [9]. noise-laden ECG signal segments are excluded from The Newton polynomials in approximations of the further consideration [14]. filter transfer characteristics are applied in view of the However, despite the studies devoted to the analy- fact that theoretically derivable properties of the fil- sis of the characteristics of affecting noises, in particu- ter successfully correspond to the multi-component lar narrow-band electrical noises, at the present time, signals structure. The above property is extremely im- we observe a steady tendency of an interrupted growth portant in processing of complexly structured pulse in the noise level due to an increase in the energy con- signals of the cardiovascular origin that justifies the sumption in all areas of activity that may lead to a de- application of the Newton polynomial for solving the terioration of the general electromagnetic background electrocardiographic data processing tasks, in partic- [17]. Besides, observed are high frequency electrical ular, the low- and high-frequency noise filtering. It noises induced by laptop internal units [18]. Taking should be noted that the above polynomial is one of into account all the above, studies in [9] suggest that the members of the automatic control theory, which during the ECG signal recording with a laptop, when is currently used for the synthesis of objects in control disconnecting the power cable of the latter, there may systems and which shows the best quality results [21]. be possible generation of wide-band electrical noise Currently, however, the application of the Newton induced by the laptop internal units. The frequency polynomial for improving efficiency of the ECG signal component of the given noise is identified as that to processing, in particular for approximation of filtering be close to the range from 44 Hz to 56 Hz with a noise means transfer characteristic, is less well discussed. center frequency of 50 Hz upon computing the dis- It is known that low-frequency noises, appearing in crete Fourier transform. The above noise, as well as a case of a poor contact of the conductive agents in mea- narrow-band network noise, may affect the amplitude suring electrodes, often lies in a low frequency range and the time parameters of the ECG signal, in partic- of the signal, and, as a rule, high frequency filters are
86 | Cardiometry | Issue 16. May 2020 used to suppress this sort of noises. At the same time, been recorded with 4 types of different electrodes de- for removing high-frequency components in electrical signed for long-term cardiac monitoring. To record the noise, which are close to a frequency of 50 Hz, typical- signals to be assessed, selected have been the following ly applied are the reject filters, the frequency charac- widely used models of wet electrodes: H92SG, H99SG, teristics of which have a dip at this frequency. In this MSGLT-05MGRT and M2202A [11]. At the same time, connection, for removing the low-frequency noise it in order to take into account the nature of occurrence is advisable to use a high-frequency filter, since it can of the low frequency noise, namely, the noise amplitude suppress noises in a low frequency range with minimal fluctuation, each multi-lead ECG signal recording has distortions of the ECG signal informative parameters. been produced in such a manner so that it has contained However, for removing electrical noise it is most rea- more than 80 cardiac cycles. sonable to employ a reject filter, which largely elimi- The noise-laden sample of the ECG signal produced nates the high frequency component at the frequency with single-lead recording has been obtained using the of the electrical noise. In approximations of the transfer multifunction measuring system of bioelectrical signals characteristics in the high-frequency filters and the re- MITSAR EEG-202, manufactured by MITSAR DIAG- ject filters the Newton polynomial should be used to NOSTICS SOLUTIONS Co., at the Research Institute of produce the lowest values of the filter’s own error, based Cardiological Techniques (INCART). Besides, in order on the frequency characteristics of the filter itself. to take into account the deterministic frequency noise In the present paper we consider our solution of the [9], the recorded single-lead noise-laden ECG signal has two ECG signal processing issues based on improv- covered more than 20 cardiac cycles. ing the filtering accuracy. The first issue is connected with the high-frequency filtering of the low-frequency Formulation of the study issue noise in the multi-lead ECG signal recording with var- Issue 1. ious electrodes in long-term cardiac monitoring. The The issue of processing of multi-lead signal record- second issue is based on the reject filtering of wide- ing is primarily associated with the proper separation band electrical noise in the single-lead ECG signal re- of the informative components Sqi () from an additive cording. To evaluate the full-scale noises in each of the mixture containing an ECG signal and low-frequency treated issues applied is a method based on the noise noise nqi (), that is interpreted in the form of (1). De- subtraction. We have defined the two issues of filter- fined is the issue of separating of informative signal ing with availability of full-scale measurements of the Sqi () with high-frequency filtering of the analyzed ECG signal. We consider the method of high-frequen- signal xq() from distorting low-frequency noises i cy and reject filtering based on the Newton polynomi- nqi (). Separating of the low-frequency noise in the als, and the accuracy of this method is compared with i-th lead from the analyzed noise-laden ECG signal re- the well recognized Butterworth high-frequency and cords xq() of form (1) was carried out with a method i reject filtering. based on the subtraction of noise nqi () of form (2) from the noise-laden recording xq() and the filtered i Aims of research informative component of the ECG signal Sqi (). The aim is to develop and study the method for fil- xqiii()= nq () + Sq (), (1) tering of low- and high- frequency noise for improv- nqiii()= xq () − Sq (), (2) ing the accuracy of ECG signal processing. where q – measurement readings, i – lead of the ECG signal in multi-lead recording. Materials and methods Materials used in our studies have been the recorded Issue 2. reference noise-laden samples produced with multi-lead Similarly to issue 1, for processing of the single-lead ECG signal recording in a human using 12-lead Holter signal recording formulated is another issue of separat- monitor KARDIOTECHNIKA-07-3/12, manufactured ing of the informative components Sq() from an ad- by INCART Company, available at the National Med- ditive mixture of an ECG signal and wide-band noise ical Research Center of V.A. Almazov. To evaluate the nq(), that is interpreted in the form of (3). Separat- characteristics of low-frequency noise, the reference ing the wide-band electrical noise from the analyzed noise-laden samples of the multi-lead ECG signal have single-lead ECG signal record xqi () of form (3) was Issue 16. May 2020 | Cardiometry | 87 carried out by the method based on the subtraction It should be noted in this case that the Newton and But- of noise nq() of form (4) from the noise-laden re- terworth polynomials of the first order coincide with cording xq() and the filtered informative component each other [20], and therefore the wide-band RF trans- ECG signal Sq(). fer functions of the second order are identical. x() q= nq () + Sq (), (3) The transformation of continuous filter transfer nq()= x () q − Sq (), (4) function W(s) into discrete function W(z) has been where q – measurement readings. carried out by bilinear transformation in the MAT- To configure the high frequency filter (HFF) pa- LAB software environment. The transformation has rameters, selected has been an edge frequency equal to been performed using function bilinear () as 1 Hz, according to [8, 22]. The advisability of selecting 21− z−1 = s −1 the given frequency is that at a frequency of 1 Hz, us- Tz1+ ing the method of frequency selection, experimentally established is a maximum low-frequency noise re- at T=1s. duction with minimum distortions in the ECG signal The calculated continuous and discrete transfer parameters, therefore it is reasonable to use this fre- function in the Newton (6) and Butterworth (7) HFF quency for filtering. The wide-band reject filter (RF) is are shown below. configured for an identified frequency of electric noise s2 Ws()= [9], namely in the range from 44Hz to 56Hz. Besides, ss2 ++0.0502426 0.00063108 selected is sampling frequency fД = 250 Hz [23, 24]. (6) The selection of the above sampling frequency is de- 0.975zz2 −+ 1.951 0.9753 Wz()= termined by the fact that it is just this frequency that zz2 −+1.95 0.951 is intended for the ECG signal processing to improve s2 the accuracy of the signal parameters measurement Ws()= ss2 ++0.035521 0.00063108 [23,24]. Using the selected values in the normalized frequency range with the help of transfer functions of (7) 0.9824zz2 −+ 1.965 0.9824 continuous analogue filters, calculated are the HFF Wz()= 2 and RF transfer functions for the Newton and Butter- zz−+1.964 0.9651 worth polynomials, taking into account (5) [25]. The calculated continuous and discrete transfer
fCC1,2 2 ω 1,2 function in the Newton (8) and Butterworth (9) cas- ωπCC1,2 = ⋅2, Ω=1,2 tg fTD 2 (5) cade wide-band RF are given below. For correction of phase distortions introduced by ΩC = Ω CC12 ⋅Ω , the above synthesized polynomial filters, the filtered where ωс1,2, Ωс1,2 – is the lower and upper limit of the signal has been repeatedly passed through the same edge frequency for calculation of the reject filter, Ωс is filter, but in the reverse order. In case of such an im- a center frequency of the filter edge. plementation, the resulting phase distortions are mu- In the synthesis of HFF selected are the Newton and tually compensated, and the resulting phase shift is Butterworth polynomials of the second order [20] to equal to zero for the entire frequency component of simplify the calculations in the synthesis of the filters ECG signal. This form of the filters implementation and avoid distortions of the ECG signal parameters in- in the theory of digital signal processing is known as duced by high order filters [8,22]. In the synthesis of a bi-directional filtering technique [26]. Figures 1 and a wide-band RF, the Newton and Butterworth polyno- 2 show diagrams of implementation of bi-directional mials of the first and second orders are selected taking high-frequency and wide-band reject filters for pro- into account that the transformation of the normalized cessing the ECG signal. analogue filter parameters is accompanied by doubling In case of the bi-directional filter technique, the of the continuous transfer function order in the reject input sequence of readings x[n] in a noise-laden sig- filters [9,25]. To cascade the wide-band reject filters nal is processed through the HFF z[n] in the forward used are the transfer functions of the second and fourth direction, then using the time inversion (TI) unit order, obtained with the Newton and Butterworth the order of the readings w[n] sequence is reversed. polynomials of the first and second order, respectively. Hence, w[n] readings are filtered in the reverse direc-
88 | Cardiometry | Issue 16. May 2020 tion v[n] using HFF, then the final time inversion (init signal x[n] is processed with the wide-band RF of the TI) reverses the order of the readings sequence. As a first sequence for suppression of noises and separation result, the appeared shifts are mutually compensated. of signal s1[n] at the filter output, and then the pro- Similarly implemented is the bi-directional cas- cessed signal is delivered to the input of the wide-band cade of wide-band reject filters, the diagram of which RF second sequence to suppress the residual noise and is presented in Figure 2 herein. separate the clean signal s2[n]. In Figure 2 herein, the In case of the bi-directional implementation of a wide-band RF of the second order is designated as "fil- wide-band RF cascade, it differs considerably from ter 1” and that of fourth order as "filter 2". the bi-directional implementation of HFF. There is a Convolution of the bi-directional HFF implementa- need for a double implementation of each cascade of tion in the frequency domain is represented in formula the wide-band RF. In the present diagram, noise-laden (10), and the wide-band RF cascade in formula (11).
s2 + 2,094 = Ws1() 2 ss++0,463 2,094 0,8681zz2 −+ 0,5427 0,8681 = Wz1() 2 zz−+0,5427 0,7362 ss42++4,189 4,388 Ws()= 2 s432+0,926 s + 4,404 ss ++ 1,940 4,388 0,7536zzzz4− 0,9422 32 +− 1,802 0,9422 + 0,7536 = Wz2 () 432 (8) zzz−1,085 + 1,767 −+ 0,799 z0,542 ss64++6,284 13,166 s 2 + 9,194 Ws()= 3 ss65+1,389 + 6,928 s 4 + 5,919 s 3 + 14,513 s 2 ++ 6,096 s 9,194 6 54 32 0,6542z− 1,277 zz +− 2,73 2,614 zz +−− 2,73 1,277 z 0,6542 Wz()= 3 zz65−+1,628 3,092 z 4 − 2,557 z 3 + 2,277 z 2 − 0,8825 z + 0,399
s2 + 2,094 = Ws1() 2 ss++0,463 2,094 0,8681zz2 −+ 0,5427 0,8681 = Wz1() 2 zz−+0,5427 0,7362 ss42++4,189 4,388 Ws()= 2 s432+0,654 s + 4,404 ss ++ 1,371 4,388 (9) 0,8078zz43− 1,01 + 1,931 zz 2 −+ 1,01 0,8078 Wz()= 2 zzz43−+1,118 1,894 2 − 0,9015 z + 0,6529 ss64++6,284 13,166 s 2 + 9,194 Ws()= 3 ss65+1,117 + 6,802 s 4 + 4,782 s 3 + 14,250 s 2 ++ 4,905 s 9,194 65 4 3 2 0,7012zz−+−+−− 1,315 2,926 z 2,802 z 2,926 zz 1,315 0,7012 Wz3 ()= zz65−1,661 + 3,237 z 4 − 2,753 z 3 + 2,536 zz 2 −+ 1,018 0,4806
Issue 16. May 2020 | Cardiometry | 89 Figure 1. Diagram of implementing a bi-directional high-frequency filter
Figure 2. Diagram of implementing a bi-directional cascade of wide-band reject filters
From above formulas (10) and (11) we can con- Results clude that in case of bi-directional implementing of Based on the above calculated transfer character- each of the filters, their order is doubled. Theoretical- istics of the filters, we have obtained the results of the ly, doubling of the filter order in the bi-directional fil- ECG signal processing when filtering the low- and ter implementation concept leads to the fact that the high-frequency noise as outlined below. resulting suppression in the band of noise retaining at the frequency characteristic will increase by two Low-frequency noise filtering in the times [26]. multi-lead recorded ECG signal An evaluation of the high-frequency and wide- Our analysis of the obtained results makes possi- band RF filters application efficiency is based on their ble to support our statement that the Newton-Butter- quantitative indices. For the above evaluation calcu- worth synthesized high-frequency filters, tuned to an lated are the values of experimental root-mean-square edge frequency of 1 Hz, are capable to provide filter- deviation (RMSD) of the signal readings and the sep- ing out low-frequency noise with minimal distortions arated noise when filtering (12), as well as the noise in informative regions and thereby separating the low attenuation coefficient (NAC) according to [26]. frequency drift of an ECG signal. As an example, Fig- ure 3 shows the result of the initial ECG signal of the N 1 2 fourth precordial V4 lead in multi-lead recording con- CKO = ∑()ni − µ N −1 i=1 taining low frequency noise, and the result of the noise 1 N (12) separation by means of the high-frequency filter on µ = ∑ ni the basis of the Newton and Butterworth polynomials. N i=1 For better visualization, the ECG signal processing re- sults in Figure 3 are scaled for the 5th cardiac cycle by A KOΠ= 20logout , the Newton and Butterworth filters (a); in (b) illustrat- 10 A in ed are the results of low-frequency noise separation. where N – number of readings, ni– readings, μ – mean Results of the quantitative indices calculation for value of readings, Аout and Аin – root-mean-square 12 different ECG signal recording, covering more than value of amplitude of output (filtered) and input 80 cardiac cycles, are presented in Table 1 herein. (noise-laden) signal readings. Our analysis of the quantitative results shows that The calculated RMSD values of the filtered signals the HFF based on the Newton polynomial generates and separated noises, in the form of a box plot for least the signal’s RMSD value, when filtering, maximal- RMSD values, have been graphically represented with ly separates the low frequency drift and to the highest Python Graphing Library, Plotly [27]. degree attenuates low-frequency noises as compared
90 | Cardiometry | Issue 16. May 2020 jω jj ωω Ze()= Xe ()() H1 e jω− j ω −− jj ωω We()()= Ze ⇒ Xe ()() He jω jj ωω−− jj ωω j ω (10) Ve()= We ()() He⇒ Xe ( )()() He He jω−− j ω jj ωω − j ω j ω j ω2 Se()= Ve ( ) = Xe ( )()() He He⇒ Xe ()() He
jω jj ωω Z11() e= Xe ()() H e jω− j ω −− jj ωω We11()()= Z e ⇒ Xe ()() H1 e jω= jj ωω⇒ −− jj ωω j ω Ve1() We 11 ()() He Xe ( )()( He11 He ) 2 jω=−− j ω = jj ωω − j ω⇒ j ω j ω Se1() Ve 1 ( ) Xe ( )()( He11 He ) Xe () He1 () 2 Ze()jω= He () j ω Se ()() jj ωω H e (11) 2 1 12 2 jjωω=− ⇒ jω−− jj ωω We22() Ze ( ) H11()()()e Se H 2 e
jω jj ωω j ω2 −− j ω jj ωω Ve2()= We 22 ()() He⇒ He 1 () Se 1 ( )( He 2 )() He 2 2 22 jω=−− j ω = j ω j ω jj ωω⇒ j ω j ω j ω Se2() Ve 2 ( ) He 1 () He 221 ()( He )() Se He 1 () He 2 () Se 1 () with the Butterworth filter, that confirms the effective- of the Newton polynomial application in enhancing ness of the Newton polynomial in enhancing the ECG the ECG signal processing efficiency. signal processing accuracy under the influence of the Basing on the ECG signal filtering results, ob- given noise. tained in single- and multi-lead signal recording, we note that the use of Newton polynomials in approxi- Filtering of wide-band electrical noise in the mations of the filter transfer characteristics increases single-lead recorded ECG signal the accuracy in filtering of low- and high- frequency We have obtained the ECG signal filtering results noises. Meanwhile, the use of the Butterworth filters with the use of synthesized transfer functions of the for suppression of low- and high-frequency noise also Newton and Butterworth wide-band RF. Our result of allows attenuating noises and separating the required the wide-band electrical noise filtering of the single-lead signal informative parameters. The efficiency of the recorded ECG signal is given in Figure 4 herein. Newton filters in comparison with Butterworth ones Using the calculated transfer functions of wide- is that they produce the lowest values of their own er- band RF (8), (9), in case of their bi-directional im- rors during the ECG signal processing. Figure 5 gives plementation (11), identified are quantitative indices, a Tukey diagram showing accuracy of the ECG signal characterizing the quality of the ECG signal pro- processing with two methods of the low-frequency cessing. Our analysis of the quality of the wide-band noise filtering. electrical noise suppressing has been performed with At the same time, the analysis of the quantitative several methods of filters connection, namely, a typ- indices, namely the low- and high-frequency attenua- ical sequence without cascade (n = 2, n = 4), a cas- tion coefficient, obtained when processing the multi- cade form (n = 2 and n = 4) and with general transfer and single-lead ECG signal recordings, shows a neg- function of cascade filter (n = 6). The results of the ative value. The negative value of the above index is quantitative indices calculation are presented in Table determined by the lowest value of the filtered ECG 2 herein. signal amplitude in relation to the noise-laden (input) Our analysis of the presented results shows that signal, so this index is expressed as a negative number. the cascade of wide-band Newton polynomial RF to The lower is the index value in filtering, the better the the least degree rejects the filtering results, maximally filter attenuates noise and the more resistant to nois- separates the noises and to the highest degree atten- es the ECG signal becomes. In comparison with the uates high-frequency noises in comparison with the Butterworth filter results, the NAC index values are Butterworth filter that also confirms the effectiveness lower in the Newton filter, i.e. the Newton filter best
Issue 16. May 2020 | Cardiometry | 91 a) b) Figure 3. Low-frequency noise polynomial filtering results
Тable 1. Evaluation of low-frequency noise filtering quality V1 V2 V3 V4 V5 V6 I III aVR aVF II aVL Lead / Filter Newton high-frequency filter RMSD, * 77,4 343,9 251,4 212,6 150,6 119,4 58,1 185,9 94,9 180 178,6 104,9 mcV ** 79,8 391,2 244,2 197,3 140,5 110,4 60,8 184,4 91,9 176,6 173,8 106,3 *** 92,4 376,3 251,8 226,9 146 102 61,4 190 99,4 184,8 184,6 106,9 Si ( q ) **** 84,5 371,1 243,2 230,6 158,1 107,3 59,7 188,7 101,1 185,1 186,3 104,4 * 719,8 296,9 1086 808,4 790,3 626,7 368,8 1717,4 1223,6 1899,3 2081,6 677,9 RMSD, ** 808 952,8 1752,6 1499,6 1867,7 1565,7 139,3 1510,6 625,2 1444,9 1379,6 821,4 mcV *** 215 257,8 395,3 328,1 449,3 617,7 149,4 69,1 174 130,9 201,6 58,2 n ( q ) i **** 207 201 565,9 422,8 424,8 388,8 103,2 963,5 494,9 966 971,2 483,4 * -39,5 -23,4 -29,9 -26,9 -33,8 -36,4 -42,4 -35 -29,4 -31,6 -25,6 -38,8 NAC, ** -35 -25,9 -33 -34,2 -39,9 -40,2 -40,6 -32,7 -29,3 -28,6 -20,7 -36,6 dB *** -25 -25,6 -26,8 -31,9 -30,1 -24,6 -39,8 -31,6 -27,6 -27,2 -16,7 -35,8 **** -27,6 -22,8 -29,5 -26,3 -30,6 -36 -32,1 -33,6 -26,4 -32,5 -31 -34,7 Butterworth high-frequency filter RMSD, * 81,4 396,6 303,4 237,1 167 132,7 68,8 197 110,2 194,2 197,4 109,7 mcV ** 84,4 450,8 292,2 216,7 152 123 71,7 191,8 105,1 186,7 188,1 110,2 *** 97,9 433,7 310,4 253,5 160,9 112,8 73,1 197,9 113,4 195,6 200 110,7 Si ( q ) **** 89,9 426,5 298,5 258,6 175,8 119,5 71,4 198,6 116,4 198,3 204,3 180,8 * 719,5 275,2 1080,7 805,9 789,2 625,9 368,3 1717,2 1223,2 1899 2081,2 677,8 RMSD, ** 807,9 944,8 1749,8 1498,7 1867,3 1565,3 137,8 1510,4 624,6 1444,6 1379,1 821,4 mcV *** 214,4 229,8 380,7 321,4 447,9 617,2 147,8 64,9 171,4 127,1 197,6 57,1 n ( q ) i **** 206,3 164,1 555 416,2 422,1 387,4 100,9 963 494 965,1 970 483,2 * -39 -22,2 -28,3 -25,9 -32,9 -35,5 -41 -34,5 -28,1 -30,9 -24,8 -38,3 NAC, ** -34,5 -24,7 -31,5 -33,3 -39,2 -39,3 -39,2 -32,3 -28,2 -28,1 -20 -36,3 dB *** -24,5 -24,3 -24,9 -30,9 -29,3 -23,7 -38,3 -31,2 -26,5 -26,7 -16 -35,5 **** -27 -21,6 -27,7 -25,3 -29,7 -35 -30,6 -33,1 -25,1 -31,9 -30,1 -34,4 Note: Designations of quantitative ECG signal processing results for electrodes: * - H92SG, ** - H99SG, *** - MSGLT-05MGRT, **** - М2202А of all attenuates the low- and high- frequency noises. nonstationarity of the signal parameters, some insig- Figure 6 offers a Tukey diagram showing an accuracy nificant differences exist. Despite the above features, of the low-frequency noise attenuation coefficient cal- the results of the low-frequency noise separation and culation. their calculated RMSD value, generated by using the Our analysis of the quantitative results of multi- filters, show that the H92SG and H99SG electrodes lead ECG signal recording processing, with various generate the highest RMSD noise value as compared electrodes, allows us to note that a minor variability to electrodes MSGLT- 05MGRT and M2202A. Elec- is available between the RMSD values in the filtered trode MSGLT-05MGRT generates the lowest RMSD signals of the same ECG signal lead, however, due to value in 7 of 12 analyzed ECG signal leads, while
92 | Cardiometry | Issue 16. May 2020 Figure 4. Filtering of the ECG signal wide-band electrical noise
Table 2. Evaluation of the high-frequency noise filtering quality The polynomial reject filter Type of reject filter Newton Butterworth № RMSD, mV RMSD, mV implementation RMSD, mV RMSD, mV S ( q ) NAC, dB S ( q ) NAC, dB i ni ( q ) i ni ( q ) 1 The first RF output, n=2. 178,719 15,100 -0,0295 178,719 15,100 -0,0295 2 The second RF output, n=4 without n=2. 178,548 15,307 -0,0367 178,886 15,246 -0,0241 3 Cascade n=2 and n=4. 178,380 15,373 -0,0430 178,716 15,322 -0,0305 With general transfer function of 4 178,386 15,373 -0,0422 178,723 15,322 -0,0302 cascade n=6. electrode M2202A generates the lowest value only in variability in the RMSD values in the filtered signals of 5 of 12. Figure 7 gives a diagram Tukey showing an the same ECG signal lead, taken with different elec- accuracy of the low-frequency noise separation gener- trodes, a high variability is demonstrated in RMSD ated by different electrodes in multi-lead ECG signal values of the separated noises. The high variability recording. in RMSD noise values let us conclude that electrodes Systematizing the results of multi-lead ECG signal H92SG, H99SG, MSGLT-05MGRT and M2202A, recording processing, we can note that despite a minor to varying degrees, generate low-frequency noises
Issue 16. May 2020 | Cardiometry | 93 caused by potentials of electrodes polarization, when recording bioelectric cardiac potentials. Assessing the RMSD noise value, we can state that the Newton syn- thesized high-frequency filter allows us to largely at- tenuate low-frequency noises generated by the various measuring electrodes. Besides, the presented Tukey diagram shows that electrode MSGLT-05MGRT has much lower RMSD value of the separated noise than other analyzed electrodes. Previously, in work [11] it was stated that the MS- GLT-05MGRT electrode demonstrated a high proba- Figure 5. Tukey diagram illustrating accuracy of ECG signal fil- bility of the true ECG signal parameters recording, in tering Electrodes are marked as follows:* - H92SG, ** - H99SG, particular it is applicable to low amplitude P waves. *** - MSGLT-05MGRT, **** - М2202А The above feature was associated with low electrical resistance in the ECG signal electrodes’ solid contact conductive agents. In electrodes H92SG and H99SG detected was a high electrical resistance of CCA, af- fecting an accuracy of the signal parameters record- ing. It has been identified that in electrode M2202A, in case of long-term cardiac parameters monitoring, liquid CCA flows and exits the measuring cell spec- ified area that reduces an accuracy of the signal re- cording [11]. The quantitative analysis of the results of sin- gle-lead ECG signal processing shows that in case of the cascade (sequence) connection of wide-band RF Figure 6. Tukey diagram showing an accuracy of the low-fre- at the output of each designed sequence the RMSD quency noise attenuation coefficient calculation. Electrodes are value of the filtered signal is greatly reduced and at- marked as follows: * - H92SG, ** - H99SG,*** - MSGLT-05MGRT, tenuates noise. However, despite that, in case of the **** - М2202А sequential implementation of the reject filters and the implementation with a general transfer function of the used filters cascade, the RMSD values of the sep- arated noise are the same. The above feature becomes apparent not only when using the Newton reject fil- ters, but also the Butterworth filters. This is due to the fact that in case of the sequential connection of the selected order reject filters, the filtered ECG signal value is generated at the output of the filters cascade. Hence, when using the general transfer function of the reject filters, obtained as a product by two reject filters, the ECG signal value is generated at the out- put of the filter with general transfer function. All the above allows us to conclude that the use of the wide- band reject filters of the cascade structure makes it Figure 7. Tukey diagram showing an accuracy of the low-frequen- possible to increase an accuracy of the ECG signal cy noise separation. Electrodes are marked as follows: * - H92SG, processing (Figure 8 herein). Figure 8 shows a histo- ** - H99SG,*** - MSGLT-05MGRT, **** - М2202А gram of ECG signal processing quantitative results by indices of filtered signal RMSD and the high frequen- cy noise attenuation.
94 | Cardiometry | Issue 16. May 2020 Significant data have been obtained using the results of the ECG signal single- and multi-lead filtering. Bas- ing on the above data, we can conclude that the Newton high-frequency and cascade reject filters greatly increase an accuracy of ECG signal processing. These findings are supported by evidence data produced by filtering of the full-scale reference samples of noise-laden ECG signal recordings, as well as quantitative assessment of indices characterizing the quality of the ECG signal processing.
Conclusions Our paper offers two methods for ECG signal pro- cessing developed by us. The first method is based on the use of the Newton high-frequency filter designed for increasing the accuracy of the ECG signal param- eters separation at low-frequency noises. The second method is based on the application of the Newton cascade wide-band reject filters for improving the accuracy of the ECG signal parameters separation at high-frequency electrical noises. Figure 8. Histogram of quantitative results of the ECG signal In order to evaluate the efficiency of the developed single-lead recording processing filtering methods, recorded have been noise-laden samples of multi- and single-lead ECG signals. Cal- 2. Milchevski A, Gusev M. Performance evaluation of culated are the quantitative results, characterizing the FIR and IIR filtering of ECG signals. Advances in In- signal filtering quality when ECG signal processing. telligent Systems and Computing. 2018(665):103-112. The obtained results of the quantitative indices calcu- DOI: 10.1007/978-3-319-68855-8_10. lation confirm an increase in the ECG signal process- 3. Rangayyan RM. Analysis of biomedical signals. Mos- ing accuracy in comparison with the known solutions. cow: Fizmatlit; 2010. [in Russian] 4. Avdeeva DK, et al. The simulation results of the high- Funding pass and low-pass filter effect on the quality of microp- The research is supported by the Russian Federation otential recordings on the electrocardiogram. European Government (Grant 08-08). Journal of Physical and Health Education. 2014(6):1-10. 5. Fedotov AA, Akulova AS, Akulov SA. Analysis of the Statement on ethical issues parameters of frequency filtering of an electrocardio- Research involving people and/or animals is in full graph signal. Measurement Techniques. 2015(57):1320- compliance with current national and international 1325.DOI: 10.1007/s11018-015-0628-z. ethical standards. 6. Fedotov AA. Selection of Parameters of Bandpass Fil- tering of the ECG Signal for Heart Rhythm Monitoring Conflict of interest Systems. Biomedical Engineering. 2016(50):114-118. None declared. DOI: 10.1007/s10527-016-9600-8. 7. Fedotov AA., Akulova AS. A QRS-complex detector Author contributions of the electrocardiogram signal for the long-term mon- The authors read the ICMJE criteria for authorship and itoring of the patient’s condition. Journal of Communi- approved the final manuscript. cations Technology and Electronics. 2017(62):415-420. DOI: 10.1134/S1064226917040064. References 8. Altay YA, Kremlev AS., Zimenko KA., Margun AA. 1. Li J, Deng G, Wei W, Wang H. Design of areal-time ECG The Effect of Filter Parameters on the Accuracy of filter for portable mobile medical systems. IEEE Access. ECG Signal Measurement. Biomedical Engineering. 2017 (5):696-704.DOI:10.1109/ACCESS.2016.2612222. 2019(53):176-180.DOI: 10.1007/s10527-019-09903-2.
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