Removal of power-line interference from the ECG: a review of the subtraction procedure
© Levkov et al; licensee BioMed Central Ltd. 2005
Received: 16 June 2005
Accepted: 23 August 2005
Published: 23 August 2005
Modern biomedical amplifiers have a very high common mode rejection ratio. Nevertheless, recordings are often contaminated by residual power-line interference. Traditional analogue and digital filters are known to suppress ECG components near to the power-line frequency. Different types of digital notch filters are widely used despite their inherent contradiction: tolerable signal distortion needs a narrow frequency band, which leads to ineffective filtering in cases of larger frequency deviation of the interference. Adaptive filtering introduces unacceptable transient response time, especially after steep and large QRS complexes. Other available techniques such as Fourier transform do not work in real time. The subtraction procedure is found to cope better with this problem.
The subtraction procedure was developed some two decades ago, and almost totally eliminates power-line interference from the ECG signal. This procedure does not affect the signal frequency components around the interfering frequency. Digital filtering is applied on linear segments of the signal to remove the interference components. These interference components are stored and further subtracted from the signal wherever non-linear segments are encountered.
Modifications of the subtraction procedure have been used in thousands of ECG instruments and computer-aided systems. Other work has extended this procedure to almost all possible cases of sampling rate and interference frequency variation. Improved structure of the on-line procedure has worked successfully regardless of the multiplicity between the sampling rate and the interference frequency. Such flexibility is due to the use of specific filter modules.
The subtraction procedure has largely proved advantageous over other methods for power-line interference cancellation in ECG signals.
Modern biomedical amplifiers have very high common mode rejection ratio (CMRR), with commercial ECG instruments manifesting values up to 120 dB. Nevertheless, recordings are often contaminated by residual power-line (PL) interference. This is due to differences in the electrode impedances and to stray currents through the patient and the cables. Thus, the common mode voltage is transformed into a false differential signal [1–4] that cannot be suppressed even by an infinitely high CMRR. The problems become more complicated if the instrument has a floating input to increase patient safety [5, 6].
CMRR of a commercial ECG instrument is typically measured under laboratory conditions using generators with low impedance output and short connecting wires. Thus, a claim of CMRR > 60 ÷ 70 dB in the real world of ECG acquisition is without legitimate basis.
Any residual PL interference may interfere with the correct delineation of ECG wave boundaries  and corrupt the proper function of automatic ECG analysis. The interference can also disturb the correct measurement of RR intervals, which is the basis for heart rate variability analysis.
Hardware solutions have been developed to increase the actual CMRR by equalization of the cable shield and the right leg potentials . This reduces the influence of stray currents through the body, but the efficiency obtained is not sufficient to significantly reduce the interference.
Traditional analogue and digital filters are known to suppress ECG components near the PL frequency. Different types of digital notch filters are widely used [8, 9] despite their inherent contradiction: tolerable signal distortion needs a narrow frequency band, which leads to ineffective filtering with larger PL frequency deviation. Moreover, the resulting transient time is often unacceptably long. Hamilton  compares the convergence times of adaptive and non-adaptive notch filters. Both introduce significant distortion in the QRS and ST-segment portions due to the filter ringing. Soo-Chang and Chien-Cheng  try to reduce to some extent the transient response time by using vector projection to find better initial values for IIR notch filters. Yoo et al.  propose a hardware notch filter with adaptive central frequency to follow the PL frequency changes, thus defining a narrower bandwidth. Filters with various Q factors have been tried. However, the resulting signal distortion cannot be correctly assessed because of the reduced scale of the examples provided .
Instead, the condition was simulated in the MATLAB environment . A synthesized ECG signal (without noise) was mixed with constant 1 mVp-p 50 Hz interference and processed by notch filters with bandwidths: 49–51, 49.5–50.5, and 49.9–50.1 Hz. This 1 Hz bandwidth is one order of magnitude narrower than that used by Yoo et al. . Acceptable distortion was found only with the 49.9 ÷ 50.1 Hz filter, but after an exclusively long tail of about 12 s. This adaptation period reappeared with abrupt power-line frequency change of 0.2 Hz, despite a synchronised identical shift of the filter centre frequency.
Ringing is also present when spectral components of the interference are removed from the ECG signals using the Fourier transform . Furthermore, this transform does not work in real time.
Mitov  uses parabolic detrending of ECG to estimate the signal components with frequencies corresponding to PL interference by using the discrete Fourier transform, to approximate averaged interference values, which are subtracted from the contaminated signal. No results with frequency-modulated interference are presented in the publication.
The interference may be suppressed by adaptive filtering [15–17]. However, this technique introduces unacceptable transient response time, especially following signals of steep and high amplitude, e.g. the QRS complex.
Kumaravel and Nithiyanandam  reported interference cancellation by an off-line working genetic algorithm.
Some authors do not present the results of their algorithms correctly or clearly enough to use for interference removal. Sometimes the original signal is not presented , no differences between original and processed signals are shown , and the performance is measured by the error square instead of amplitude differences .
The subtraction procedure for PL elimination was first elaborated some two decades ago . This procedure does not affect the ECG components neighbouring the PL frequency. This theoretical study is carried out for the basic PL frequency, but the conclusions are also valid for its harmonics and, consequently, for an arbitrary interference waveform. The efficiency of the procedure does not depend on the amplitude of the interference, as long as the amplifier is not saturated. Moreover, the procedure copes successfully with changes in amplitude and frequency of the interference. The procedure has been continuously improved over the years [12, 13, 23–32], and implemented in thousands ECG instruments and computer-aided systems [33, 34]. Similar approaches have also been published by other researchers [35–41].
The subtraction procedure is applied originally with sampling frequency f S , a multiple of, and hardware synchronized with the PL frequency f PL . The procedure consists of the following steps :
ECG segments with frequency band near zero are continuously detected using an appropriate criterion. They are referred to as linear segments and are found mainly in the PQ and TP intervals, but also in sufficiently long straight parts of the R and T waves.
The samples of these segments are moving averaged, i.e., subjected to a linear phase comb filter  with first zero set at f PL . Thus, the filtered samples do not contain interference.
Interference amplitudes, called corrections, are calculated for each of the phase-locked samples, n, in the PL period, T PL , by subtracting the filtered samples from the corresponding ones of the contaminated (original) ECG signal.
The set of corrections obtained is continually updated in linear segments and used in non-linear segments (usually around QRS complexes and high-amplitude T waves) to subtract the interference from the original ECG signal.
A linear criterion, Cr, usually corresponds to the second difference of the signal (mathematical evaluation of the linearity). The first Cr  is defined in the following manner. Six consecutive first differences, FD i , are calculated using signal samples, X i , spaced at one T PL :
FD i = X i+n - X i , for i = 1 ... 6 (1)
The PL interference in the first differences is suppressed if n = f S /f PL . In this case n = 5, since the procedure was developed initially for rated f PL = 50 Hz and f S = 250 Hz. Furthermore, the maximum FD max and minimum FD min values are taken to determine Cr:
Cr = | FD max - FD min | <M, (2)
where M is the threshold value.
This criterion works accurately, but can hardly be applied in real time because its relatively slow implementation. This drawback is overcome by Christov and Dotsinsky  who use a modified criterion of just two subsequent differences.
Cr = | FDi+1- FD i | <M. (3)
The first sample, which does not fulfill equation (3), is associated with the beginning of a non-liner segment. In the non-linear to linear transition, equation (3) should be satisfied consecutively n times in order to avoid premature detection of the linear segment. The criterion is implemented in real time for f S = 400 Hz and n = 8.
Later, Dotsinsky and Daskalov  defined the criterion as two non-subsequent differences:
Cr = |FDi+k- FD i | <M, for k >1 (4)
This approach makes the transition from linear to non-linear segment more precise.
Compensation of PL amplitude variations
The more frequently the corrections are updated, the better compensation of the amplitude variations of the PL is achieved. Therefore, the linear criterion threshold, M, has to be reasonably less restrictive so that the errors, committed by averaging some segments that depart from the ideal linear signal, are smaller than the errors, that will appear if M initiates sporadic updating of the correction. Initially, M was fixed at 160 μV . Later, heuristic values were found to be M = 150 μV  and M = 100 μV .
For odd sample number n = 2m + 1 in one period of the PL interference, the filtered value:
is phase-coincident with the non-filtered one.
In case of even number n = 2m, the two values are phase-shifted by a half of the sample period:
but become in-phase coincidence using the formula
It is possible to take for averaging every second, third or q th sample if n/q is integer. Depending on whether n/q is odd or even, equation (7) or (8) is used, respectively.
A special case of maximum sample reducing arises with q = n/2 . The corresponding formula:
is called 'three-points' filter. In addition to equation (8), the following formula
can also be applied if q is even. In case of q = n/2, the filter becomes 'two-points' and is represented by:
Reduced sample number in a period of the interference will lead to enhanced steep slope of the comb filter lobes and will shorten the computation time. However, these 'advantages' must be assessed carefully in order not to violate the Nyquist rule with a large amount of the third harmonic present. The other harmonics are not taken into consideration since the highest odd harmonics are usually suppressed by low-pass filters with cut-off in the range of 100–150 Hz, while the even ones are practically absent because of the precise pole manufacturing of the electric power station generators.
Compensation of PL frequency variation
The allowed deviation from the rated PL frequency is limited in some countries up to 1% by the standards. In practice, deviation is oftentimes higher. Kumaravel et al.  reported for variation of 3%. McManus et al.  found considerable changes in the interference frequency, which is superimposed on recordings taken from the Common Standards for Electrocardiography (CSE) database.
Frequency variations lead to a special case of non-multiple sampling with real n, instead of integer one. This complication can be bypassed if the deviations are detected by continuous hardware measurement of f PL and corrected by small adjustments of the sample interval t S around its rated (R) value, t RS = T RPL /n (here, T RPL = 20 ms is the rated T PL for f RPL = 50 Hz). For f PL , deviation between 49.5 and 50.1 Hz, the t S variations are in the range of 1%, and consequently they do not introduce errors beyond the accepted measuring accuracy of parameters that are usually used for automatic ECG classification.
A first approach associates the triggering of each first sample, S 1 , of the sequences S k (k = 1, 2...n) in the periods T PL with arbitrary chosen but constant amplitude of the PL voltage. The next samples, S k (k = 2...n), are spaced at t S , which is obtained by t S = T RTL /n. For 50 Hz, and n = 5, t S = 4 ms. Two types of errors committed using this approach are studied by Dotsinsky and Daskalov . The first, due to inter-sample irregularities, may reach 1% at f S = 400 Hz and 1.2% at f S = 250 Hz, in case of 1% deviation around the f RPL . The second type of error does not exceed 3% and is a consequence of the additionally shifted location of the filtered sample.
Dotsinsky and Daskalov  reported an improved approach. The ongoing period T PL is measured and divided by n. The obtained t S is used in the subsequent T PL .
Efficiency assessment of the procedure
Influence of EMG noise
Linear segments cannot be regularly found in patients with atrial and ventricular fibrillation. However, the total preservation of the wave shape is not necessary for fibrillation detection and therefore, all kinds of traditional filters may be applied.
Interference suppression in high-resolution ECG
The subtraction procedure is not directly applicable to the body-surface His-ECG, as the low amplitude and relatively low frequency His-wave can not be distinguished in linear segments. Thus, the His-wave will be, in practice, suppressed or even removed from the signal. The EMG noise is usually of higher amplitude and with much higher frequency content compared to the surface His-wave. Therefore, simple change of the threshold value, M, does not result in acceptable delineation of linear and nonlinear segments.
The subtraction procedure and three other methods: notch filters, spectral interpolation , and regression subtraction  are tested against minimal distortion of the original signal . The subtraction and the regression-subtraction procedures proved to be the best, as Baratta et al.  use a similar concept for noise estimation in linear segments. Regression-subtraction deals poorly with amplitude changes of the interference within the current segment.
Case of battery-supplied devices and computer aided ECG systems
The hardware measurement of f PL , necessary for compensation of the interference frequency modulation, is not feasible in battery-supplied devices and in some computer aided ECG systems. Dotsinsky and Stoyanov  studied the range of frequency changes of interference with constant amplitude, for which the residual part is restricted to acceptable levels without use of synchronized sampling. They found that residual interference below 20 μVp-p could be obtained with the procedure by: i) interference amplitude ≤ 0.4 mVp-p and ii) frequency change with a rate ≤ 0.0125 Hzs-1. Since such requirements for the power-supply can often be exceeded, a software interference measuring was developed.
In case of T PL change, t S is redefined using
The next logical step to be taken consists of: i) keeping the rated t S of the ECG instrument, ii) re-sampling the signal according to the ongoing measured f PL in order to eliminate the interference and iii) returning to the rated t S . The first results of such an approach are highly promising . Thus, the software compensation of the variable f PL , as well as a total implementation of the subtraction procedure in an instrument, including automatic adjustment for f RPL of 50 or 60 Hz, will be completed regardless of the hardware circuits and the corresponding software.
Automatic adaptation to the rated PL frequency
A common program for alternative interference subtraction in 50 and 60 Hz environment leads to non-multiple sampling, i.e. to real n. Widely used values of t S for f RPL = 50 Hz, such as 250, 500 and 1000 Hz, correspond to irrational n of 4.1(6), 8.3(3) and 4.1(6) if 60 Hz interference has to be eliminated. In the inverse case, f S = 360 Hz requires n = 7.2. Rounded values n* are unacceptable to use, since they would introduce considerable error.
A very simple solution not needing f S change was found by Dotsinsky and Stoyanov . The original procedure applies a comb filter over one period, T PL , of the interference. Thus, the program runs faster. Generally, n may be taken from k > 1 entire periods. The procedure is operated if:
n = kT PL /t S is an integer.
Theoretical procedure development
The theory of the subtraction procedure was developed further by Mihov , Levkov and Mihov , and Mihov et al. . They proposed four types of filters, implemented in a generalized structure that may overcome the problems with almost all cases of non-multiple sampling, including interference frequency variations, without using synchronized AD conversion.
The so-called D-filter in multiple sampling is defined as is Cr in equation (2), where the second difference, D i , is obtained with FD s that are spaced at one T PL :
D i = (X i+n - X i ) - (X i - X i-n ) = X i-n - 2X i + X i+n (15)
The equation used for ongoing calculation of the interference components:
B i = X i - Y i (16)
actually defines a digital filter called (1-K)-filter.
Furthermore, the filters are re-defined for non-multiple sampling, and f S = 250 Hz in conjunction with f RPL = 60 Hz is taken in consideration to illustrate the software improvement.
In order to preserve the transfer function zeros, the D-filter has to be subtracted with a correction filter with zero at f = 0 and gain of D RPL at f = f RPL , equal to the gain of the D-filter for the same frequency, f RPL . The correction filter synthesis is based on a three-points auxiliary filter given by the equation:
where (n/2)* is the rounded value of n/2.
Since A RPL is the gain of the auxiliary filter for f = f RPL , the correction filter is multiplied by the ratio D RPL /A RPL . Using the corresponding transfer functions, D RPL and A RPL are computed in advance by:
Finally, the corrected D*-filter is presented as
The transfer function of the K-filter must preserve zero for f = f RPL , unity gain for f = 0 and linear phase response. The procedure of the K-filter correction is similar to the previous one. An auxiliary filter is given by the formula used for corrections computation:
A i = X i - Y i , (20)
The filter gain is equal to 1 - K RPL for f = f RPL , where K RPL is the K-filter gain for the same frequency f RPL . The auxiliary filter is multiplied by K RPL /(1 - K RPL ) and subtracted from the K-filter. The equation for the corrected K*-filter is:
The constant K RPL can be estimated by:
for odd or even multiplicity, respectively.
where K RPL is the gain for the interference of the averaging filter given by equation (22).
The restored buffer value B i can be calculated by:
In case of even n*:
Linearity detection. D-filter is applied to evaluate the linearity of each signal sample neighbourhood.
Interference extraction. (1-K)-filter is used to calculate the interference component.
Criterion. The condition Cr <M sends either extracted or restored PL interference to Subtraction.
Interference temporary buffer. The extracted or restored interference component used as correction in non-linear segment is saved at the position locked with the ongoing phase of the power-line interference.
Interference restoring. B-filter is called in case of non-multiple sampling in order to restore the true correction values, which have to be subtracted from the input signal samples in non-linear segments.
Delay buffer. Compensates the delay, which appears with the D-filter and (1-K)-filter and is imperative if the procedure is run in quasi-real time. Otherwise, the buffer could be disregarded.
Subtraction. Extracted or restored interference value is subtracted from the delayed input signal to output 'clean' ECG signal. In case of non-linearity both Interference extraction and Subtraction implement the K-filter.
As first elaborated two decades ago and continually improved since then, the subtraction procedure eliminates power-line interference from the ECG signal without affecting its spectrum. The procedure operates successfully even with amplitude and frequency deviations of the interference. The frequency deviations are first compensated by hardware measurement of the power-line frequency. Software measurement of the interference period was developed for battery supplied units and some ECG modules connected to personal computers.
The improved structure of on-line going subtraction procedure leads to its extended implementation regardless of multiplicity between sampling rate and interference frequency. The structure flexibility is due to the introduced filtering modules, which are called into use depending on the type of sampling.
The presented analysis of the subtraction procedure and the different types of notch filters confirms the advantages of this method for interference cancellation in ECG signals.
The authors gratefully acknowledge the contribution of the Ph.D. students Mrs. Ts. Georgieva and Mr. T. Stoyanov in the theoretical investigations and the software synchronized sampling rate.
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