Introduction
ECG signals represent the heart electrical activity and they are obtained through electrodes placed in specific regions of the human body. There are five main waves characterizing ECG signals: P, Q, R, S, and T. Each wave or complex has an exclusive significance. The combination of Q, R and S waves forms which is known as QRS complex. The P wave and the QRS complex represent the atrial and ventricular depolarization, respectively. On the other hand, the T wave characterizes the ventricular repolarization. The spectrum of the QRS complex is located in the ECG frequency bands whose typical frequency components range from 10 Hz to 25 Hz ( ^{Köhler et al., 2002} ) and its detection is still subject of many studies. ^{Pan and Tompkins (1985)} developed an objective QRS detection algorithm using a bandpass filter from 5 Hz to 12 Hz. ^{Zidelmal et al. (2012)} computed the power spectrum for four QRS types concluding that their energies are concentrated in the range from 5 Hz to 22 Hz. Such spectral information is used to QRS complexes detection in Challenge 2011 (Training Set A) database ( ^{Oliveira et al., 2015} ). In addition, it is important to remark that ECG signals are nonstationary, nonsymmetric in relation to the
The specific morphology of the ECG signals allows identifying various cardiac diseases. However, for an accurate analysis, signals should have high SignaltoNoise Ratio (SNR) ( ^{Łęski and Henzel, 2005} ). Low SNR can difficult the analysis performed by experts or computational applications, since it changes the signal waveform. Typical noise present in ECG signals are due to powerline interference in a frequency band varying from 50 Hz to 60 Hz ( ^{Łęski and Henzel, 2005} ; ^{Patil and Chavan, 2012} ; ^{Rahman et al., 2010} ) depending on the country. It occurs due to interferences of electrical equipment as Xray, air conditioners, elevators ( ^{Patil and Chavan, 2012} ), and also due to the differences in electrode impedances ( ^{Bahoura and Ezzaidi, 2010} ).
Several researchers have proposed denoising approaches to enhance ECG signals and preserve their original characteristics. Some noise reduction techniques are based on digital filters, wavelet transform and adaptive filtering ( ^{AlMahamdy and Riley, 2014} ); singular value decomposition ( ^{Bandarabadi and KaramiMollaei, 2010} ); independent component analysis ( ^{Phegade and Mukherji, 2013} ) and Stransform ( ^{Das and Ari, 2013} ). Among the algorithms for PLI removal there are digital processing methods based on: fuzzy thresholding ( ^{Üstündağ et al., 2012} ); nonlinear filter bank ( ^{Łęski and Henzel, 2005} ); Fast Fourier Transform and adaptive nonlinear noise estimator ( ^{Shirbani and Setarehdan, 2013} ); Empirical Mode Decomposition ( ^{Agrawal and Gupta, 2013} ); neural networks ( ^{Mateo et al., 2008} ) and wavelet transform ( ^{Agrawal and Gupta, 2013} ; ^{Garg et al., 2011} ; ^{Poornachandra and Kumaravel, 2008} ; ^{Rahman et al., 2010} ).
Wavelet analysis has been successfully used for ECG signal denoising because it deals well with nonstationary signals and also presents better resolution in timefrequency domain than Fourier analysis ( ^{Rahman et al., 2010} ). In the comparative study presented by ^{AlMahamdy and Riley (2014)} , the wavelet transform produced better results in most of the experiments. ^{Chouakri et al. (2006)} compared the performance of Butterworth filters and the multilevel wavelet transform, concluding that improved results were achieved by the wavelet technique. Usually, waveletbased methods for ECG denoising use thresholding techniques with some additional processing ( ^{Agante and Sa, 1999} ; ^{AlMahamdy and Riley, 2014} ; ^{Awal et al., 2014} ; ^{Bahoura and Ezzaidi, 2010} ; ^{Chouakri et al., 2006} ; ^{Garg et al., 2011} ; ^{GermánSalló, 2010} ; ^{Karthikeyan et al., 2012} ; ^{Li et al., 2009} ; ^{Patil and Chavan, 2012} ; ^{Poornachandra and Kumaravel, 2008} ; ^{Üstündağ et al., 2012} ). ^{Patil and Chavan (2012)} compared the PLI removal for different wavelet basis using hard and soft shrinkage functions. They conclude that hard thresholding achieves better SNR scores than soft thresholding, and the best wavelet basis depends on the analyzed signal.
^{Garg et al. (2011)} worked on optimal waveletbased algorithm for ECG denoising, analyzing SNR for several wavelet families, decomposition level and threshold selection method. In order to calculate the threshold, four rules were used: minmax, rigorous sure, universal and heuristic sure. The best configuration was achieved with the Symlet wavelet with ten vanishing moments and five decomposition levels, hard shrinkage function and heuristic sure rule or rigorous sure thresholding. ^{Poornachandra and Kumaravel (2008)} proposed to use of hyper shrinkage function in the subbands that contained the PLI noise at some decomposition level. The obtained results were better when compared to those of the stateoftheart algorithms.
In this paper, it is proposed to use discrete wavelet transform (DWT) to decompose an ECG signal degraded by high powerline interference. The goal is to have the ECG signal represented by the approximation coefficients and the noise by the detail coefficients. The basic idea is to inspect the ECG and noise frequency range in each subband of the wavelet filter bank. The wavelet scale whose frequency range exceeds the maximum frequency of the ECG signals is set to zero. Then, the IDWT is applied in order to obtain a better quality signal without the use of thresholding techniques. It is common that such techniques do not completely eliminate noise, generating residual noise that can still distorts the QRS waveform. Therefore, this original ECG analysis methodology eliminates the need of thresholding function and is based solely on wavelet filter bank and the characteristics of PLI. Comparisons with a thresholding technique and a classical digital filter were carried out to demonstrate the effectiveness of the proposed method. Furthermore, the proposed method presents low computational load, reduces the residual noise and can be easily implemented.
Methods
A noisy ECG,
where
Dynamical model for generating synthetic ECG signals
In order to analyze ECG denoising algorithms performances, many metrics based on comparisons between the estimated signal and the original one have been proposed. Real ECG signals may have other noise besides PLI. To focus only on this kind of noise, synthetic ECG signals are used in some experiments. The mathematical model for generating such signals was given by ^{McSharry et al. (2003)} . They proposed a dynamical model that generates a trajectory in the threedimensional statespace given by three coupled ordinary differential equations (ODE). The displacement around the “attracting limit cycle of unit radius” describes the ECG signal for each RRinterval ( ^{McSharry et al., 2003} ). ECG characteristic waves are events with fixed angles in relation to the unit circle, given by
This dynamical model yields realistic signals when compared to real ECG signals ( ^{McSharry et al., 2003} ). By setting parameters
Some specific features of the heart rate can also be set, such as mean and standard deviation, besides spectral properties. Generated waveforms are similar to the 12lead ECG lead I. Although it is possible to produce multilead signals ( ^{McSharry et al., 2003} ), in this work they were not considered.
In order to set parameters of the proposed method and perform experiments for validation, twenty synthetic signals were generated using the described model. Model parameters and features of the generated ECG signals are summarized in Table 1 and Table 2 . All signals were sampled at
Variable 











Signal  

60  100  45  82  98  142  90  132  71  89 

9.9574  6.1875  2.9491  3.9308  10.6917  18.7064  6.3261  11.3478  0.8604  12.8859 

50  60  50  60  50  60  120  100  50  60 

0 

2

11

−37

0  0  0  63

−57


1.0  0.7  0.2  0.4  0.1  2.7  0.7  1.2  0.3  1.5 

1.2217  1.3882  1.1370  1.3209  1.3811  1.5153  1.3520  1.4879  1.2742  1.3483 

1.2  1.2  1.2  1.2  1.2  1.2  1.2  1.2  1.2  1.2 

0.25  0.3227  0.2165  0.2922  0.3195  0.3846  0.3061  0.3708  0.2719  0.3044 

0.2618  0.3380  0.2267  0.3060  0.3345  0.4027  0.3206  0.3883  0.2847  0.3188 

5  5  5  5  5  5  5  5  5  5 

0.1  0.1290  0.0866  0.1169  0.1278  0.1538  0.1224  0.1483  0.1087  0.1217 

0  0  0  0  0  0  0  0  0  0 

30  30  30  30  30  30  30  30  30  30 

0.1  0.1290  0.0866  0.1169  0.1278  0.1538  0.1224  0.1483  0.1087  0.1217 

0.2618  0.3380  0.2267  0.3060  0.3345  0.4027  0.3206  0.3883  0.2847  0.3188 

7.5  7.5  7.5  7.5  7.5  7.5  7.5  7.5  7.5  7.5 

0.1  0.1290  0.0866  0.1169  0.1278  0.1538  0.1224  0.1483  0.1087  0.1217 

1.7453  1.9831  1.6242  1.8870  1.9730  2.1647  1.9315  2.1256  1.8203  1.9261 

0.75  0.75  0.75  0.75  0.75  0.75  0.75  0.75  0.75  0.75 

0.4  0  0.3464  0.4676  0.5112  0.6153  0.4899  0.5933  0.4351  0.4871 
Variable 











Signal  

112  88  102  102  143  48  83  112  32  32 

26.6488  24.5940  7.2742  12.2446  30.4465  20.9463  18.0920  25.9964  25.2101  21.3714 

50  180  240  60  60  50  240  100  60  50 

−37π/180  0  0  −57π/45  11π/180  −37π/180  0  0  0  0 

7.2  5.8  0.8  1.4  10.4  3.3  2.7  6.9  4.7  3.1 

1.4280  1.3444  1.3950  1.3950  1.518  1.1554  1.3249  1.4280  1.0440  1.0440 

1.2  1.2  1.2  1.2  1.2  1.2  1.2  1.2  1.2  1.2 

0.3415  0.3027  0.3259  0.3259  0.3860  0.2236  0.2940  0.3415  0.1825  0.1825 

0.3576  0.3170  0.3413  0.3413  0.4042  0.2341  0.3079  0.3576  0.1911  0.1911 

5  5  5  5  5  5  5  5  5  5 

0.1366  0.1211  0.1304  0.1303  0.1544  0.0894  0.1176  0.1366  0.0730  0.0730 

0  0  0  0  0  0  0  0  0  0 

30  30  30  30  30  30  30  30  30  30 

0.1366  0.1211  0.1304  0.1303  0.1544  0.0894  0.1176  0.1366  0.0730  0.0730 

0.3576  0.3170  0.3413  0.3413  0.4042  0.2341  0.3079  0.3576  0.1911  0.1911 

7.5  7.5  7.5  7.5  7.5  7.5  7.5  7.5  7.5  7.5 

0.1366  0.1211  0.1303  0.1303  0.1543  0.0894  0.1176  0.1366  0.0730  0.0730 

2.0400  1.9207  1.9929  1.9929  2.1685  1.6506  1.8928  2.0400  1.4915  1.4915 

0.75  0.75  0.75  0.75  0.75  0.75  0.75  0.75  0.75  0.75 

0.5465  0.4844  0.5215  0.5215  0.6175  0.3577  0.4704  0.5465  0.2921  0.2921 
Real ECG signals
In order to validate the proposed method using real ECG signals that have been originally corrupted by PLI, the Challenge 2011 (Training Set A) database from Physionet was chosen ( ^{Goldberger et al., 2000} ). Their records were sampled at 500 Hz with
Record (Lead) 




1007823 (II)  0.6460  0.2051  1.5345 
1034914 (III)  0.3982  0.1875  1.2290 
1086219 (III)  0.3969  0.2147  1.3232 
1098605 (V1)  0.4421  0.2969  1.3742 
1105115 (V2)  0.4136  0.1507  30.7853 
1124627 (aVL)  0.5272  0.1676  1.0693 
2209843 (I)  0.5557  0.2565  1.5421 
1138505 (I)  0.4139  0.3344  1.2085 
Average  0.4742  0.2267  2.6881 
Discrete wavelet transform
The wavelet analysis has been applied to various problems in biomedical engineering including noise removal in ECG signals ( ^{Agante and Sa, 1999} ; ^{AlMahamdy and Riley, 2014} ; ^{Awal et al., 2014} ; ^{Bahoura and Ezzaidi, 2010} ; ^{Chouakri et al., 2006} ; ^{Garg et al., 2011} ; ^{GermánSalló, 2010} ; ^{Karthikeyan et al., 2012} ; ^{Li et al., 2009} ; ^{Patil and Chavan, 2012} ; ^{Poornachandra and Kumaravel, 2008} ; ^{Üstündağ et al., 2012} ). Due to its better timefrequency resolution, it overcomes other classical methods, such as short time Fourier Transform, for instance ( ^{Üstündağ et al., 2012} ). One of the advantages when using wavelets is the computational efficiency of Mallat’s pyramidal algorithm ( ^{Mallat, 1989} ). This algorithm is indeed a twochannel filter bank that splits the input signal in low and high frequencies by using quadrature mirror filters. The filters can be described through the wavelet
where
and
where
Therefore, the wavelet decomposition output is a smooth signal representing the original one in a coarse way. In addition, the details are obtained when moving from a lower to a higher scale. Note that the smooth signal and details represent the similarity between the scaling and wavelet functions, according to Equations (7) and (6) , respectively. For an ECG signal, the approximation coefficients represent its smoothed version. On the other hand, detail coefficients capture abrupt changes, such as highfrequency noises. In order to reconstruct the signal
In the analysis step, the output wavelet filter bank frequency spectrum is divided into two octave bands. In each new decomposition level, the lowfrequency spectrum is again divided into two new octave bands, at the ideal cutoff frequencies, and so on, resulting in a logarithmical set of bandwidth ( ^{GermánSalló, 2010} ). Therefore, if
Thresholding techniques
Classical methods for ECG denoising based on thresholding techniques present good performances ( ^{AlMahamdy and Riley, 2014} ; ^{Garg et al., 2011} ; ^{Patil and Chavan, 2012} ; ^{Poornachandra and Kumaravel, 2008} ). Basically, in such methods, the goal is to estimate the signal
In order to implement the wavelet shrinkage method, it has considered the Symlet 8 wavelet with three DWT decomposition levels and universal threshold (given by
Notch filter
^{McManus et al. (1993)} present four categories of digital filters for PLI removal: lowpass, notchrejection, adaptive and global. For the implementation of the narrowbandrejection filter (notch) it is considered a recursive filtering that includes a twopole and twozero filter. The filter output is given by
In order to compare the proposed method with a classical approach, the recursive notch filter was selected. ^{Lynn (1971)} apud ^{McManus et al., (1993)} , set
Considering that the objective of this work is to introduce a new method that overcomes the thresholding techniques, the results were compared to the ones obtained by a classical approach.
Evaluation metrics
In the literature, many objective measures are proposed to assess denoising techniques. One of them is the SNR, given by
The measures presented before are appropriate for synthetic ECG signals, but not for real signals, since, in that case, there is no prior access to noiseless ECG signals samples. In this way, two metrics, proposed by ^{Li et al. (2014)} , are used: the relative QRS complexes energy, given by
Statistical analysis
In order to evaluate whether the differences among the means in the experimental results are merely due to some random samples in the population, it is used the KruskalWallis test. In this statistical test, ranks are used instead of the original observations. Firstly, all observations are ranked together and then the sum of the ranks is computed for each sample by means of the equation:
Proposed method
According to equation (1) , the ECG signal represented by
In the wavelet domain, the signal
Choosing
As suggested by ^{Peng et al. (2009)} , the upper limit for the approximation coefficients is higher than 25 Hz, which is the frequency of interest. Therefore, setting the sampling rate at 125 Hz is suitable. Obviously, for other sampling rates that are integer multiple of 125 Hz, the ECG signal and PLI noise can also be separated, but for higher decomposition levels. Nevertheless, for the experiments performed in this work the best results were obtained at a sampling frequency of 500 Hz. In Table 4 it is shown the frequency distribution in each decomposition level for such sampling rate. Columns two and three show the frequency range for ideal cutoff frequencies according to the range shown in the Figure 1 . Columns four and five show the real ranges, which are approximated values, obtained by analyzing the frequency response with the Symlet 8tap. In the column six are presented the approximate band overlap ranges, considering the quadrature mirror analysis filters from Equations (4) and (5) .
Level  Ideal frequency range (Hz)  Real frequency range (Hz)  Band overlap range (Hz)  

Approximation  Detail  Approximation  Detail  
1  0125  125250  0138.6  111.4250  111.4138.6 
2  062.5  62.5125  069.30  55.72138.58  55.7269.30 
3  031.25  31.2562.5  034.60  27.8762.49  27.8734.60 
In a noisefree ECG signal reconstruction, detail coefficients are not so important, since they do not have relevant information about the ECG signal waveform, as shown in Table 4 . Therefore, in order to obtain the signal
The proposed method can be summarized in four steps: 1) The ECG signal is sampled at
The choice of the parameter
Results
The wavelet function choice
When applying the wavelet transform, besides the decomposition level choice discussed in the last section, it is also important to choose the wavelet function that best fits the signal. When ECG is the subject and threshold based methods are used, some researchers prefer Symlet wavelets because their scaling function resembles more its waveform ( ^{Awal et al., 2014} ; ^{Chouakri et al., 2006} ; ^{Karthikeyan et al., 2012} ; ^{Li et al., 2009} ). Good results are also found using Daubechies wavelets ( ^{Karthikeyan et al., 2012} ; ^{Patil and Chavan, 2012} ; ^{Üstündağ et al., 2012} ) and Coiflet ( ^{Agante and Sa, 1999} ; ^{Karthikeyan et al., 2012} ). On the other hand, ^{Poornachandra and Kumaravel (2008)} compared some wavelet families with Mayer’s wavelet and conclude that the last one is better. Commonly, each method uses different thresholding techniques and they have influence on the wavelet function choice. However, there is some agreement about the use of Daubechies and Symlet wavelets. As the proposed method does not use thresholding techniques, the choice of wavelet function can be made by analyzing the results of experiments using the synthetic signals from Table 1 and Table 2 . Preliminary experiments with the proposed method showed that the relative error obtained when using Symlets is smaller than the one using Daubechies wavelet functions. Furthermore, it was noted that higher wavelet order leads to better result. However, runtime increases substantially.
For instance, the difference between the relative errors metrics, for the synthetic signal
Figure 2 shows the boxplots of the experiments for denoising synthetic signals with worse SNR:
Experiments
In order to validate the proposed method, evaluation measures were computed for each synthetic signal. According to the analysis in last section, Symlet 8 was used for simulations. Superscripts PM, TT and NF refer to proposed method, thresholding technique and notch filter, respectively.
Analyzing column eight in Table 5 , it can be seen a significant
Signal 











0.0075  0.0098  0.0189  39.5135  37.1723  31.4736  0.9994  0.9991  0.9972 

0.0080  0.0103  0.0149  35.8650  33.6532  30.4104  0.9995  0.9991  0.9988 

0.0049  0.0018  0.0086  29.1643  38.0101  24.3344  0.9997  1.0000  0.9998 

0.0040  0.0053  0.0094  36.9897  34.5251  29.5679  0.9998  0.9996  0.9991 

0.0075  0.0103  0.0099  19.4379  16.7149  17.0817  0.9995  0.9991  0.9997 

0.0190  0.0292  0.0474  40.0431  36.3182  32.1079  0.9963  0.9913  0.9802 

0.0062  0.0015  0.0143  37.9753  50.1589  30.7739  0.9997  1.0000  0.9989 

0.0148  0.0059  0.0228  35.1591  43.2127  31.4330  0.9979  0.9997  0.9972 

0.0043  0.0048  0.0100  33.8243  32.8589  26.4913  0.9998  0.9998  0.9996 

0.0067  0.0088  0.0281  44.0353  41.6684  31.5227  0.9996  0.9993  0.9941 

0.0259  0.0472  0.1282  45.8751  40.6579  31.9784  0.9941  0.9809  0.8867 

0.0060  0.0152  0.0986  56.7105  48.6041  32.3823  0.9997  0.9980  0.9306 

0.0100  0.0003  0.0105  35.0189  65.0196  34.6267  0.9992  1.0000  0.9998 

0.0089  0.0113  0.0265  40.9507  38.8206  31.4428  0.9993  0.9989  0.9949 

0.0208  0.0371  0.1793  50.9574  45.9358  32.2579  0.9955  0.9859  0.7850 

0.0125  0.0207  0.0589  45.3992  41.0428  31.9638  0.9982  0.9951  0.9655 

0.0056  0.0010  0.0375  50.6373  65.5897  34.1308  0.9997  1.0000  0.9891 

0.0245  0.0312  0.1182  45.9789  43.8886  32.3125  0.9950  0.9920  0.9065 

0.0122  0.0385  0.0806  48.6787  38.7278  32.3051  0.9978  0.9788  0.9204 

0.0148  0.0304  0.0534  43.3985  37.1499  32.2712  0.9969  0.9870  0.9646 
Average  0.0112 ± 0.0065  0.0160 ± 0.0140  0.0488 ± 0.0471  40.7806 ± 8.2487  41.4865 ± 10.4377  30.5434 ± 3.8225  0.9983 ± 0.0017  0.9952 ± 0.0066  0.9654 ± 0.0538 
H  14.704  27.927  8.2435  

0.0006  0.0000  0.0162 
In Figure 3 , one can see the results in time and frequency domain, when applying the denoising methods for signal
Table 6 shows results obtained by the proposed method, thresholding technique and notch filter for real signals. Comparing the original values in fourth column of Table 3 with the ones from the eighth to the tenth columns of Table 6 , it is noted that the frequencies over 25 Hz are less relevant for the denoised ECG signal than in the noisy ECG for all analyzed signals.
Record (Lead) 










1007823 (II)  0.650  0.647  0.645  0.208  0.207  0.204  2.771  2.301  1.556 
1034914 (III)  0.448  0.442  0.428  0.192  0.192  0.192  3.531  2.243  1.237 
1086219 (III)  0.393  0.404  0.396  0.214  0.214  0.214  2.716  2.056  1.326 
1098605 (V1)  0.468  0.460  0.453  0.340  0.340  0.300  3.425  2.085  1.397 
1105115 (V2)  0.428  0.418  0.500  0.785  0.135  0.131  57.92  38.16  2.681 
1124627 (aVL)  0.543  0.530  0.529  0.168  0.168  0.168  2.200  1.988  1.088 
2209843 (I)  0.676  0.608  0.430  0.331  0.330  0.330  3.460  1.779  1.261 
1138505 (I)  0.438  0.434  0.602  0.263  0.264  0.263  2.760  1.922  1.573 
Average  0.506±0.099  0.493±0.085  0.062±0.083  0.313±0.187  0.233± 0.069  0.028± 0.063  2.649± 18.175  1.749± 11.944  0.143± 1.341 

0.1350  1.4982  18.005  

0.9347  0.4728  0.0001 
Discussion
Comparing the proposed method results to the ones obtained with hard thresholding method, it can be seen that the proposed method was worse than hard thresholding only for
By means of the KruskalWallis test, we conclude that there exists significantly statistical difference for at least two methods. In comparison to notch filter, the proposed method was better for all measures. However, the proposed method and the thresholding technique have a similar performance in statistical terms.
Note, from Figure 3 (f), that the energy of the QRS complexes remains practically unchanged when compared to the original. The original signal energy is close to
For real ECG signals, from Table 6 , it is notorious that the proposed method reached better results for all signals, except for record 1086219 with respect to
From KruskalWallis test results, it is noted that only for the
From Figure 4 , one can observe that thresholding technique and notch filter removed the PLI only for some segments in the observed ECG signal, leaving the others attenuated. Hereby, the result for record 1105115 obtained by the proposed method is much better ( Table 6 , fifth row) than the other methods, since the high frequency noise (180 Hz, see spectrogram in Figure 4 ) was not removed by the thresholding technique and notch filter. Note that 180 Hz is 2nd harmonic frequency of 60 Hz.
Although the proposed method have obtained better results for the most of the analyzed signals, it is important to note that it depends on ECG signals sampling rate. So, one must be careful on the sampling rate and DWT decomposition level choices, since these parameters have great influence in the estimated signals quality, according to steps 1 and 4.2 of the proposed method. When, by technical reasons, the sampling rate cannot be changed, decomposition level must be chosen in such a way that a minimum amount of noise crosses into the signal subband.
Other limitation of the proposed method refers to the frequency content removed. In a scenario where frequencies over 34.60 Hz (see Table 4 ) are relevant, detail coefficients in the first level can be retained (frequencies in the range 111.40 to 250 Hz). Even so, PLI noise is removed. Though, in any case, the frequency content around 50/60 Hz is lost. In this way, the cardiac disorders that generate frequencies into the interval from 34.60 to 111.40 Hz are despised. It is essential to note that bandwidth mentioned in Table 4 can be distinct, provided that other cutoff frequency is considered. Therefore, the frequencies higher than 34.60 Hz are preserved in the reconstructed ECG signal.
In overview, in this paper it was proposed a new method for PLI noise removal based on the wavelet transform without the use of thresholding techniques. For such purpose, it was used a filter bank architecture implemented by the multiresolution analysis that allows splitting a signal in frequency subbands. By setting the sampling rate in 500 Hz, it is possible to separate PLI noise from ECG signal in distinct frequency subbands by using the wavelet representation. In order to choose this sampling rate, the energy leakage was considered, such that, for a DWT decomposition level, the frequency content of interest was close to half of the maximum signal frequency. Therefore, by zeroing detail coefficients, the ECG signal is reconstructed using only the approximation coefficients, obtaining a denoised ECG.
Energy conservation analysis for each cardiac cycle showed that the proposed method does not insert distortion in the estimated ECG signals. For real ECG signals, it was noted that the estimated QRS complexes waveforms are smooth and keep the expected morphology. On the other side, the thresholding technique added abrupt changes in some QRS complexes for records 1086219 and 2209843. Besides, other advantage of the proposed method is that there is no computational requirement for a threshold computation.
Although the proposed method depends on the sampling rate, it can be applied to other databases, with sampling rates different from a multiple of 125 Hz, since the signals resampling are considered. Finally, the proposed method can be applied for denoising other signals, with frequency content known in a specific range. In future works such applications will be considered.