Noise Cancellation in ECG Signals using Computationally

Md. Zia Ur Rahman, Rafi Ahamad Shaik & D V Rama Koti Reddy
Signal Processing: An International Journal (SPIJ) Volume (3) : Issue (5) 120
Noise Cancellation in ECG Signals using Computationally
Simplified Adaptive Filtering Techniques: Application to
Biotelemetry
Md. Zia Ur Rahman mdzr_5@yahoo.com
Department of Electronics and Communication Engg.
Narasaraopeta Engg. College
Narasaraopet, 522601, India
Rafi Ahamed Shaik rafiahamed@iitg.ernet.in
Department of Electronics and Communication Engg.
Indian Institute of Technology
Guwahati, 781039, India
D V Rama Koti Reddy rkreddy_67@yahoo.co.in
Department of Instrumentation Engineering
College of Engineering, Andhra University
Visakhapatnam, 530003, India
Abstract
Several signed LMS based adaptive filters, which are computationally
superior having multiplier free weight update loops are proposed for noise
cancellation in the ECG signal. The adaptive filters essentially minimizes the
mean-squared error between a primary input, which is the noisy ECG, and a
reference input, which is either noise that is correlated in some way with the
noise in the primary input or a signal that is correlated only with ECG in the
primary input. Different filter structures are presented to eliminate the diverse
forms of noise: 60Hz power line interference, baseline wander, muscle noise and
the motion artifact. Finally, we have applied these algorithms on real ECG signals
obtained from the MIT-BIH data base and compared their performance with the
conventional LMS algorithm. The results show that the performance of the signed
regressor LMS algorithm is superior than conventional LMS algorithm, the
performance of signed LMS and sign-sign LMS based realizations are
comparable to that of the LMS based filtering techniques in terms of signal to
noise ratio and computational complexity.
Keywords: Adaptive filtering, Artifact, ECG, LMS algorithm, Noise cancellation.
1. INTRODUCTION
The extraction of high-resolution ECG signals from recordings contaminated with back ground
noise is an important issue to investigate. The goal for ECG signal enhancement is to separate
the valid signal components from the undesired artifacts, so as to present an ECG that facilitates

easy and accurate interpretation. Many approaches have been reported in the literature to
address ECG enhancement [2]-[5]. In recent years, adaptive filtering has become one of the
effective and popular approaches for the processing and analysis of the ECG and other
biomedical signals. Adaptive filters permit to detect time varying potentials and to track the
dynamic variations of the signals. Besides, they modify their behavior according to the input
signal. Therefore, they can detect shape variations in the ensemble and thus they can obtain a
better signal estimation.
Several papers have been presented in the area of biomedical signal processing where an
adaptive solution based on the LMS algorithm is suggested [5]-[8]. The fundamental principles of
adaptive filtering for noise cancelation were described by Widrow et al. [1]. Thakor and Zhu [5]
proposed an adaptive recurrent filter to acquire the impulse response of normal QRS complexes,
and then applied it for arrhythmia detection in ambulatory ECG recordings. The reference inputs
to the LMS algorithm are deterministic functions and are defined by a periodically extended,
truncated set of orthonormal basis functions. In these papers, the LMS algorithm operates on an
"instantaneous" basis such that the estimate. In a recent study, however, a steady state
convergence analysis for the LMS algorithm with deterministic reference inputs showed that the
steady-state weight vector is biased, and thus, the adaptive estimate does not approach the
Wiener solution. To handle this drawback another strategy was considered for estimating the
coefficients of the linear expansion, namely, the block LMS (BLMS) algorithm [7], in which the
coefficient vector is updated only once every occurrence based on a block gradient estimation. A
major advantage of the block, or the transform domain LMS algorithm is that the input signals are
approximately uncorrelated.
Complexity reduction of the noise cancellation system, particularly in applications such as
wireless biotelemetry system has remained a topic of intense research. This is because of the
fact that with increase in the ECG data transmission rate, the channel impulse response length
increases and thus the order of the filter increases. Thus far, to the best of our knowledge, no
effort has been made to reduce the computational complexity of the adaptive algorithm without
affecting the signal quality. In order to achieve this, we considered the sign based adaptive
algorithms. These algorithms enjoy less computational complexity because of the sign present in
the algorithm. In the literature, there exist three versions of the signed LMS algorithm, namely, the
signed regressor algorithm, the sign algorithm and the sign-sign algorithm. All these three require
only half as many multiplications as in the LMS algorithm, thus making them attractive from
practical implementation point of view [9]-[11]. In this paper, we considered the problem of noise
cancellation and arrhythmia detection in ECG by effectively modifying and extending the
framework of [5]. For that, we carried out simulations on MIT-BIH database. The simulation
results shows that the performances of the sign based algorithms are comparable with LMS
counterpart to eliminate the noise from ECG signals.
2. PROPOSED IMPLEMENTATION
When the doctors are examining the patient on-line and want to review the ECG of the patient in
real-time, there is a good chance that the ECG signal has been contaminated by noise. The
predominant artifacts present in the ECG includes: Power-line Interference (PLI), Baseline
wander (BW), Muscle artifacts (MA) and Motion artifacts (EM), mainly caused by patient
breathing, movement, power line interference, bad electrodes and improper electrode site
preparation. The low frequency ST segments of ECG signals are strongly affected by these
contaminations, which lead to false diagnosis. To allow doctors to view the best signal that can be
obtained, we need to develop an adaptive filter to remove the noise in order to better obtain and
interpret the ECG data.

2.1 Basic Adaptive Filtering Structure
Figure 1 shows an adaptive filter with a primary input that is an ECG signal s1 with additive noise
n1. While the reference input is noise n2, possibly recorded from another generator of noise n2
that is correlated in some way with n1. If the filter output is y and the filter error e= (s1+n1)-y, then
2
= (s1 + n1)
2
– 2y (s1 + n1) + y
2
= (n1 – y)
2
+ s1
2
+ 2 s1 n1 – 2y s1. (1)
Since the signal and noise are uncorrelated, the mean-squared error (MSE) is
E[e
2
]=E[(n1 – y)
2
]+E[s1
2
] (2)
Minimizing the MSE results in a filter error output that is the best least-squares estimate of the
signal s1. The adaptive filter extracts the signal, or eliminates the noise, by iteratively minimizing
the MSE between the primary and the reference inputs.
FIGURE 1: Adaptive Filter Structure.
FIGURE 2: Alternate Adaptive Filter Structure.
Figure 2 illustrates another situation where the ECG is recorded from several electrode leads.
The primary input s1 + n1 is a signal from one the leads. A reference signal s2 is obtained from a
second lead that is noise free. The signal s1 can be extracted by minimizing the MSE between the
primary and the reference inputs. Generally in biomedical signal processing the filter structure

shown in figure 1 is used, since it is difficult to obtain a noise free signal. Using the same
procedure similar to (1) we can show that
E[e
2
]=E[(s1 – y)
2
]+E[n1
2
] (3)
Minimizing the MSE results in a filter error output y that is the best least-squares estimate of the
signal s1.
2.2 Simplified Adaptive Algorithms
The LMS algorithm is a method to estimate gradient vector with instantaneous value. It changes
the filter tap weights so that e(n) is minimized in the mean-square sense. The conventional LMS
algorithm is a stochastic implementation of the steepest descent algorithm. It simply replaces the
cost function ξ(n) = E[e
2
(n)] by its instantaneous coarse estimate.
The error estimation e(n) is
e(n) = d(n) – w(n) Φ(n) (4)
Coefficient updating equation is
w(n+1) = w(n) + µ Φ(n) e(n), (5)
Where µ is an appropriate step size to be chosen as 0 < µ < ( 2 / tr R ) for the convergence of
the algorithm.
The most important members of simplified LMS algorithms are:
The Signed-Regressor Algorithm (SRLMS): The signed regressor algorithm is obtained from
the conventional LMS recursion by replacing the tap-input vector x(n) with the vector sgn{x(n)}.
Consider a signed regressor LMS based adaptive filter that processes an input signal x(n) and
generates the output y(n) as per the following:
y(n) = w
t
(n)x(n), (6)
where, w(n) = [ w0(n), w1(n), … , wL-1(n) ]
t
is a L-th order adaptive filter. The adaptive filter
coefficients are updated by the Signed-regressor LMS algorithm as,
w(n+1) = w(n) + µ sgn{Φ(n)}e(n), (7)
Because of the replacement of Φ(n) by its sign, implementation of this recursion may be cheaper
than the conventional LMS recursion, especially in high speed applications such as biotelemetry
these types of recursions may be necessary.
The Sign Algorithm (SLMS): This algorithm is obtained from conventional LMS recursion by
replacing e(n) by its sign. This leads to the following recursion:
w(n+1) = w(n) + µ Φ(n) sgn{e(n)}, (8)
The Sign – Sign Algorithm (SSLMS): This can be obtained by combining signed-regressor and
sign recursions, resulting in the following recursion:
w(n+1) = w(n) + µ sgn{Φ(n)} sgn{e(n)}, (9)
where sgn{ . } is well known signum function,
e(n) = d(n) – y(n) is the error signal.
The sequence d(n) is the so-called desired response available during initial training period. The
performance of these algorithms compared from the convergence characteristics shown in figure
3. From the convergence curves it is clear that the performance of the signed-regressor
algorithm is only slightly worse than the conventional LMS algorithm. However the sign and sign –
sign algorithms are both slower than the LMS algorithm. Their convergence behavior is also
rather peculiar. They converge very slowly at the beginning, but speed up as the MSE level
drops.

0 1000 2000 3000 4000
-5
0
5
10
15
Convergence curve of the LMS
Number of iterations
MSE
0 1000 2000 3000 4000
0
5
10
15
20
Convergence curve of the SRLMS
MSE
0 1000 2000 3000 4000
15
20
25
30
Convergence curve of the SLMS
MSE
0 1000 2000 3000 4000
20
25
30
35
Convergence curve of the SSLMS
MSE
FIGURE 3: Convergence Characteristics of various algorithms
2.3 Noise Generator
The reference signal n2 shown in figure 1 is taken from noise generator. A synthetic PLI with 1mv
amplitude is simulated for PLI cancellation. No harmonics are synthesized. In order to test the
filtering capability in non-stationary environment we have considered real BW, MA and EM
noises. These are taken from MIT-BIH Normal Sinus Rhythm Database (NSTDB). This database
was recorded at a sampling rate of 128Hz from 18 subjects with no significant arrhythmias. A
random noise with variance of 0.001 is added to the ECG signals to evaluate the performance of
the algorithm. The input SNR for the above non-stationary noise is taken as 1.25dB. In these
three simplified algorithms because of the sign present in the recursion some tiny noise remains
along the ST segment of the ECG signal. In order to extract the residual noise a tiny PLI is added
to the noise reference signal. This improvers the performance of the filter.
2.4 Computational Complexity Issues
The computational complexity figures required to compute all the three versions of sign LMS, as
proposed above are summarized in Table 1, offers significant reduction in the number of
operations required for LMS algorithm. Further, as these sign based algorithms are largely free
from multiplication operation, these algorithms provides elegant means for removing the noise
from the ECG signals. For LMS algorithm L+1 multiplications and L+1 additions are required to
compute the weight update equation (5). In case of signed regressor algorithm only one
multiplication is required to compute µe(n). Where as other two signed LMS algorithms does not
require multiplication if we choose µ value a power of 2. In these cases multiplication becomes
shift operation which is less complex in practical realizations.

Algorithm Multiplications Additions Shifts
LMS L+1 L+1 Nil
SRLMS 1 L+1 Nil
SLMS Nil L+1 L
SSLMS Nil L+1 Nil
TABLE 1: A Computational Complexity Comparison Table.
. .
3. SIMULATION RESULTS
To show that signed LMS algorithms are appropriate for ECG denoising we have used real ECG
signals. We used the benchmark MIT-BIH arrhythmia database ECG recordings as the reference
for our work. The data base consists of 48 half hour excerpts of two channel ambulatory ECG
recordings, which were obtained from 47 subjects, including 25 men aged 32-89 years, and
women aged 23-89 years. The recordings were digitized at 360 samples per second per channel
with 11-bit resolution over a 10 mV range. In our simulation, first we collected 4000 samples of
ECG signal. In this simulation µ for all the filters is chosen as 0.001 and the filter length as 5. For
all the figures in this section number of samples is taken on x-axis and amplitude on y-axis,
unless stated. Figure 4 shows the clean ECG signal (data105) and its frequency spectrum. In our
experiments we have considered a dataset of five ECG records: data100, data105, data108,
data203 and data228 to ensure the consistency of the results
0 500 1000 1500 2000 2500 3000 3500 4000
-1
0
1
2
Samples
(a)
Amplitude
10 20 30 40 50 60 70 80 90 100
-80
-60
-40
-20
0
Frequency in Hz
(b)
Magnitude(dB)
FIGURE 4: Clean ECG signal (data105) and its Spectrum.
3.1 Adaptive Power-line Interference (PLI) Cancellation
In this experiment, first we collected 4000 samples of ECG signal and corrupted with synthetic
PLI with frequency 60Hz, sampled at 200Hz. This signal is applied as primary input to the
adaptive filter shown in figure 1. The experiment is performed over the dataset average SNR
improvement is considered to compare the performance of the algorithms. The reference signal is
a synthesized PLI, the output of the filter is recovered signal. These results for data105 are
shown in figure 5. Table 2 shows the SNR improvement for the dataset. In SNR measurements it
is found that signed-regressor LMS algorithm gets average SNR improvement 29.5441dB, sign
LMS gets 22.5405dB, sign-sign LMS improves 20.5345dB and conventional LMS algorithm

improves 31.0146dB. Figure 4 shows the power spectrum of the noisy signal before and after
filtering with sign regressor LMS algorithm. The spectrum clears that the sign regressor LMS
algorithm filters the PLI efficiently comparable to LMS filter with reduced number of computations.
0 500 1000 1500 2000 2500 3000 3500 4000
-5
0
5
(a)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(b)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(c)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(d)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(e)
FIGURE 5: Typical filtering results of PLI Cancelation (a) MIT-BIH record 105 with 60Hz noise, (b)
recovered signal using LMS algorithm, (c) recovered signal using signed regressor LMS algorithm, (d)
recovered signal using sign LMS algorithm (e) recovered signal using sign sign LMS algorithm.
LMS SRLMS SLMS SSLMS
Rec.
No
SNR
Before
Filtering
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
100 -2.9191 28.7206 31.6397 26.6853 29.6044 17.8050 20.7241 14.1486 18.6195
105 -2.6949 28.5262 31.2211 26.9251 29.6200 20.3215 23.0164 18.0484 20.7433
108 -3.0647 28.4051 31.4698 26.4778 29.5425 22.4489 25.5136 19.3579 22.4226
203 -1.4531 27.3762 28.8293 26.8677 28.3208 18.5911 20.0442 17.1029 18.5560
228 -3.5242 28.3893 31.9135 27.1089 30.6331 19.8804 23.4046 18.8069 22.3311
Avg.
(dBs) -2.7312 28.2834 31.0146 26.8129 29.5441 19.8093 22.5405 17.4929 20.5345
TABLE 2: SNR Improvement of various algorithms for PLI Cancellation

10 20 30 40 50 60 70 80 90 100
-100
-50
0
Frequency in Hz
(a)
Magnitude(dB)
10 20 30 40 50 60 70 80 90 100
-100
-50
0
Frequency in Hz
(b)
Magnitude(dB)
FIGURE 6: (a) Frequency spectrum of ECG with PLI, (b) Frequency spectrum after filtering with Sign
regressor LMS algorithm.
3.2 Baseline Wander (BW) Reduction
In this experiment, first we collected 4000 samples of ECG signal (data105) and corrupted with
real baseline wander (BW of MIT-BIH NSTDB), it is used as primary input to the adaptive filter of
figure 1. The algorithms are applied on entire dataset. Simulation results for data105 are shown in
figure 7. For the evaluating the performance of the proposed adaptive filter structures we have
measured the average SNR improvement and compared with LMS algorithm. The sign-regressor
LMS algorithm gets SNR improvement 10.1255dB, sign LMS gets 6.0443dB, sign-sign LMS
improves 4.9937dB and conventional LMS algorithm improves 9.7282dB. Table 3 shows the SNR
improvement for the dataset.
Rec.
No
SNR
Before
Filtering
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
100 1.2500 11.1571 9.9071 11.6220 10.3720 6.7036 5.4536 6.4829 5.2329
105 1.2500 12.3824 11.1324 13.1645 11.9561 8.0460 6.7960 6.4677 5.4177
108 1.2500 11.6224 10.3724 12.1420 10.8920 7.1091 5.8591 5.8679 4.6179
203 1.2500 6.8122 5.5622 6.6976 5.7260 6.4628 5.2128 5.0930 3.8430
228 1.2500 12.9172 11.6672 12.9314 11.6814 8.1500 6.9000 7.1053 5.8553
Avg.
(dBs)
1.2500 10.9782 9.7282
11.3115 10.1255 7.2943 6.0443 6.2033 4.9937
TABLE 3: SNR Improvement of various algorithms for Baseline wander removal

0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(a)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(b)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(c)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(d)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(e)
FIGURE 7: Typical filtering results of baseline wander reduction (a) MIT-BIH record 105 with real baseline
wander, (b) recovered signal using LMS algorithm, (c) recovered signal using signed regressor LMS
algorithm, (d) recovered signal using sign LMS algorithm, (e) recovered signal using sign sign LMS
algorithm.
3.3 Muscle Artifacts (MA) Removal
The MA originally had a sampling frequency of 360Hz. The original ECG signal with MA is given
as input to the adaptive filter. The results of data105 are shown in figure 8. The average SNR
improvement of sign-regressor LMS algorithm is 12.2192dB, sign LMS gets 7.6995 dB, sign-sign
LMS improves 6.9517dB and conventional LMS algorithm improves 11.4306dB. Table 4 shows
the SNR improvement for the dataset.
Rec.
No
SNR
Before
Filtering
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
100 1.2500 11.4058 10.1558 12.3791 11.1291 7.8347 6.5847 7.0363 5.7863
105 1.2500 12.4265 11.1765 12.9827 11.7327 8.5680 7.3180 8.2148 6.9648
108 1.2500 12.3752 11.1252 13.4397 12.1897 8.0919 6.8414 7.4295 6.1795
203 1.2500 13.8786 12.6286 15.1749 13.9249 10.0800 8.8300 9.2585 8.0085
228 1.2500 13.3169 12.0669 13.3698 12.1198 10.1735 8.9235 9.0695 7.8195
Avg.
(dBs)
1.2500 12.6806 11.4306 13.4692 12.2192 8.9496 7.6995 8.2017 6.9517
TABLE 4: SNR Improvement of various algorithms for adaptive cancellation of muscle artifacts

0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(a)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(b)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(c)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(d)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(e)
FIGURE 8: Typical filtering results of muscle artifacts removal (a) MIT-BIH record 105 with real muscle
artifacts (b) recovered signal using LMS algorithm, (c) recovered signal using signed regressor LMS
algorithm.
3.4 Motion Artifacts (EM) Removal
To demonstrate this we used MIT-BIH record number 105 ECG data with real electrode motion
artifact (EM) added. The ECG signal corresponds to record 105 is corrupted with EM is given as
input to the adaptive filter. The reference signal is taken from noise generator. The algorithms are
tested for dataset. Figure 9 shows the results correspond to data105. The average SNR
improvements for various algorithms are 11.8950dB, 7.2525dB, 5.7464dB and 10.3374dB for
signed regressor, sign, sign-sign and LMS algorithms respectively. Table 5 shows the SNR
improvement for the dataset.
Rec.
No
SNR
Before
Filtering
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
SNR
After
Filtering
SNR
Imp
100 1.2500 11.5749 10.3249 13.3180 12.0680 7.6309 6.3809 6.4164 5.1664
105 1.2500 12.5709 11.3209 14.4069 13.1569 8.2145 6.9645 6.7265 5.4765
108 1.2500 12.4709 11.1809 14.9770 13.7270 9.0952 7.8455 7.0101 5.7601
203 1.2500 8.9543 7.7043 10.4778 9.2278 8.6879 7.4379 7.0210 5.7710
228 1.2500 12.4062 11.1562 12.5457 11.2957 8.8840 7.6340 7.8080 6.5580
Avg.
(dBs)
1.2500 11.5954 10.3374 13.1450 11.8950 8.5025 7.2525 6.9964 5.7464
TABLE 5: SNR Improvement of various algorithms for motion artifacts Cancellation.

0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(a)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(b)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(c)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(d)
0 500 1000 1500 2000 2500 3000 3500 4000
-2
0
2
(e)
FIGURE 9: Typical filtering results of motion artifacts removal (a) MIT-BIH record 105 with real motion
artifacts, (b) recovered signal using LMS algorithm, (c) recovered signal using signed regressor LMS
algorithm.
4. CONCLUSION
In this paper the problem of noise removal from ECG using Signed LMS based adaptive filtering
is presented. For this, the same formats for representing the data as well as the filter coefficients
as used for the LMS algorithm were chosen. As a result, the steps related to the filtering remain
unchanged. The proposed treatment, however exploits the modifications in the weight update
formula for all categories to its advantage and thus pushes up the speed over the respective
LMS-based realizations. Our simulations, however, confirm that the corresponding show-down
effect with regard to the algorithm convergence is quit minor and is acceptable for all practical
purposes. From the simulation results it is clear that the signed regressor LMS algorithm performs
better than LMS in both SNR improvement and computational complexity, hence it is more
suitable for wireless biotelemetry ECG systems.

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