In many situations, the Electrocardiogram (ECG) is recorded during ambulatory or strenuous conditions such that the signal is corrupted by different types of noise, sometimes originating from another physiological process of the body. Hence, noise removal is an important aspect of signal processing. Here five different filters i.e. median, Low Pass Butter worth, FIR, Weighted Moving Average and Stationary Wavelet Transform (SWT) with their filtering effect on noisy ECG are presented. Comparative analyses among these filtering techniques are described and statically results are evaluated.

1. Multidimensional Approaches for Noise
Cancellation of ECG signal
Akash Kumar Bhoi, Karma Sonam Sherpa, Devakishore Phurailatpam, Jitendra Singh Tamang, Pankaj Kumar Giri
Abstract: In many situations, the Electrocardiogram (ECG) is
recorded during ambulatory or strenuous conditions such that the
signal is corrupted by different types of noise, sometimes
originating from another physiological process of the body. Hence,
noise removal is an important aspect of signal processing. Here five
different filters i.e. median, Low Pass Butter worth, FIR, Weighted
Moving Average and Stationary Wavelet Transform (SWT) with
their filtering effect on noisy ECG are presented. Comparative
analyses among these filtering techniques are described and
statically results are evaluated.
Index Terms- Electrocardiography, Active noise reduction, Filters,
Noise cancellation.
I. INTRODUCTION
A physician can detect a heart problem from this
information and can suggest timely measures. But during the
acquisition of ECG signal, it may get corrupted by different
types of noises [21] which make it difficult for the physician to
give his diagnosis. Power Line Interference (PLI) is one such
kind of noise which superimposes on the vital information. The
frequency range of ECG signal is 0.05Hz to 150Hz, and the
frequency of the PLI noise is 50/60 Hz which lies within the
frequency spectrum of the ECG signal, so for the meaningful and
accurate detection, steps have to be taken to filter out or discard
all these noise sources. Hamilton PS in his article compared
adaptive and non adaptive filters for reduction of power line
interference in the ECG [5]. Iders YZ, Saki MC, Gcer HA have
developed a method for line interference reduction to be used in
signal averaged electrocardiography [6].
Cramer E, McManus CD, Neubert D has introduced a global
filtering approach. In this method two types of the digital filters
are used where, one is using lest square method and other is
using special summation method [7]. Different scientists have
tried for removing the power line interference and base line
wonder specifically from the ECG signal [8-17]. Zschorlich VR
and Zschorlich VR, have also designed digital filters to cope
with EMG signals [18-19]. Webster has explained the
instrumentation requirements for the ECG [20].
Akash Kumar Bhoi is with the Applied Electronics & Instrumentation
Engineering Department, Sikkim Manipal Institute of Technology (SMIT), India
(email: akash730@gmail.com).
Karma Sonam Sherpa is with the Electrical & Electronics Engineering
Department, Sikkim Manipal Institute of Technology (SMIT), India (email:
karmasherpa23@gmail.com).
The wavelet coefficients represent a measure of similarity in
the frequency content between a signal and a chosen wavelet
function [1]. These coefficients are computed as a convolution of
the signal and the scaled wavelet function, which can be
interpreted as a dilated band-pass filter because of its band-pass
like spectrum [2]. Sander et al. designed a 50/60Hz notch filter to
eliminate baseline drift from high resolution ECG Signal [3].
Markovsky et al. used band pass, kalman adaptive filter for
removal of resuscitation artifacts from human ECG signal [4].
For wavelet transform, daubechies wavelets were used
because the scaling functions of this wavelet filter are similar to
the shape of the ECG. From the decomposition of the ECG
signal it was seen that the low frequency component cause the
baseline shift, theses component were deducted to get a signal
without baseline drift. Also the high frequency components of
the signal were removed for getting denoised signal [22].
Below chapters sequentially elaborate the filtering
performances of five different filters.
II. METHODOLOGY
Fig.1. Block diagram of proposed methodology
“Fig. 1” illustrates the workflow of proposed
methodology. Filtering operations are performed for the selected
initial waveform (i.e. 4 sec data) “fig.2” of the full length noisy
ECG signal for better visualization of filtering results “fig.3-7”.
The statistical analysis results are shown in “fig.8-12”.
Devakishore Phurailatpam is with the Electrical & Electronics Engineering
Department, National Institute of Technology, Manipur, India (email:
bungcha@gmail.com).
Jitendra Singh Tamang is with Electronics & Communication Department,
SMIT, India (email: js.tamang@gmail.com).
Pankaj Kumar Giri is with and Applied Electronics & Instrumentation
Engineering Department, SMIT, India (email: pankajdav09@gmail.com).
ECG signal Noise Cancellation
Filtering Efficiency
Analysis
International Conference on Communication and Signal Processing, April 2-4, 2015, India
ISBN 978-1-4799-8080-2 Adhiparasakthi Engineering College, Melmaruvathur
060

2. Fig.2. Input Noisy ECG signal
A. Median Filter
The median filter is a nonlinear digital filtering technique,
often used to remove noise. Such noise reduction is a typical pre-
processing step to improve the results of later processing. The
main idea of the median filter is to run through the signal entry
by entry, replacing each entry with the median of neighboring
entries. The pattern of neighbors is called the "window", which
slides, entry by entry, over the entire signal. The function
considers the signal to be 0 beyond the endpoints. The output has
the same length as x.
For odd n, y (k) is the median of ( − ( − 1)/2: + ( −
1)/2).
For even n, y(k) is the median of ( − /2), ( − ( /2) +
1), . . . , ( + ( /2) − 1).
In this case, medfilt1 sorts the numbers, then takes the
average of the n/2 and (n/2) +1 elements with window=15.
Fig.3. Filtered ECG signal (using Median filter)
B. Low Pass Butter Worth Filter
The generalized equation representing an “nth” Order
Butterworth filter, the frequency response (1) is given as:
( ) = (1)
where, n represents the filter order, Omega ω is equal to 2πƒ ,
Epsilon ε is the maximum pass band gain, (Amax).
If Amax is defined at a frequency equal to the cut-off -3dB
corner point (ƒc), ε will then be equal to one and therefore ε2
will also be one. However, if you now wish to define Amax at a
different voltage gain value, for example 1dB, or 1.1220 (1dB =
20logAmax) then the new value of epsilon, ε is found by (2):
= (2)
where, H0 = the Maximum Pass band Gain, Amax. H1 = the
Minimum Pass band Gain.
Transpose the equation to give:
= 1.1220 = (1 + ) (3)
gives ε = 0.5088
The Frequency Response (3) of a filter can be defined
mathematically by its Transfer Function with the standard
Voltage Transfer Function H(jω) (4) written as:
( ) =
( )
( )
(4)
where:
Vout = the output signal voltage.
Vin = the input signal voltage.
ω = the radian frequency (2πƒ)
Fig.4. Filtered ECG signal (using LP Butterworth filter with order 10)
C. Finite Impulse Response (FIR) Filter
fir1 implements the classical method of windowed linear-
phase FIR digital filter design. It designs filters in standard low
pass, band pass, high pass, and band pass configurations.
Here the output of filtered signal contains the n + 1
coefficients of an order n low pass FIR filter. This is a
Hamming-windowed, linear-phase filter with cutoff frequency
Wn. The output filter coefficients, b, (5) are ordered in
descending powers of z.
061

3. ( ) = (1) + (2) + ⋯. + ( + 1) (5)
Wn, the cutoff frequency, is a number between 0 and 1,
where 1 corresponds to half the sampling frequency (the Nyquist
frequency).
Fig.5. Filtered ECG signal (using FIR1 filter with order 15)
D. Weighted Moving Average
A weighted average is any average that has multiplying
factors to give different weights to data at different positions in
the sample window. Mathematically (6), the moving average is
the convolution of the datum points with a fixed weighting
function.
=
( ) ⋯ ( ) ( )
( ) ⋯
(6)
The denominator is a triangle number equal to
( )
. In the
more general case the denominator (8) will always be the sum of
the individual weights. When calculating the WMA across
successive values, the difference between the numerators of
WMAM+1 (9) and WMAM is − − ⋅⋅⋅ − − +
1. If we denote the sum + ⋅⋅⋅ + − + 1 by Total M,
then
+1 = + +1
− − +1
(7)
= + +
1 − − + 1 (8)
=
+ ( − 1) + ⋯ + 2 + 1
(9)
Fig.6. Filtered ECG signal (using WMA filter with window size 7)
E. Stationary Wavelet Transform (SWT)
The Stationary Wavelet Transform (SWT) is a wavelet
transform algorithm designed to overcome the lack of
translation-invariance of the discrete wavelet transform (DWT).
Translation-invariance is achieved by removing the down
samplers and up samplers in the DWT and up sampling the filter
coefficients by a factor of 2( )
in the jth
level of the algorithm.
Fig.7. Filtered ECG signal (using SWT filter with level 5 & wavelet ‘db1’)
III. STATISTICAL ANALYSIS
A. Amplitude
Fig.8. Amplitude changes after filtering ECG signal
0.10963
0.103966
0.109587
0.107243
0.108252
0.110528
0.1
0.102
0.104
0.106
0.108
0.11
0.112
Noisy FIR btrworth Median Moving
Window
Swt
AMP
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4. Nonlinearities that give rise to amplitude distortion can be
analyzed from the amplitude changes after filtering from the bar graph
where, the input noisy ECG signal amplitude compared with filtered
ECG signals of five different filters.
B. Frequency
Fig.9. Frequency changes after filtering ECG signal
The use of these filters is to remove undesired frequency
imbedded in the ECG signal. The effect of filtering clearly
shown in SWT while, compared to other filters.
C. RMS
RMS is a statistical measure of the magnitude of a varying
quantity.
In the case of a set of n values { , , … … } the RMS (10) is
= ( + + ⋯. + ) (10)
Fig.10. RMS changes after filtering ECG signal
D. Power Spectral Density
The power spectral density (PSD) of a wide sense stationary
random process X (t) is computed (11) from the Fourier
transform of the autocorrelation function R(τ);
( ) = ( ).
∞
∞
(11)
where, the autocorrelation (12) function
( ) = [ ( + ) ( )] (12)
The nonparametric methods are methods in which the estimate
of PSD is made directly from a signal itself. One type of such
methods is called periodogram.
The periodogram estimate for PSD for discrete time
sequence , , ,…., is defined as square magnitude of the
Fourier transform (13) of data:
%( ) =
1
. . (13)
Fig.11. PSD changes after filtering ECG signal
E. Kurtosis
Fig.12. kurtosis changes after filtering ECG signal
In probability theory and statistics, kurtosis is any measure
of the "peakedness" of the probability distribution of a real-
valued random variable. There are various interpretations of
kurtosis, and of how particular measures should be interpreted;
these are primarily peakedness (width of peak), tail weight, and
0.007378
0.007509
0.007377
0.007281
0.007372
0.00687
0.0064
0.0066
0.0068
0.007
0.0072
0.0074
0.0076
Noisy FIR btrworth Median Moving
Window
Swt
FREQUECY
-91.103
-141.047
-166.582
-82.7685
-140.601
-93.0256
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
Noisy FIR btrworth Median Moving
Window
Swt
RMS
-67.3009
-117.244
-142.78
-58.9664
-116.798
-68.9432
-160
-140
-120
-100
-80
-60
-40
-20
0
Noisy FIR btrworth Median Moving
Window
SwtPSD
4.98065
3.38912
4.92353
3.44756
4.04205
5.06952
0
1
2
3
4
5
6
Noisy FIR btrworth Median Moving
Window
Swt
KURTOSIS
063

5. lack of shoulders (distribution primarily peak and tails, not in
between).
The fourth standardized moment (14) is defined as
=
[( − ) ]
( [( − ) ])
= (14)
where, is the fourth moment about the mean and is the
standard deviation. The fourth standardized moment (15) is
bounded below by the squared skewness plus 1.
≥ ( ) +1 (15)
IV. DISCUSSION
The morphological changes in ECG waveforms are shown
in the filtering results of median and FIR filters where as there is
no significant change in the noisy and filtered signal in case of
LP Butterworth filter. There are no morphological changes (other
than filtering of noises) in the filtered signals of WMA and SWT
filters and the filtering result is quite promising. The statistical
parameters like PSD, RMS and kurtosis showed that the SWT
filter is performing better than the other filters where, the power
of signal is not utterly disturbed. Moving average type regression
line is drawn for PSD and RSM bar graphs and it clears shows
the variation of filtering operations other than SWT filter. WMA
filter is also performed well as compared to median, LP
Butterworth and FIR-1.
V. CONCLUSION
In many situations, the ECG is recorded during ambulatory
or strenuous conditions such that the signal is corrupted by
different types of noise, sometimes originating from another
physiological process of the body, so significant filtering
technique is required. Here, five different filters performances
are analyzed and their statistical parameters are extracted to
compute the filtering efficiencies. SWT is found to be a suitable
filter for noise cancellation from ECG signal. The further
research involves real-time implementation of these filters for
removal of different types of noise from ECG signal.
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