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Comparison of
Comparison of Comparison of
Comparison of ECG Signal ECG Signal ECG Signal Denoising Using FIR ECG Signal Denoising Using FIR Denoising Using FIR Denoising Using FIR and IIR
and IIR and IIR
and IIR Filter Filter Filter Techniques Filter Techniques Techniques Techniques
Pallavi V. Lengare1, Kishori Degaonkar 2 and Rupali Tornekar3
1 Student, Vishwakarma Institute of Technology, Pune University Pune, Maharashtra, India
2
Associate Professor, Vishwakarma Institute of Technology, Pune University Pune, Maharashtra, India
3 Assistant Professor, Vishwakarma Institute of Technology, Pune University Pune, Maharashtra, India
Abstract
Cardiovascular disease is the leading cause of death in the world. An Electrocardiogram (ECG) represents the electrical activity of the heart. ECG signal is time varying in nature. The ECG plays an important role in the process of monitoring and preventing heart attacks. There are various artifacts which always degrades the quality of the ECG signal. The ECG signal must be properly denoised to make primary diagnosis of the heart diseases. This paper deals with application of digital FIR and IIR filter for denoising noisy real ECG signal. In this paper Hamming, Kaiser, Butterworth, Chebyshev Type- I filters are utilized. The dataset used is MIT-BIH arrhythmia database. The results were evaluated using MATLAB software.The result tables comparing the performances of all four filters, based on average signal power and Mean Square Error are also included.
Keywords: ECG, Denoising, FIR digital filter, IIR digital filter, Average Signal Power, Mean Square Error (MSE).
1. Introduction
The electrocardiogram (ECG) is the recording of the electrical activity of the heart which is extensively used for diagnosis of heart diseases. One cycle of the normal ECG is composed of a P wave, a QRS complex and a T wave, corresponding to the atrial depolarization, the ventricular depolarization and the rapid repolarization of the ventricles, respectively [1]. Figure1 shows a sample of ECG signal. Most of the clinically useful information embedded in the ECG is related to the duration and amplitude of its individual components.
The ECG signal is corrupted by different types of noises such as Power line interference, Electrode contact, Muscle contraction, Base line drift noise [2]-[4].These noises reduce the clinically useful information embedded in the ECG signal. Thus, filtering of ECG signal plays important role to conserve the clinically useful
information.The performance of ECG signal denoising algorithm is evaluated based on average power and Mean Square Error (MSE).
The rest of this paper is arranged as follows. The various types of noises which contaminates ECG signal are presented in section II, in section III digital filter techniques are discussed. In section IV digital filter design steps are given, in section V performance parameters are discussed. In section VI results are discussed and finally we conclude in section VII.
Figure 1 :- A Sample ECG signal showing P-QRS-T wave
2. Noise Artifacts in ECG
The various types of noises which degrades the quality of ECG signal are as given below [2]-[9].
2.1 Power Line Interference Noise
Power line interference consist of 50/60 Hz pickup and its harmonics and 50% peak to peak ECG amplitude. Factors causing 50Hz interference are improper grounding of ECG machines, disconnected electrodes, electromagnetic interference from power lines, electrical equipments such as air conditioners, elevators, X-ray machines [6].
2.2 Electrode Contact Noise
The loss of contact between electrode and patient skin causes electrode contact noise. The amplitude of this noise is the maximum recorded output of ECG signal, duration is 1 sec and frequency is 50/60 Hz [7].
2.3 Muscle Contraction Noise
The muscle contraction noise is millivolt level in range. It is also called as electromyography (EMG). It is caused due to patient’s movements. The standard deviation of noise is 10% of peak to peak ECG signal amplitude with frequency contents of dc to 10000 Hz and duration of 50 ms [8].
2.4 Baseline Wander Noise
The drift of baseline is caused by respiration. The amplitude variation is 15% of peak to peak ECG amplitude. The baseline variation is 15% of peak to peak ECG amplitude at frequency of 0.15 to 0.3 Hz [2].
3. Digital Filter Techniques
The analog filters can also be used to remove noises present in ECG signal, but nonlinear phase shift is introduced by them. Digital filters are more accurate and precise than analog filters [10]-[11].
Digital filters are of two kinds:- 1. Finite Impulse Response (FIR).
2. Infinite Impulse Response (IIR).
3.1 FIR Filter Techniques
FIR filters have the impulse response of finite duration. FIR filters are always stable, with exact linear phase, can be designed in both recursive and non-recursive form. The window techniques used in this paper are Hamming and Kaiser window.
3.1.1
Hamming WindowThe hamming window function can be expressed as ,
() = 0.54 − 0.46 , 0 ≤ < − 1
0, ℎ !"
(1) Among rectangular, triangular, hanning, blackman, the hamming window is most widely used [11].
Here, N= Filter order.
3.1.2
Kaiser WindowThe kaiser window is superior to other windows, because, for given specification its transition width is always small. By varying the side lobe attenuation of α db, Kaiser window parameter β that affects the side lobe attenuation of the Fourier transform of the window is given by,
# = $ 0.1102 (& − 8.7) ; & > 50
0.5842(& − 21)+.,+ 0.07886(& − 21) ; 21 ≤ α ≤ 50
0 ; α < 21
(2) Where, α = -20log10 δ is the stop band attenuation expressed in decibels. Increasing β widens the main lobe and decreases the amplitude of the side lobes (i.e., increases the attenuation) [12].
3.2 IIR Filter Techniques
IIR filters have the infinite impulse response. The IIR filter are recursive type i.e. present output sample depends on present input, past input and output samples. It can be designed using filters like Butterworth, Chebyshev Type- I.
3.2.1
Butterworth FilterThe magnitude of Butterworth filter decreases monotonically as the frequency Ω increases from 0 to ∞.
The magnitude response of filter closely approximates the ideal response as the order N increases [12].
The magnitude response of Butterworth filter is given by, │H(jΩ)│ =
34 5 6768 9:;
</9
for N=1,2,3…. (3)
Where N is the filter order and Ω c is the cut off frequency.
3.2.2
Chebyshev Type I FilterThe Chebyshev Type- I filter exhibit equiripple behavior in passband and a monotonic behavior in stopband. The transfer function of Chebyshev filter is given as,
│H(jΩ)│ =>4? @
:5 6768A
(4)
Where ɛ is parameter of filter related to the ripple in the passband and C N (x) is N th order Chebyshev polynomial.
4. Digital Filter Design
Most of the energy of ECG lies in the 0.5 - 40 Hz frequency band [14] .The block diagram of ECG signal denoising is as shown below in figure 2.
Figure 2 :- Block diagram of ECG signal denoising
The input to the low pass filter is noisy ECG signal .The noisy ECG database used in this study is obtained from physio-Bank entitled MIT-BIH Arrhythmia Database [18] available on-line. The source of the ECGs included in the MIT-BIH Arrhythmia Database is a set of over 4000 long-term Holter recordings that were obtained by the Beth Israel Hospital Arrhythmia Laboratory. The database contains 48 records sampled at 360 Hz .The duration of the signal we have selected is 10sec and it is downloaded in .mat format. In most records, the upper signal is a modified limb lead II (MLII), obtained by placing the electrodes on the chest.
The low pass filter removes the high frequency noise, while high pass filter removes low frequency noise such as baseline wander noise [13]-[16]. The notch filter removes power line interference noise [17]. The output of notch filter is denoised i.e. noise free ECG signal.
The design steps of FIR low pass/ high pass filter are as listed below.
1. Define the low pass / high pass cut off frequency and sampling frequency.
2. Define the desired transfer function of the filter as h d(n).
3. Define transfer function of the window as w(n).
4. Find the transfer function of required filter as h(n) = h d(n) × w(n).
The design steps of IIR low pass/ high pass filter are as listed below.
1. Define the low pass / high pass cut off frequency and sampling frequency.
2. Find out the filter coefficients.
3. Using these filter coefficients perform the zero phase filtering.
The design steps of Notch filter are as listed below.
1. Define the notch cut off frequency and sampling frequency.
Low Pass Filter
High Pass
Filter Notch Filter Denoised
ECG Noisy
ECG Signal
s
2. Define notch filter width parameter.
3. Find out the filter coefficients.
The table 1 gives the specification of the filters used.
Table 1:- Filter Specifications
Type of Filter Filter Order
Lower Cutoff Frequency (Hz)
Higher Cutoff Frequency (Hz)
Sampling Frequency (Hz)
FIR 51 2 50 1000
IIR 3 2 50 1000
5. Performance Measures
The performance of ECG signal denoising algorithm is evaluated based on average signal power and Mean Square Error (MSE).
5.1 Average Signal Power
The average power of ECG signal is calculated as below.
BC DE F (GH) = 10 I E+
JLK() (5) Where x(n) is original noisy ECG signal, N is number of sampling points. The average power of ECG signal before filtering and after filtering are calculated and compared. The table 2 shows the comparison of average power of ECG signal before and after filtering.
5.2 Mean Square Error (MSE)
The Mean Square Error (MSE) of ECG signal is calculated as below.
M D NOD P (MP) =J [L K() − R()]
(6)
Where N is number of sampling points, x(n) is original noisy ECG signal and y(n) is denoised ECG signal.
The MSE should be as minimum as possible. The table 3 shows the comparison of MSE of all four Filter Techniques.
Table 2:- Comparison of average power of ECG signal before and after filtering in db
Record Average power of ECG
signal before filtering (db)
Average power of ECG signal after FIR filtering (db)
Average power of ECG signal after IIR filtering (db)
Hamming Kaiser Butterworth Chebyshev I
100m -8.8165 -27.7435 -11.1418
-21.6707-23.0925
101m -8.6323 -27.2575 -10.7653
-18.8618-20.3799
103m -8.1892 -26.8917 -10.6386
-15.0439-16.5122
105m -8.3189 -25.9995 -10.0297
-13.4271-15.0316
106m -7.3661 -25.7768 -9.9184
-12.6130-13.8525
Table 3:- Comparison of Mean Square Error (MSE) of ECG signal
Record MSE of ECG signal for FIR
filter
MSE of ECG signal for IIR filter
Hamming Kaiser Butterworth Chebyshev I
100m 0.0385 0.0426
0.11980.1206
101m 0.0609 0.0641
0.11670.1181
103m 0.1611 0.1647
0.10180.1052
105m 0.1603 0.1602
0.07830.0837
106m 0.2537 0.2545
0.09750.1022
6. Results and Discussion
The 100m record of ECG signal downloaded from MIT-BIH arrhythmia database is as shown in figure 3.The record is downloaded in .mat form for duration of 10 sec The original 100m record and resulting waveforms of all four filters are as shown below.
Figure 3:- Record 100m of MIT-BIH arrhythmia database contaminated with noise
Figure 4:- FIR Hamming filtered and Kaiser filtered ECG signal
Figure 4:- IIR Butterworth filtered and Chebyshev type - I filtered ECG signal The figure 3 shows the record 100m of MIT-BIH arrhythmia database. It is contaminated with various types of noises.
As seen from filtered waveforms of figure 3, it is clear that FIR filter output introduced a group delay. As the filter order increases, the complexity of the filter increases. However, if the filter order is selected to be low, then the noise suppression performance of the filter will decrease.
As seen from filtered waveforms of figure 4, IIR filter does not introduce any group delay. Infinite impulse response (IIR) filters can achieve a sharp transition region with a small number of coefficients. However, an IIR filter that has a cutoff frequency high enough to remove baseline wander has a nonlinear phase response which distorts meaningful components of the ECG waveform. To avoid this distortion, bidirectional filters are used, in which the signal is filtered in a forward direction over a selected window and then the same window is filtered in a reverse direction.
7. Conclusion
The noises present in ECG signal leads to wrong diagnosis, so the digital filters can be used to remove these noises. The FIR filters are used for ECG signal processing due to the property of linear phase.
However, the higher orders of filters are required and the signal is delayed proportionally to the orders of filter. IIR filters need only a few filter orders. So, regarding the hardware complexity and computational cost, IIR filters are chosen. For the phase linearity, forward/backward IIR filters are designed and implemented.
As seen from table 2 among butterworth and Chebyshev type –I filter, it clear that the average signal power of ECG signal after filtering with Butterworth filter is greater for each record as compared to Chebyshev type –I filter. From table 3, it is clear that the Mean Square Error (MSE) for each record is less in the case of Butterworth filter as compared to Chebyshev type –I filter. So, among available IIR filters, Butterworth filter is more suitable for denoising ECG signal.
Acknowledgments
I would like to thank Professor Kishori Degaonkar for teaching me this course. I would not have known how to even approach this problem, or design a filter without this class. I would also like to acknowledge Professor Rupali Tornekar with whom many conversations about digital signal processing took place throughout the semester. She made me going deeper into the material fun and interesting when it would have been easy to settle for the basics.
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