Comparative Study of Different Filters with Several Window Techniques Using Wavelet for Removing Noise from ECG Signal

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1 Comparative Study o Dierent Filters with Several Window Tehniques Using Wavelet or Removing Noise rom ECG Signal Manoj 1,Vinod Kumar 2, Sanjeev Kumar Dhull 3 GJUS&T Hisar (Haryana) 1,2,3 manojrapria@yahoo.om 1,vinodspe@yahoo.o.in 2,Sanjeevdhull2011@yahoo.om 3 Abstrat This paper presents removal o noise rom the ECG signal by using Digital ilters designed with FIR and IIR tehnique. Results are obtained or the given order o the ilter using windowing tehnique or the FIR ilter. The wavelet transorm is used to redue the eet o noise to get reined signal. The power spetral density and average power, beore and ater iltererationusing dierent window tehniques and wavelet utilization at 4 and 6 db are ompared. Order o the ilter is also dierent. Filter with the Kaiser window shows the best result Index ECG, FIR Filter, Windowing Tehnique, Wavelet Transorm, power spetral density and average power. I. INTRODUCTION Intererene ours in ECG signal is very ommon and serious problems. Digital ilter are designed to remove this limitation. FIR with dierent windowing method is used. The results are obtained at low order. The input signals are taken rom ECG database whih inludes the normal and abnormal waveorms. FDA tool is used in MATLAB to design these ilters [1]. Many times when ECG signal is reorded rom surae eletrode that are onneted to the hest o patient, the surae eletrode are not tightly in ontat with the skin as the patient breath the hest expand and ontrat produing a relative motion between skin and eletrode. This results in shiting o baseline whih is also known as low requeny baseline wander. The undamental requeny o baseline wander is same as that o respiration requeny. It is required that baseline wander is removed rom the ECG beore extration o any analyze ECG, espeially in the detetion o ST-segment deviations. A. FIR-Filter II. FILTER DESIGN The design parameters and the blok diagram o the ilter is shown in igure 2. Funtion signal toolbox Calulation o oeiients Order estimation Filtering Type and uto Frequeny Frequeny Response Fig. 2 Blok diagram o design proess o ilter Steps or designing the ilter are given explained as ollows: Step 1: Seletion o standard ECG data and extration o ECG signal. Step 2: Design and implementation o FIR and IIR ilters or the removal o Baseline noise rom ECG signal. (a) (b) Fig. 1 ECG data with 8000 samplesed on the onerene website. meaningul eature. Baseline wander makes it diiult to Step 3: Implementation o Wavelet or overall denoising.[5] Step 4: Design and implementation o adaptive ilters or the removal o Powerline noise rom ECG signal. This paper over, all the steps that preeded projet 283

2 implementation. A major element o this stage was the extration o ECG signals the standard database that hosen or the work. Ater extration, the signals are subjet to proessing, using several tools available in the MATLAB[6]. B. Window Use In Designing FIR ilters an also be designed using the windowing method. The ideal ilter have ininite number o samples in time domain given in equation 3. Windows are perormed in order to have inite number o samples in time domain or realiable ilter design. Fig. 3 Magnitude response o an ideal ilter. The ut-o requeny is w. The ideal high pass ilter harateristi is given in Fig. 2. The ontinuous requeny response and the disrete-time impulse response are related by the equation 1. The aim is giving the relation between ideal requeny domain ilter and its impulse response in time domain and to show the importane o windowing method [15]. jkw ( w ) = d ( k e (1) k = D ). π D ( w ) jwk d ( k ) = e dw (2) 2. π π The ilter s impulse response an be obtained by using the inverse Fourier transorm. The ilter oeiients will simply be the impulse response samples. The desired low pass ilter s response is given by equation 3. 1, i w < w D w) = 0, elsewhere ( (3) Fig 4 :Magnitude response o an ideal window. A window untion rom w to w is employed to show the windowing eet[15]. There are dierent windowing untions. The important window untions are retangular window, Hamming, Hanning, Blakman windows [15]. Retangular Window The ilter is required to have inite number o values within a ertain interval, rom -M to M. This is equivalent to multiplying d (k) by a retangular untion given by 1, i n < M w ( n ) = (4) 0, otherwise Hamming Window Disontinuties in the time untion ause ringing in the requeny domain. The retangular window is replaed by a window untion ending smoothly at both ends whih will ause redution in ripples. The hamming window is an important window untion. The hamming window is deined as: w ( n ) n = = 1,2,3,4... N + os 1 2 π n N 1 (5) Where N is the order o the ilter and M is the window length. This equation deines the window samples as already shited (indies rom 0 to N-1 ). So the impulse response o the FIR low pass ilter designed using the hamming window is [15]: h ( n ) = w ( n ). d ( n M 2πn sin(( n M). wn) h( n) =.54.46os N 1 ( n M). π (6) The ripples that our in retangular windowing in both the pass band and the stop band are virtually eliminated. Thus, the iltered data will have a wider transition width. The Hamming window is deined mathematially as: ) 284

3 2π n w ( n ) =.5.5 os N 1 = 0,1,2,3,4... N 1 n (7) The dierene o Hamming window is perormed window untion. This untion is quite similar to the Hamming window. Blakman Window The Blakman window exhibits a lower maximum stop band ripple in the resulting FIR ilter than the Hamming window. It is deined mathematially as: = os π +0.08osπ (8) The width o the main lobe in the magnitude response is wider than that o the Hamming window. High Pass Filter Design The amplitude response o a low pass ilter is shown in Fig. 5. Low pass ilter is irst applied, and with simple transormations the high pass ilter an then be easily perormed. wp w 2 π 2π pass stop =, ws = & s s 2π = (9) The ideal ut o requeny,, is at the midpoint between the pass band and stop band edge requenies set in equation 10: pass + stop = (10) 2 The transition width is deined as: = (11) stop pass Sine the role o pass and stop are interhanged in order to design high pass ilter. The ideal high pass impulse response is obtained rom the inverse Fourier transorm o the ideal high pass requeny response. It is speiied by equation 12: ( δ ( k ) sin ( w. k ) d ( k ) = (12) π k The windowed ilter impulse response is: h ( n ) = w ( n ) δ [ ( n M )] sin[( n ( n M ). w M ) sin[( n M ). w ] h( n) = δ ( n M ) w( n) (13) ( n M ) π ] C. IIR Filter Design An IIR ilter is one whose impulse response theoretially ontinues or ever beause the reursive terms eedbak energy into the ilter input and keep it as speiied in the ollowing equation: Fig. 5: Magnitude response o a low pass ilter. Pass-band and stop-band regions are illustrated with equation 9 and equation 10. The derivation o the transormation is speiied with the ollowing equations: N M y ( n ) = a ( k ). y ( n k ) + b ( k ). x ( n k ) k = 1 k = 0 M k b ( k ) z k = 0 H ( z ) = (14) N k a ( k ) z k = 0 The theory o Butterworth untion is explained here but, the order o the ilter should be high and implementing a ilter o that order is not easy to perorm. In addition to this diiulty, solving these high order equations is not straightorward. D. Wavelet 285

4 A wavelet[11] is a wave-like osillation with amplitude that starts out at zero, inreases, and then dereases bak to zero. It an typially be visualized as a "brie osillation" like one might see reorded by a seismograph or heart monitor. Generally, wavelets are purposeully rated to have speii properties that make them useul or signal proessing. Wavelets an be ombined, using a "shit, multiply and sum" tehnique alled onvolution, with portions o an unknown signal to extrat inormation rom the unknown signal. As wavelets are a mathematial tool they an be used to extrat inormation rom many dierent kinds o data, inluding - but ertainly not limited to audio signals and images. Sets o wavelets are generally needed to analyze data ully. III. RESULTS AND CONCLUSION In this paper various noise removal tehniques are applied to ECG signals[10], ECG database data sample, and the perormane o these approahes are studied on the basis o spetral density and average power o signal. In the irst step, the most simple approah whih is linear trend or a pieewise linear trend to remove baseline drit is applied ater that various digital ilters are applied to the noisy ECG data having Baseline noise as shown in ig 4.1 then the wavelet approah is used or overall denoising o ECG signal and inally the digital ilter is applied on the sample ECG signal to remove Power line noise. All o the above steps are perormed using MATLAB sotware Calulation o parameters The two important parameters to hek the suppression o Baseline noises are spetral density and average power o signal[6] Power spetral density : Table1 and 2 shows the omparison o dierent ilters. The trade-o between spetral density and average power is best among all the ilters. But it an also visualize that the waveorm got distorted to some extend in ase o retangular window. The Kaiser Window and retangular window is also showing better results at the expense o some more omputational load as the order o the ilter is large. But in ase o remaining windows i.e. Hanning and Blakman windows, the order o ilter easily grow very muh high. It inreases the number o ilter oeiients whih inreases the large memory requirement and problems in hardware implementation. So, the Kaiser Window ilter an be best hoie or the removal o Baseline wandering among ilters[2]. Filter Table1 Comparison o various ilters or Removal o noise at ECG sample input 1. Filter Order Spetral Density beore Filtration Spetral Density ater Filtration Wavelet at 4dB Wavelet at 6dB Butterworth Kaiser Retangular Hanning Blakmann Spetral density o data 1 using dierent ilters is shown as ollows: Fig.6 Spetral Density using Butterworth ilter 286

5 Fig.7 Spetral Density using Kaiser Filter Fig.9 Spetral Density using Hanning ilter Fig.8 Spetral Density using Retangular ilter Fig.10 Spetral Density using Blakmann ilter 287

6 Average power Comparison o various ilters or Removal o noise at ECG sample input 1 in Table 2. Table 2 Average power Comparison o various ilters or Removal o noise at ECG sample input 1 Filter Filte r Orde r Average Power beore Filtration Average power ater Filtratio n Wavel et at 4dB Butterwo rth Kaiser Retangu lar 0 Hanning Blakma nn 6 Wavel et at 6dB IV CONCLUSION This paper onludes the work in this thesis; digital FIR and IIR ilter with wavelet or removal o Baseline noise were implemented in MATLAB. It is observed that the hoie o the ut-o requeny is very important, a lower than required ut-o requeny does not ilter the atual ECG signal omponent, however some o the noise suessully, but the ECG signal is distorted in the proess. Cut-o requeny varies orresponding to heart rate and baseline noise spetra. Thus, onstant ut-o requeny is not always appropriate or baseline noise suppression; it should be seleted ater a areul examination o the signal spetrum. When FIR ilter with wavelet is applied on signal it an be observe that the ombination o Kaiser and wavelet yield the smallest phase delay among all the FIR ilters ombination. It an remove the Baseline noises without distorting the waveorm. But the order o ilter is 450.However, high ilter orders are required to obtain this satisatory result and this inreases the omputational omplexity o the ilter. Furthermore, there is signiiant delay in the ilter result, thus this ombination an be applied to long data window. Thereore, this ombination is appropriate only or oline appliation, but or real time appliation, in whih short intervals o data is iltered and ast implementation is important, FIR is not an appropriate iltering method.iir and wavelet ombination is more appropriate or real time iltering appliation due to its lower omputational omplexity, and its better trade-o between average power and spetral density. It ompletely eliminates the osillations produed at the starting o the waveorm alled ringing eet. For perormane analysis we use dierent baseline noise removal methods or the purpose o omparison. The results are presented in the tabulation orm. From the table it an onlude that it outperorm the other method. REFERENCES [1] Allen, J.; Anderson, J. MC.; Dempsey, G.J.; Adgey, A.A.J., Eiient Baseline Wander Removal or Feature Analysis o Eletroardiographi Body Surae Maps, IEEE proeedings o Engineering in Mediine and Biology Soiety. vol. 2, pp , [2] Arunahalam, S.P.; Brown, L.F., (Real-Time Estimation o the ECG Derived Respiration (EDR) Signal Using A New Algorithm or Baseline Wander Noise Removal, IEEE Conerene o Engineering in Mediine and Biology Soiety. pp , [3] Barati, Z.; Ayatollahi, A., Baseline Wandering Removal by Using Independent Component Analysis to Single-Channel ECG dataǁ, IEEE onerene on Biomedial and Pharmaeutial Engineering, pp , [4] Carr, J. J. and Brown John M., Introdution to Biomedial Equipment Tehnology (3rd ed.), Prentie Hall, In., [5] Chavan M. S., R.A. Aggarwala, M.D.Uplane, Intererene redution in ECG using digital FIR ilters based on Retangular window, WSEAS Transations on Signal Proessing, Issue 5, Volume 4, May, pp , [6] Chavan M. S., Agarwala R., and Uplane M.D., Suppression o Baseline Wander and power line intererene in ECG using Digital IIR Filter, International Journal O Ciruits, Systems And Signal Proessing, issue 2,volume 2, [7] Chendeb, M.; Mohamad, K.; Jaques, D., Methodology o Wavelet Paket Seletion or Event Detetion, Signal Proessing arhive vol. 86, issue 12, pp , [8] Dai Min and Liana Shi-Liu, Removal o Baseline Wander rom Dynami Eletroardiogram Signals, IEEE Conerene on Image and Signal Proessing. pp

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