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1 Variability of QRS Signal in Electrocardiogras Using Wavelets R.Shantha Selva Kuari S.Issac iwas Dr.V.Sadasiva 3 Selection grade lecturer ECE Departent epco Schlenk Engg. College Sivakasi. III seester.e. (Counication Systes) epco Schlenk Engg.College Sivakasi. 3 Prof. & Head/CSE anonaniu Sundaranar University Tirunelveli. E-ail: {< r_sskp@yahoo.co > < issacniwas@yahoo.co > } Abstract Electrocardiogra (ECG) is extensively used as a low cost diagnostic tool to provide inforation concerning the heart perforance. To analyze the ECG signal cofortably accurately ECG signal decoposition is very uch essential. Wavelets are a new proising approach to analyze characterize non-stationary signals such as ECG EEG etc. In this paper the of the electric signals fro the heart during depolarization phase is investigated a signal processing ethod is developed which provides estiates for the beat-to-beat of the depolarization signal into b-pass signals by eans of the orlet wavelet transfor (WT). Fro that the of the depolarization signal is estiated by noralized variances of the envelope instantaneous frequency of bpass signals. The experiental data are taken fro electrocardiograph easureents of the healthy persons patients prone to alignant ventricular Tachycardia (VT) or ventricular Fibrillation (VF). The calculated variance paraeters perit the characterization of beat variable depolarization signals distinguish VT/VF patients fro healthy persons.. Introduction Electrocardiogra (ECG) signals are curves displaying heart beat rhyths. ECG signals are coonly used in edical care for onitoring diagnosis the treatent of patients suffering fro heart diseases. ECG is characterized by a recurrent sequence of five principal waves denoted by P Q R S T each one showing soe beat-to-beat. The analysis of this can be found in cardiovascular diagnosis. The tie interval between consecutive beats in the ECG is the siplest cardiovascular signal to characterize Heart Rate Variability (HRV) in tie frequency doains has been applied in various clinical situations. The QRS-signal ay provide essential inforation for the hidden cardiopathy. HRV is usually investigated as QRS-signal since the R- wave (QRS-signal) is far easier to detect due to its peaked shape. Therefore the co-ordinated study between the ECG signals its intrinsic can be a powerful tool to access the integrity of the cardiovascular syste. Late potentials (LPs) [] abnoral intra-qrs potentials (AIQPs) [] reflect abnoral ventricular activation during the depolarization of the yocardiu in the huan heart. In coparison to the depolarization signal of the noral yocardiu these signals exhibit high frequency low aplitude coparable to the ro noise signals of electrocardiogras (ECGs) or agneto cardiogras (CGs) which can identify post-yocordial infarction patients who are prone to ventricular tachycardia (VT) or ventricular fibrillation (VF). Signal processing ethods developed for detecting quantifying LPs or AIQPs are usually based on an analysis of the signal averaged ECG or CG (SAECG or AECG) which are characterized by an iproved signal-to-noise (SR). The detection of late potential using bidirectional high-pass filtering [] ethods of spectral analysis [] [3] spectroteporal apping [4] have been developed which are based on the assuption of high-frequency coponents. In addition several authors have studied fractionated potentials in signal-averaged high resolution ECGs by eans of a wavelet transfor [5]-[8]. For exaple D.orlet et al. [8] developed a ethod based on coherent detection of aligned local axia of the wavelet transfor of the QRS coplex which show that local axia of the so-called vector agnitude of the wavelet transfor can be used detect abnoral depolarization signal. P.Endt et al. [9] have studied the fragentation of bpass filtered depolarization signals of patients prone to alignant arrhythia. After averaging broad-b filtering of ECG records with a binoial bpass filter the fragentation of the QRS coplex was quantified by a score value covering the nuber of peaks heights of the filtered signal. P. uller et al. [0] have used this approach to investigate the spatial distribution of high-frequency coponents in agnitude heart signals during the QRS coplex found that cobination of score of different agnetic channels provides results with a sufficiently high sensitivity specificity for detecting patients prone to VT or VF. Considering AIQPs as a tie doain phenoenon Gois et al. [] [] proposed a signal processing ethod for quantifying AIQPs in the tie doain. Their ethod for notches slur extraction of the QRS-coplex is based on the identification of the QRS coplex as ipulse response of a discrete-tie syste with a rational transfer function. However signal averaging attenuates beat-variable signal coponents. Since the physiological basis for the hypothesis of beat-variable signal coponents is coonly

2 accepted [3] [4] several studies have been undertaken to quantify the variation of the QRS-orphology or to easure LP in a beat to beat analysis [5] - [7]. In earlier studies [8] [9] the authors investigated the beat of envelope instantaneous frequency of narrow b depolarization signals. After filtering of ECG or CG records with coplex binoial filters the two filter output signals connected by the Hilbert transfor were used to calculate envelope instantaneous frequency of the depolarization signal. In this paper the analysis is done by using a series bpass filtered signals at different center frequencies. Since the wavelet transfor provides a natural tool for realizing a bank of bpass filters orlet wavelet transfor (WT) is used to analyze the beat-to-beat of the depolarization signal. The wavelet transfor allows various coputational approaches in dependence on the way in which the scale translation paraeters are discretized [0]. This paper focus on the basic algorith for evaluating the beat of the depolarization signal. The proposed signal processing ethod is ipleented as an algorith tested by ATLAB siulation with the aid of experiental data obtained fro IT-BIH Arrhythia database which is the ost popular data source for evaluation of ECG analysis tools. The paper is organized as Wavelet transfor in Section ethods to evaluate the Signal in Section 3 Processing algorith in Section 4 Experiental result in Section 5. Finally Section 6 concludes this paper.. Wavelet Transfor Wavelet techniques have been applied in any fields of research including science edicine engineering finance. The wavelet transfor has becoe a valuable analysis tool because of its ability to elucidate siultaneously local spectral teporal inforation within a signal. It overcoes soe of the liitations of the ore widely used Fourier transfor which only contains globally averaged inforation has the potential to lose transient or location-specific features in the signal. Wavelet applications to bio-edical signals include the electroencephalogra electroyogra acoustic signals the ECG [5]. Wavelet based studies of ECG have focused ainly on exainations of heart rate the classification of ECG wavefors ECG data copression [6]-[3]. The wavelet transfor of a continuous tie signal x(with respect to the wavelet function g is defined as T(ab)= a g t b x(dt [] a where g((t-b)/a) is the coplex conjugate of the analyzing wavelet used in the coefficient convolution in this application x( is the ECG signal. The wavelet transfor T(ab) can therefore be the cross correlation of the analyzed signal (ECG signal) with a wavelet function that has been translated by a value b dilated by a factor a. These values are often referred to as the location dilation paraeters respectively. 3. ethods 3. Decoposition of Cardiac Signals into Bpass signals There is a lack of localization in tie in the Fourier transfor that ake it less suitable for detecting nonstationary signals. A further step to adapt the tie resolution of signal transforation to nonstationary signals x( leads to the wavelet transforation W x (t b) = ğ b t x(ξ ) dξ [] b a introducing the scaling factor b. ğ denotes the coplex conjugate of the wavelet g. In this ethod used the orlet wavelet i.e. the odulated Gaussian g( = exp(jc exp( -0.5t ) [3] which is suitable for realizing signal decoposition with an optial tie-bwidth product. The wavelet transfor [] can be interpreted as a tie-frequency analysis of x( with filters having a relative bwidth /c. The continuous WT provides two bpass signals Re{W X (tb)} I {W X (tb)} which can be written as Re{ W x (tb)}= y( = E(cos c t ϕ ( b = E( cosφ( [4] I{ W x (tb)}= y(= E(sin c t ϕ ( b = E( sinφ( [5] where the filter center frequency is given by w=c/b. The envelope E( the instantaneous frequency V(=dΦ/dt of these bpass signals are given by the relationships E( = y () t y () t V( = dφ/dt = w+v( + [6] = d arctan y ( [7] dt y(

3 where v( denotes the ean-free instantaneous frequency. Using a set of discrete scaling paraeters b b...b n for the continuous wavelet transfor explained above decoposed the tie signal x( into set of bpass signals y (y (...y ( y (y (.y ( at different center frequencies w w w 3...w. The cardiac signal x( consists of a sequence of say 00 heart beats. To copare the tie axes of the individual beat signals have to be aligned. The tie axis of the individual beats in relation to the deterined fiducial point of the beat. On these tie axes the fiducial point of the beat located at a value t A chosen to include the P-wave of every beat. Fro x( having the tie axes of individual beats to extract the individual beat signals x k ( with k=... fro the sets of bpass signals y (y ( y ( y ( y (. y ( the corresponding beat signals y (y (. y (y ( y ( y ( y ( y (. y ( y ( y ( y (y ( y (.y (.. y ( y (. y (. These bpass beat signals for the atrices calculated as tie integral of the ean-free frequency v k (. The tie interval of interest calculated for the row vector bpass signal y (...y ( y (...y ( at the center frequency. The variance of both the envelope the instantaneous frequency during the tie interval of interest can be calculated for the enseble of row-vector saple points at t i. 3. Estiation of the Signal For a noralized easure the ean-to-variance ratios [ En (t i )/ σ En (t i )] [ Vn (t i )/ σ Vn (t i )] which reflects sall by high values high by sall values is used. To characterize the of envelope instantaneous frequency of the entire interval of interest the integral ean to variance ratio is calculated as p L = E n E n i= σ E n ( t i ) [0a] y( Λ Λ Λ y ( Y= [8a] Μ Ο Μ y ( ) ( ) t Λ Λ Λ y t p L = V n F n i= σ V n ( t ) i [0b] y ( Λ ΛΛ y ( Y = Μ Ο Μ [8b] y ( Λ ΛΛ y( Applying this decoposition procedure also to the envelope instantaneous frequency signals E( V( the X signal atrices E V of the envelopes instantaneous frequencies are fored. The envelope instantaneous frequency atrices E V describe signal power signal structure of the set of bpass signals. The phase of a row vector bpass signal is described by the phase variances of a row vector signal defined as σ ( ] [9a] [ ϕ( = ϕk ( ϕ k= where the phase signal ϕ K ( t ) = t 0 v k ( ξ ) d ξ [9b] is related to the k-th signal of a row vector in the V atrix. The phase signals ϕ ( k =... are characterized by k the ean φ (= 0. This property reflects that φ k ( is where i =...n are tie saples located within the interval Ψn. Then E (t i ) σ E (t i ) v (t i ) σ v ( t i ) denote ean variance calculated at tie t i by using the following equations X ( ti ) = X K ( ti ) [a] K= K = σ X( ti) = [ XK( ti) K ( ti) ] [b] for the enseble of signals of a row vector of E V. It is known that patients after yocardial infarction with VT/VF have usually wider QRS-coplex than healthy persons. Using the integral ean to variance ratios p En p Fn instead of using integral variance to ean ratios to avoid that a expected higher of patients can be covered by the influence of possibly wider QRS coplex signals on the deterination of the p En p Fn paraeters. Finally to cobine the inforation of a nuber of row vectors i.e. to cobine the inforation of bpass signals deterined the paraeters PE = p E [] n n= 3

4 P = F p F n n= [3] 4. Proposed Processing Algorith The deterination of paraeters P E P F involves a nuber of discrete tie signal processing steps such as continuous wavelet transfor coputation of the derivative the integral of a signal. The proposed algorith for the ipleentation coputation of the P E P F paraeters includes the following steps. Step : Estiate the fiducial point of the individual beats of the cardiac signal x(. Step : Take orlet wavelet transfor (WT) of signal x( extract the signal of individual beats by eans of the fiducial points to obtain the signal atrices Y Y of bpass signals. Copute the atrices E V of the envelopes instantaneous frequencies. Step 3: The k-th row vector of the E V atrices consists of envelopes instantaneous frequency of the depolarization signals of individual beats. Step 4: Copute the phase variances curve σ φ( for every row vector. Step 5: Calculate the integral paraeters p En p Fn for the row vector bpass signals fro n =. which are located within a desired frequency range. Step 6: Calculate the paraeters P E P F which are used to estiate the of the depolarization signals for a desired frequency range. Step 7: Calculate the cobined paraeter P = P E + P F for a robust estiate of the of the depolarization signal. 5. Experiental Result The proposed algorith is tested with the IT-BIH Arrhythia data base ECG records taken for the 4 healthy persons 5 post-yocardial infarction patients with docuented events of sustained VT or VF. Saple data to 4 of Table represents the paraeters for a healthy person the rest of the saple data represent the paraeters for an abnoral patient (VT/VF). Healthy person record has bit resolution with sapling rate as 360 Hz. Patient prone to alignant ventricular tachycardia or ventricular fibrillation (VT/VF) record has bit resolution with sapling rate as 50 Hz. Coparing the values of paraeters it is easy to discriinate the healthy person VT/VF patients. And also found that the frequency paraeter P F generally exhibits very lower values than the envelope paraeter P E for the VT/VF patients at higher frequency range. ECG Data-base Saple record Envelope ( P E ) Frequency ( P F ) Total ( P ) Saple data.0873e e Saple data.07e e Saple data e e Saple data e e Saple data e e Saple data 6 3.6e e Saple data 7.850e e Saple data 8.30e e Saple data 9.060e e Table. Coparison of variable paraeters for a healthy person VT/VF patients at higher frequency range. 6. Conclusion Using the WT bpass signals of the depolarization signal covering a frequency range fro about 00 to 50 Hz is generated. Envelope instantaneous frequency of the bpass signals reflect the of the depolarization signals. The variance of the signal is used to calculate the enseble of heartbeats analyzed. This is used as a easure to characterize the of the depolarization signal. The signal processing procedure developed provides paraeters which characterize the ean variance of these signals for selected tie intervals of interest. Evaluating the beat-to-beat of the envelope instantaneous frequency fro about 00 to 50Hz it is clear that in the high frequency (50-50 Hz) range VT/VF patients can be distinguished fro healthy persons by the proposed integral paraeters P E P F by the cobined paraeter P. The beat-to-beat variance appears to be of higher significance at high frequencies. This was also reported by Alfred Link et al. [5] who found discriinative values for the beat-to-beat variance of the QRS coplex in the frequency range for 0 Hz to 50 Hz. The result suggest that the calculated variance paraeters perit the characterization of beat variable depolarization signals distinguish VT/VF patients fro healthy person. References [].B. Sison W.J.Unterekar S.R. Speilann L..Horowitz.H.arcus R.A.Falcone A.H. Harken.E. Josephson Relative between late potentials on the body surface directly recorded fragented electrocardiogras in patients with ventricular tachycardia Aer.J. Cardiol. vol.5 pp [] P.Ler D.Albert E.J. Berbari Principles of frequency doain analysis in High Resolution Electrocardiography. El-Sherif Ed. t.kisco Y: Futura 998 pp

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