Frequency-domain Analysis of ECG Signal

Tu Chengyuan et al: Frequency-domain Analysis of ECC SignalVol.5 No.1Frequency-domain Analysis of ECG SignalTu Chengyuan, Zeng Yanjun， Li Shuxin(College of Mechanical Engineering & Electro-Technique, Bejjing University of Technology, Beijing 100022)Received 2 November 2005Abstract: A new simple approach to efectively detect QRS-T complexes in ECG curve is described, so as toeasily get the P-wave (when AF does not happen) or the f-wave (when AF happens). By means of signalprocessing techniques such as the power spectrum function, the ato-correlation function and cross- correlationfunction, two kinds of ECG signal when AF does or does not happen were successively analyzed, showing theevident diferences between them.Key words: ECG curve; P-wave; f-wave; histogram; AF ( atrial fibillation); cross. correlation; powerspectrum; auto-correlationsuitable scale so that the signal abrupt after a1 Forewordwavelet transform may be a representation of theabruptness of the original signal9 ' 10)。Otherwise,ECG ( electrocardiogram) is one of theit is quite possible that there appears a failureconventional clinical examination methods, and is(some of the QRS-T complexes may not bevery important and valuable to the cardiovasculardetected this time ) or a mistake ( somethingdisease diagnosis. Key point in the automaticdetected is far from a QRS-T complex).analysis of ECG signal is the detection of its QRS-In order to get rid of this trouble, the authorsT complexes' 'When someone’ s QRS-Tdeveloped the following simple and effectivecomplexes been detected, we can analyze hismethod based on histogram to search for QRS-T( her ) HRV ( heart rat variations )， andcomplexes.distinguish between the normal and the abnormalones，and carry out an all-round research on the2 P-wave or f-wave of the ECG Curveinformation of their ECG's.ECG' s processing methods early used for2.1 Fast Searching for the Region Wheredetecting QRS-T complexes are band- passQRS-T Complexes Stayfiltering，adaptive filtering， nonlinear adaptiveQOP ( quantity of pixels) is defined as thefiltering，etc. 1Owing to the outstandingnumber of figure elements per unit width of relatedcomplexity and the enormous amount of operationsstrip, whereas a histogram shows the distributionin the algorithms of these filtering methods, theirof these elements in the related figure .applications ( especially, the clinical applications )Information embodied in the histogram, showingare restricted. Recently， along with thethe characters of this figure, may be utilized fordevelopment of the analysis technique by means ofast determining at which region the QRS-Twavelet，some methods based on wavelet transformcomplex stays. .for detecting QRS-T com- plexes came to theFirstly，the ECG signal is filtered by afore' 5- 81. These methods demand, however， adifferential filter ，and then an excellent t-domainsuitable mother- wave to be constructed accordingcurve can be obtained, as shown in Fig. 1 .to the property of the signal researched so that theNow, we define a series of terms: .wavelet transform may posses an ability to show allX一ECG' s figure matrix ( binary:the local characters of this signal in the timewhite中国煤化工domain as well as in the frequency domain.:ments per columnMYHCNM H G。Moreover，these methods demand to select aand column90Engineering Sciences Vol. 5 No. 1 , March 2007Vol.5 No.1Tu Chengyuan et al: Frequency- domain Analysis of ECG Signal.0 t0t20- '-0.52.03.0Time /sTime/sFig.1 ECG's waveformFig.3 The threshold-form of the histogramof ECG's waveformcoordinate respectivelyand we have2.2 Detection of QRS-T Complexesd(j)= Zx(i,j) .Let the size of figure matrix to be analyzed beD = Id(j)}(1)M x N(row x column)， and that of the figure :The value range of i and that of j are allmatrix Qqs of QRS-T mould be M; x N, andrestricted to the size of ECG figure researched.the characteristic vector of the mould be DAs for one frame of picture on the screen， wethen we can easily find out by means of this mouldgenerally let:the positions of related QRS-T complexes throughi = 1,2,.*,600; j = 1,2,,1200.a few sequential searching at the correspondingFig. 2 shows the picture corresponding to setcoordinates in Fig.1, as shown in Eq. (3).D, namely the histogram, in which the abscissaThe criterion utilized in this search process isis time, and the ordinate is the QOP. Fig.3 is therelated with the quantity of unmatched point ekthreshold form of Fig. 2，namely a pictureand the characteristic vector Dcorresponding to the new set Du obtained byUnmatched points is defined as a point in themeans of selecting a related threshold value d0searched region such that at this point the values(see Eq.(2)).between the corresponding elements of two matrixD。= {d+(j)}Qqpu and Qk are different, where Qk is a figureda(j) = d(j) (d(j) ≥d)da(j) =0 (d(j) < d)(2)matrix with the same size as mould matrix Qqst .Comparing Fig. l,Fig.2 and Fig.3, we easilyAs for the quantity of unmatched point ex，it cansee that the relative maximums in Fig. 3be calculated as follows:correspond to those peaks of related R- wave .en =己( QxorQpu(4)Again, let n(k) be the column coordinate of thewhere xor denotes an‘exclusive-or operation,peak of k-th R-wave, then a new set, constructedand this operation is carried out between thefrom these column coordinates, is as follows:corresponding elements of Qk and those of QqmN= In(h)| = in(1),n()...n(N)| (3)and results in a new matrix 。Thereafter weperform the 2 operation with all the elements ofthis new matrix. .As for the characteristic vector Dy，it is a set,40whose element corresponds to QOP per column in20the sub-region to be searched .The matching principle is as follows: a pattermthat satisfies the following two requirements is justthe中国煤化工Fig.2 The histogram of ECG' s waveform(1-C,)c,∈(0,1)fHCNMHG(5)Engineering Sciences Vol. 5 No. 1, March 200791Tu Chengyuan et al: Frequency-domain Analysis of ECG SignalVol.5 No.1e = minle,} (h = .2.....(6)spectrum curve as shown in Fig.5.2.3 The Way to Obtain f-wave; 1.0As an example, we discuss how to utilize the0.6-1above method to obtain the f-wave in ECG curve.斗0.4While QRS T complexes are removed from ECG0.2curve，the remainder is nothing but the P-wave05101520253035 4045 50when AF( atrial fibrillation ) does not happen, orFrequency/Hz(a) When AF does not hapenthe f-wave when AF happens. (See Fig.4 )As shown in Fig.4, the P-wave appears to be aseries of small wave packets with relativelyg 0.60.4concentrated energy， whereas the f-wave be aseries of irregular oscillations with their energyquite dispersed.(b) When AF happens1.25-宜0.75-Fig.5 The power spectrum0.25县-0.29豆20.75It is easily seen that the spectrum lines areuniformly distributed and the spectrum valleys stay0一T0一203.040-5.0Time/sat or near the zero value points when AF does not(a) P-wavehappen , whereas those lines distributed quite non-，0.75tuniformly and the valleys stay somewhat far awayE 0.50↑事0.25from the zero value points when AF does happen.Now we discuss the dynamic frequency0 2.3.0.05.spectrum.Timne/sFor each sampling， ECG signal of eight(b) f-wavcsequential time intervals (10 s as one interval) isFig.4 The curves of P-wave and f-waveas a group of data prepared. So far as QRS-Tcomplexes are removed, the remainder will be P-3 The Signal Processing and Analysis ofwave( when AF does not happen)， or be f-wave(when AF does happen), and then we do a FFTECG Signaloperationon each sample and draw aData used in our work are taken from MTT/BIHcorresponding dynamic frequency spectrum, asdatabase as well as from Beijing Chao- Yangshown in Fig.6.Hospital，among them there are 50 examplesComparing Fig. 6(a) with Fig. 6(b)，thewhile AF happened, and the other 50 ones whiledifference between these two kinds of dynamicAF did not happen.spectrum is very evident. The energy distributionOur methods of signal processing and analysisof f-wave looks concentrating in quite an arrowrelate to many techniques: the power spectruminterval (such as 0- 5 Hz) when AF happens,function，the auto-correlation function and thewhereas that of P-wave looks dispersing within across-correlation function. Curves correspondingrelatively wide interval when AF does not happen.to the related functions have been normalized soMoreover，f-wave' s dynamic frequency spectrumthat we can easily deal with them.curves in different time interval differ one3.1 The Power Spectrumanother ，showing the iregularity of f-wave.After a FFT operation on ECG s data, we can3.2|中国煤化工ctiondiscoverthe relatedamplitude-frequencyEon is utilized forcharacters，so as to draw the ECG's powerdesclMH. CNM H Gion of values ofa9Engineering Sciences Vol.5 No. 1 , March 2007Vol.5 No.1 .Tu Chengyuan et al: Frequency-domain Analysis of ECG Signaldescends relatively slowly (Rmn/Rmw2) <3 when， 1.0AF does not happen.& 0.80.3.3 The Cross-correlation Functionh- (ms)i 0.The cross-correlation function denotes thecorrelation between the values of two different020304050 - 60 70二Frequency/Hzsignals sampled at different time .(a) When AF does not happensLet the sampling series of the signal values ofg 1.0QRS-T mould be y(n), and that of ECG signal名0.8|be x(n), the cross-correlation function is then asfollows: ._(ms)10 230 405060市R,(m) = lim2w2x(n)y(n- m) (8)(b) When AF happensThis function, shown as a corresponding curve,is given in Fig.8(a) when AF does not happen,Fig.6 The dynamic frequency spectrumor in Fig. 8(b) when AF happens.signal sampled at different time, being a kind of0.85measurement of the degree of interrelation between宝0.6these values.0.40.2-Let the sampling series of values of ECG signalbe x(n), its auto- correlation function is then as00511522.5 33.544.5Time/sfollows:R.(m) = lim2w2x(n)x(n- m) (7).8主0.6is given in Fig. 7(a) when AF does not happen,04or in Fig.7(b) when AF happens .0.2F.8[850051152253 35 4 4.5g 0.60.4 t.2[1.1111.1111..Fig.8 The cross correlation function-10-8-6-4-20246810It is easily seen from Fig.8, that the degree of.0-correlation between ECG signal and the QRS-T.8-.6mould signal appears to be relatively maximal at0.4[points where QRS-T complexes occur, and that on0.25the cross-correlation curve there appear all thecorresponding waves quite similar to the QRS-Tcomplexes. It is also seen that , when AF does nothappen, QRS T complexes separate each otherFig.7 The auto-correlation functionrelatively uniformly， and within the spacesbetween these complexes there are some relativelyComparing Fig.7(a) with Fig.7(b), we see thatregular oscillations;whereas whenever AFthe amplitudes on the auto-correlation curvehappe中国煤化工es separate eachdescends rapidly with their amplitude ratio( RmalotherMYHs a series of veryRmw2) > 4.5 when AF happens, whereas thatirregu. CNMHG spaces betweenEngineering Sciences Vol.5 No.1, March 200793Tu Chengyuan et al: Frequency-domain Analysis of ECC SignalVol.5 No.1two successive complexes .methods used in this paper such as the powerspectnum function， the auto-correlation function,4 Summarythecross-correlationfunctionetc.,distinctions, even too small to be observed by aThe authors developed a simple and effectivecommon people，between these two kinds of ECGnew approach to remove QRS-T complexes fromcurve ( when AF does or does not happen), wouldECG curve, so as to easily get the P-wave whenbe evident between the corresponding frequency-AF does not happen, or gain the f-wave when AFdomain pattermns， so as to enable us to easilyhappens. By means of the signal processingdiagnose whether AF happens or not.References[ 1 ] Kohler B U, Henning C，Orglmeister R. TheWavelet transfomn-based QRS complex detectorprinceiples of software QRS detection[J]. IEEE[J]. IEEE Trans. Biomed. Eng., 1999 ，46:Engineering in Medicine and Biology， 2002,838 - 848.January /February: 42- 57.[7]LiCw,ZhengCX,YuanCW.Dectionof[2]Keselbrener L，Keselbrener M，Akselrod s.ECG characteristic points using wavelet transfommNonlinear high pass filter for R-wave detection in[J]. IEEE Trans on BME, 1995, 42(1): 21-ECG signal [J]. Med. Eng. Phys., 1997, 1928.(5): 481-48.[ 8] Bahoura M， Hassami M，Hubin M. DSP[3] Kohler B U, Hennig C, 0Orglmeister R. QRSimplementation of wavelet transform for real timedetection using zero crossing counts[J]. Int. J.ECG waveformns detection and heart rate analysisMed. Informatics, 1998,52(1-3): 191 - 208.[J ]. Computer Methods anProgram in[ 4] Mahalingam N, kumar D. Neural networks forBiomedicine, 1997, 55 (1): 35 -44.signal processing appli-cations: ECG classification[ 9] SahambiJS，TandonSN, BhattR KP. A new[J]. Australas. Phys. Eng. Sci. Med., 1997,approach for in-line ECG characterization[ A].20(3): 147- 151.Proceeding of Ffeenth Southem Biomedical[ 5]lnoue H, Iwasaki S, Shimazu M，Katsura T.Engineering Conference [ C]. Dayton， USA,Detection of QRS complex in ECG using wavelet1996: 409-411.transform ( in Japanese) [A]. IEICE Gen. Conf.[10] SahambiJS, TandonS N, Bhatt R K P. Using[C]. 1997, 67(A-4): 198 - 207.wavelet transform for ECG characterization [ J].[6] Kadambe S, Muray R, Boudreaux Bartels G F.IEEE Eng. Med Biol, 1997, 16(1): 77- 83.AuthorTu Chengyuan, female, bor in 1963, PnD, graduated from Beijing Polytechnic University, Associate professor,engaged in the reseach work and education work in automatic control as well as biological and medical infornationprocessing, with 3 monographs and 56 papers published. She can be contacted by e-mail: tuchengyuan8029 @ vip. sina.com中国煤化工MYHCNMHG)4Engineering Sciences Vol. 5 No. 1, March 2007