Abstract: This article introduces a method for constructing a heart-beat signal from a long record of phonocardiogram(PCG). The method comprises a series of algorithms that decompose a long data record of heart sound to its heart-beatcycles using the simultaneously recorded electrocardiogram (ECG). First the cardiac cycles are identified using the syn-chronized ECG signal. The corresponding heart-beat cycles are then extracted from the PCG signal and used to con-struct a template signal. Using the correlation of the heart-beat signals with the template signal, the heart-beatscorrupted by noise are identified and discarded. The remaining heart-beats are then used to construct a heart-beat signalwhich is free of artefacts and can be used for various heart sound analysis purposes.

1 INTRODUCTION

A phonocardiogram (PCG) is a recording of an acousticwave produced by periodical contractions and relax-ation of the heart muscles along with acceleration anddeceleration of blood within the cardiac structure. Thesequence of events occurring during such activities iscalled the cardiac cycle. Each cardiac cycle is catego-rized into four basic groups: first, second, third, andforth heart sounds [1]. Phonocardiograms have beenstudied for diagnostic purposes for various heart dis-eases [2]-[5]; and also for better understanding of heartsounds [6]-[8].

The PCG signals are oscillatory in nature; although itmay not be exactly periodic in strict mathematicalsense. Observation of the evolution of these signalsreveals that there are similar events or periods, but theymay not exactly reproduce themselves. Furthermore,phonocardiograms are quasi-stationary signals; conse-quently, their characteristics do not change drasticallywithin few minutes of recordings.

However, analyzing long data records of PCG signalsusing some signal processing techniques such as time-frequency or wavelet methods imposes a huge computa-tional burden. The heart-beat signal extraction tech-nique presented herein can be used to obtain a singleheart-beat signal encapsulating the characteristics of thePCG signal. The extracted heart-beat signal can then beused for analysis or diagnostic purposes.

The proposed heart-beat signal extraction technique isexplained in the succeeding two sections. First the elec-trocardiogram beat cycle detection algorithm is intro-duced in Section 2. In Section 3, the segmentation of thePCG signal and the reconstruction of a single heart-beatsignal are explained. Then in Section 4 experimentalresults are presented, followed by a concluding remarksin Section 5.

2 HEART-BEAT CYCLE DETECTION

The central idea of the proposed heart-beat separationscheme is the decomposition of phonocardiograms intoheart-beat signals through the detection of the heart-beatcycles of the synchronized electrocardiograms; beatcycle detection is easier using ECG signals. In order toaccomplish this, first the QRS peaks of the ECG signalare detected, and then the corresponding beat cycles areidentified.

2.1 QRS Peak Detection

QRS detection is one of the important tasks in ECGanalysis; a great deal of research effort has been devotedto this task [2]. Most of the QRS detectors described inthe literature are aimed for analysis of the ECG signalitself. Our aim, however, is to find the temporal locationof the peaks of the QRS complexes and use them to sep-arate the heart-beat cycles from the PCG signal. OurQRS detection scheme is divided into two sub-systems:the preprocessor and the decision rule system, as shownin Figure 1. The main concern in the QRS detector is toavoid detection of false peaks, if any.

Figure 2 shows the QRS detection algorithm. The inputsignal, Secg(t), is initially normalized in amplitude. Thisis essential since a thresholding scheme is employed fordetection of peaks of the QRS complexes. There areusually some fluctuations in the QRS amplitudes, hencethe threshold level is set to a value Vth given in Eq. (1).

Figure 1 QRS peak detector.

DecisionRule

Low-Pass

AmplitudeNormalization

Processor

x n( ) y n( )

(1)

The input data is scanned with a rectangular window thewidth of which is much less than a heart-beat period,whose length could vary from about half a second tomore than one second depending on the person. A smallwindow size reduces the possibility of missing any QRSpeaks during the scanning process. Within each windowthe parts of the data that are above threshold areselected and their maximum value is found. The thresh-olding scheme ensures that only regions of the signalthat are in the vicinity of the peak of the QRS complexare considered for peak detection. In Figure 3 showsone cycle of an ECG signal with threshold level and a scanning window of length m.

In order to distinguish and locate the position of theactual QRS peak, the slope of the signal above thresholdis calculated within each window. Let bethe ith window and Secg(t) be the portion of the QRS

complex above threshold. The slope of the windowedECG signal above threshold level is

(2)

The zero crossing in represents a local maximumin the ECG signal, i.e., a potential QRS peak.

2.2 True QRS Interval Detection

The primary objective of the true QRS interval detec-tion is to ensure that the peaks detected with the algo-rithm of Figure 2 are real QRS peaks; that is, we want toidentify any false detections and remove them. Thereare two situations in which a false detection may occur:a presence of an artefact whose height is higher than thethreshold level, or the presence of small fluctuations(due to noise) near the QRS peak.

The mean interspike (i.e., QRS peak-to-peak) interval iscalculated as

(3)

0.8 Vth 1≤ ≤

VthWm

No

Yes

No

i i 1+=

Yes

Yes

No

Sw t( ) Secg t( )Wm t mi–( )=

zerocrossing in β

Figure 2 QRS peak detection algorithm.

Sw t( ) Vth>

Set threshold VthSet scanning window Wm

i = 0

Is Secg(t) scanned all?

End

Start

Secg(t)

β ddt-----Sw t( )=

PK i( ) t max sw t( )( )=

Wm t mi–( )

βi t( ) ddt----- Secg t( )Wm t mi–( )[ ]=

βi t( )

0.295 0.3 0.305 0.31 0.315 0.320.7

0.75

0.8

0.85

0.9

0.95

1

0 0.2 0.4 0.6 0.8 1

−0.5

0

0.5

1

Vth

10 milli-secondswindow

τ2τ1

Figure 3 The process of thersholing and windowing the ECG signal.

Wm

tkm

–(

)

Wm t k 1+( )m–( )

Wm

tk

2+

()m

–(

)

Threshold

Time (sec)(a) One ECG cycle.

Time (sec)

(b) Peak of QRS Complex.

T 1M 1–------------ PK j 1+( ) PK j( )–

j 1=

M 1–

∑=

where is the number of detected QRS peaks, and is a vector containing the locations of the QRS

peaks. We define the minimum and the maximumacceptable time interval between two consecutive QRSpeaks as:

(4)

(5)

The average interval between the ith peak and its near-est neighbours is calculated as follows:

(6)

where and are the time intervals betweenthe ith peak and its preceding and succeeding peaks,respectively; that is,

(7)

(8)

The interval, , for every detected peak is comparedwith and . If it is within the interval

, it is accepted as a true QRS peak, oth-erwise it is considered to be a false peak, and hencerejected. That is, for a true QRS peak, Eq. (9) must besatisfied.

(9)

When a false QRS peak occurs at position i, the value ofits average interval , and possibly those of adjacentpeaks, will not satisfy Eq. (9). In particular, there will bea local valley centred on i in the values of the vector ,the vector whose elements are the intervals . In orderto find the location of the false QRS peak, it is neces-sary to find the position of the bottom of the valley. Thisis accomplished by calculating the derivative of thevecotr and finding the position at which the deriva-tive becomes zero. The proposed QRS interval detec-tion algorithm is shown in Figure 4.

2.3 ECG Beat Cycle Detection

In order to detect the beat cycles, the beginning of eachcardiac cycle with respect to QRS peaks must be identi-fied. The P-wave is chosen as the beginning of the car-diac cycle. If the time interval between two consecutiveQRS peaks is divided into three sections, the P-waveoccurs in the third section. The onset of the third sectionof the ith QRS peak is given by Eq. (10).

(10)

where its offset time is the ith entry in the vector .This is illustrated in Figure 5.

MPK

∆Tmn T 0.1T–=

∆Tmx T 0.1T+=

δti∆ti ∆ti 1++

2----------------------------=

∆ti ∆ti 1+

∆ti PK i( ) PK i 1–( )–=

∆ti 1+ PK i 1+( ) PK i( )–=

δti∆Tmx ∆Tmn

∆Tmn ∆Tmx,[ ]

∆Tmn δti ∆Tmx≤≤

δti

δtδti

δt

tri PK i( ) 13--- PK i( ) PK i 1–( )–[ ]–=

PK

δti∆ti ∆ti 1++

2-------------------------------= i i 1+=

i M=

Yes

Φ i( ) PK i( )=No

No

Yes

β dΦdt-------=

q iβ i( ) 0==

i 1=

Figure 4 QRS interval detection algorithm.

Tmn δti Tmx≤≤

QRS Peak Locations, PK

End

Mean InterspikeInterval, T

Start

PK q( ) [ ]=

3.4 3.6 3.8 4 4.2 4.4 4.6 4.8 5−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

(3)(2)(1)

τf τt

Figure 5 Two consecutive cycles of ECG signal for P-wave recognition.

onsetand off-set

P-Wave

Since we are going to use the QRS peak detector to findthe peaks of the P-waves, it is essential to remove theportion of the QRS complex that falls within sectionthree. This is the part of the signal between and in Figure 5. This is accomplished by calculating theslope of the signal from to as:

(11)

The signal is scanned in a bottom-up fashion; thatis, scanning starts from the end and proceeds towardsthe beginning. When the first zero crossing is encoun-tered, the scanning is stopped. This point corresponds tothe first minimum in the signal just before the QRScomplex. The part of the signal to the right of the zerocrossing is discarded. In order to detect the peak of theP-wave, the algorithms of Figure 2 and 4 are applied tothe remaining part of the signal. This process is repeatedfor all detected QRS intervals. The final outcome is avector the same size as the ECG signal , the ele-ments of which are all zeros except at the locations ofthe P-wave peaks, where a value of one is recorde. Theflow chart of this algorithm is shown in Figure 6.

3 SEGMENTATION OF PCG SIGNAL

The prime purpose for developing the QRS detectionalgorithm was to devise a scheme which would enableus to decompose the PCG signal into its beat cycleswith minimum error of miss-detection. As was men-tioned earlier, the ECG and PCG signals must berecorded simultaneously. Therefore, the decompositionprocess of the PCG signal into its constituent beatcycles can be accomplished by simply aligning it withthe signal obtained by the algorithm of Figure 6,

, which is a train of impulses located at the startsof the cardiac cycles.

3.1 Identification of Artefact-Free Beat Cycles

Among the separated heart-beat cycles, it is necessaryto identify and discard those cycles that contain arte-facts. Let each PCG heart-beat signal be denoted by

, where i is the order of the beat cycle withinthe PCG signal. A correlation scheme is devised to dis-tinguish the artefact-free heart-beat cycles within thePCG signal. A template signal is constructed for thispurpose, and every beat cycle is compared with it. Thetemplate signal, is constructed by taking theensemble average of all the beat cycles.

(12)

where M is the total number of heart-beat cycles.

The degree of similarity between the beat cycle wave-forms and this template signal is measured by calculat-ing the correlation coefficient of the template signalwith each of the beat cycles. The correlation coefficientbetween the template signal and a given beat cycle isdefined as

(13)

where is the cross-covariance between thetemplate signal and the beat cycles, and are,respectively, the covariances of the template signal andthe beat cycle.

In order to obtain the maximum correlation coefficientpossible, the beat cycle is shifted with respect to thetemplate signal. In other words, the correlation coeffi-cient is computed at the smallest time-lag which yieldsmaximum cross-correlation between the two signals.

τf τt

tri PKi

mpiddt-----Secg t( ) for tri t PK i( )≤ ≤=

mpi

Secg t( )

vecg t( )

S ipcg t( )

Stmp t( )

Stmp t( ) 1M----- S i

pcg t( )i 1=

M∑=

Λ t( ) Secg t( )=

i i 1+=

i M= No

Yes

mp ddt----- Λ t( )( )=

Mxi Secg t( )=

r t PKi≤ ≤for

µ t mp 0==

r t µ≤ ≤for

Figure 6 ECG beat cycle detection.

r PKi PKi PKi 1––( )– 3⁄=

ν t( ) t peaks of P-wave= 1=

End

Start

QRS Peak Locations, PKInitialize v(t) to zero

i = 1

Peak Detector of Fig. 2with Vth = 0.

ρCtmp, btc

Ctmp C× btc

--------------------------------=

Ctmp, btcCtmp Cbtc

The cross-correlation of the template signal with thebeat cycle is defined as

(14)

where is the length the template signal, which isequalt to the length of the beat cycle.

In order to identify the beat cycles corrupted with arte-facts, a threshold level for the correlation coefficients isset to 0.9; that is, those beat cycles that have their corre-lation coefficient below of the maximum correla-tion coefficient are rejected.

3.2 The Heart-beat signal

The final heart-beat signal is reconstructed using onlythe artefact free beat cycles. The mean signal of the beatcycles is computed in the frequency domain. Frequencydomain averaging is used to avoid errors that may occurdue to small miss-alignments of the beat cycles in thetime domain. To obtain the time domain signal, theaveraged frequency domain signal is converted back tothe time domain using the inverse discrete Fouriertransform (IDFT). The heart-beat cycle reconstructionalgorithm is presented in Figure 7.

4 RESULTS

In this section we present the results of applying thealgorithms presented in this article to real signalsrecorded from patients suspected with coronary arterydisease. Thirty seconds of synchronously recorded PCGand ECG signals are shown in Figure 8 below; clearlythe PCG signal contains some artefacts.

The ECG signal was scanned with a 10 millisecondlong rectangular window. A threshold level of 0.8 wasselected, and the QRS detection algorithm was applied.The detected QRS peaks were examined with the algo-rithm of Figure 4 for false detections. Then the startingpoints of the cardiac cycles were detected using theECG beat-cycle detection algorithm (Figure 6). Theoutput of the ECG cycle detection algorithm, the signal

, is shown in Figure 9.

X τ( ) Stmp n( )Sbtc n τ–( )n 0=

N∑=

N

90%

Start

Pecg t( );Spcg t( );

S mpcg t( )

τm 0=Yes

No

β 1=

i M= No

β β 1+=

Yes

α 1=

ρ α( ) K≥

Yes

No

α M=No

Yesend

decompose PCG to its beat cycles;

Figure 7 Heart-beat construction algorithm.

Stmp t( ) 1M----- S i

btc t( )i 1=

M∑=

X τ( ) Stmp n( )Sbtc n τ–( )n 0=

N∑=

τm t max X τ( )( )=

S ibtc t( ) S i

btc t τm–( )=

ρ β( )Ctmp, btc

Ctmp Cbtc×-------------------------------=

K ma x ρ β( )( ) 0.1max ρ β( )( )–=

α α 1+=

Yα t( ) S αbtc t( )=

Figure 8 Synchronously recorded PCG (a) and ECG (b) signals.

νecg t( )

Figure 9 The signal obtained from the ECG beat-

cycle detection algorithm.

νecg t( )

0 5 10 15 20 25 30

0

0.2

0.4

0.6

0.8

1

The PCG cardiac cycles were separated by aligning thePCG signal (Figure 8(a)) with the signal ofFigure 9. These extracted PCG cardiac cycles, shown inFigure 10(a), were then used to reconstruct the PCGtemplate signal presented in Figure 10(b).

The correlation coefficients of the template signal ofFigure 10(b) with each beat cycle of Figure 10(a) werecalculated; the computed correlation coefficients aretabulated below (TABLE 1) and plotted in Figure 11. InTable 1, four correlation coefficients fall below 0.9, butone of them is equal to 0.8946), very close to 0.9. If thethreshold level is set at 0.88, as shown in Figure 10,only tree beat cycles that have their correlation coeffi-cients below the threshold level, and hence are rejected.Figure 12 illustrates the accepted and rejected PCG beatcycles. The final heart-beat cycle is constructed usingonly the artefact free beat cycles as described in Section3.2. The final PCG beat signal is presented in Figure 13.It is an artefact free signal, which represents the typicalheart-beat cycle of the person from who the signal wasrecorded.

TABLE 1 – Correlation coefficients of PCG template signal with individual beat cycles.

0.9660 0.9625 0.9395 0.9505 0.9375

0.9634 0.9482 0.9387 0.9170 0.6944

0.6568 0.9181 0.8946 0.9060 0.8681

0.9194 0.9455 0.9198 0.9322 0.9323

0.9613 0.9400 0.9172 0.9359 0.9490

0.9405 0.9400 0.9278 0.9448 0.9669

0.9645 0.9394 0.9500 0.9389 0.9658

0.9485 0.9386 0.9171

νecg t( )

Figure 10 (a) Beat cycles of PCG signal of Figure 8 (a). (b) PCG template signal.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−1

−0.5

0

0.5

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

−0.5

0

0.5

1

(a)

(b)

Time (sec)

Time (sec)

0 5 10 15 20 25 30 35 400.65

0.7

0.75

0.8

0.85

0.9

0.95

1

Figure 11 Correlation coefficients for signals of Fig. 10(a) with the template signal of Fig. 10(b).

Order of Beat Cycles as they appear in PCG signal

Figure 12 (a) Accepted beat cycles, and (b) rejected beat cycles for PCG signal of Figure 8 (a).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−1

−0.5

0

0.5

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8−1

−0.5

0

0.5

1

(a)

(b)

Time (sec)

Time (sec)

Figure 13 Final PCG heart-beat signal.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

−0.5

0

0.5

1

Time (sec)

5 Conclusions

In this article a method was described which decom-poses the PCG signal into its constituent heart-beatcycles using the ECG signal. Five algorithms have beendevised to carry out this task. These algorithms are sum-marized in TABLE 2.

First the QRS peaks are detected in the ECG signal,then the false peaks are identified and removed usingthe true QRS interval detector. The third algorithm isused to isolate the cardiac cycles from the ECG signal.This is done by detecting the peak of the P-wave as thebeginning of the cardiac cycle. The starting points of thecardiac cycles are then used to decompose the PCG sig-nal into beat-cycles. A template signal is formed fromthe PCG beat cycles. The correlation coefficients of thetemplate signal with the individual beat cycles are usedto identify the artefact free heart-beat cycles. Using fre-quency domain averaging, the mean of the heart-beatcycles is found and converted back to the time domainas the final heart-beat signal. These algorithms weresuccessfully applied to real signals recorded frompatients suspected with coronary artery disease.

REFERENCES

[1] Rushmer, R. F., 1970, “Cardiovascular dynamics,”W. B. Sanders Company, Philadelphia, PA.

[2] Akay, M., Welkowitz, W., Semmlow, J. L., et al.,1991, Med & Biol. Eng. & Computing, 29, 365-372.

[3] Tinati, M. A., Bouzerdoum, A, Mazumdar, J., andMahar, L., 1997, “Time-Frequency analysis of heartsounds before and after angioplasty”, Proc. IEEEInt. Conf. on Digital Signal Processing (DSP’ 97),75-79, July, 1997, Santori Greece.

[4] Tinati, M. A., Bouzerdoum, A, Mazumdar, J., andMahar, L., 1998, “Short time Fourier analysis ofphonocardiograms before and after angioplasty”,Proc. of Third Biennial Eng. Math. and ApplicationConf., (EMAC’ 98), 495-498, July 1998, AdelaideAustralia.

[5] Benetley, P. M., Grant, P. M., and McDonnell, J. T.E., 1998, IEEE Trans. Biomed. Eng., 45, 125-128.

[6] Friensen, G. M., Jannett, T. C., Jadallah, M. A., et. al.,1990, IEEE Trans. Biomed. Eng., 37, pp. 85-98.

[7] Wood, J. C., and Barry, D. T., 1994, Med. Biol. Eng.Comput., 32, S71-S78.

[8] Zhang, X., Durand, L.-G., et. al, 1998, IEEE Trans.Biomed. Eng., 45, 972-979.

TABLE 2 – Algorithms used to decompose the PCG signal and reconstruction of an artefact-free heart-beat signal.

1) QRS peak detector.2) QRS interval detector.3) ECG beat cycle detector. 4) PCG beat cycle detector.5) Heart-beat signal reconstruction algorithm.