Libro Wiley

ELECTROCARDIOGRAM (ECG) SIGNALPROCESSING

LEIF SORNMO

Lund UniversitySweden

PABLO LAGUNA

Zaragoza UniversitySpain

1. INTRODUCTION

Signal processing today is performed in the vast majorityof systems for ECG analysis and interpretation. Theobjective of ECG signal processing is manifold and com-prises the improvement of measurement accuracy andreproducibility (when compared with manual measure-ments) and the extraction of information not readilyavailable from the signal through visual assessment. Inmany situations, the ECG is recorded during ambulatoryor strenuous conditions such that the signal is corruptedby different types of noise, sometimes originating fromanother physiological process of the body. Hence, noisereduction represents another important objective of ECGsignal processing; in fact, the waveforms of interest aresometimes so heavily masked by noise that their presencecan only be revealed once appropriate signal processinghas first been applied.

Electrocardiographic signals may be recorded on a longtimescale (i.e., several days) for the purpose of identifyingintermittently occurring disturbances in the heartrhythm. As a result, the produced ECG recording amountsto huge data sizes that quickly fill up available storagespace. Transmission of signals across public telephonenetworks is another application in which large amountsof data are involved. For both situations, data compressionis an essential operation and, consequently, represents yetanother objective of ECG signal processing.

Signal processing has contributed significantly to anew understanding of the ECG and its dynamic propertiesas expressed by changes in rhythm and beat morphology.For example, techniques have been developed that char-acterize oscillations related to the cardiovascular systemand reflected by subtle variations in heart rate. Thedetection of low-level, alternating changes in T waveamplitude is another example of oscillatory behaviorthat has been established as an indicator of increasedrisk for sudden, life-threatening arrhythmias. Neither ofthese two oscillatory signal properties can be perceived bythe naked eye from a standard ECG printout.

Common to all types of ECG analysis—whether itconcerns resting ECG interpretation, stress testing, am-bulatory monitoring, or intensive care monitoring—is abasic set of algorithms that condition the signal withrespect to different types of noise and artifacts, detectheartbeats, extract basic ECG measurements of waveamplitudes and durations, and compress the data forefficient storage or transmission; the block diagram inFig. 1 presents this set of signal processing algorithms.Although these algorithms are frequently implemented to

operate in sequential order, information on the occurrencetime of a heartbeat, as produced by the QRS detector, issometimes incorporated into the other algorithms to im-prove performance. The complexity of each algorithmvaries from application to application so that, for example,noise filtering performed in ambulatory monitoring ismuch more sophisticated than that required in restingECG analysis.

Once the information produced by the basic set ofalgorithms is available, a wide range of ECG applicationsexist where it is of interest to use signal processing forquantifying heart rhythm and beat morphology proper-ties. The signal processing associated with two suchapplications—high-resolution ECG and T wave alter-nans—are briefly described at the end of this article.The interested reader is referred to, for example, Ref. 1,where a detailed description of other ECG applicationscan be found.

2. ECG PREPROCESSING

Considerable attention has been paid to the design offilters for the purpose of removing baseline wander andpowerline interference; both types of disturbance implythe design of a narrowband filter. Removal of noisebecause of muscle activity represents another importantfiltering problem being much more difficult to handlebecause of the substantial spectral overlap between theECG and muscle noise. Muscle noise present in the ECGcan, however, be reduced whenever it is appropriate toemploy techniques that benefit from the fact that the ECGis a recurrent signal. For example, ensemble averagingtechniques can be successfully applied to time-alignedheartbeats for reduction of muscle noise.

The filtering techniques are primarily used for prepro-cessing of the signal and have as such been implementedin a wide variety of systems for ECG analysis. It should beremembered that filtering of the ECG is contextual andshould be performed only when the desired informationremains undistorted. This important insight may be ex-emplified by filtering for the removal of powerline inter-ference. Such filtering is suitable in a system for theanalysis of heart rate variability, whereas it is inappropri-

Wavedelineation

Noisefiltering

QRSdetection

Datacompression

ECG

Storage or transmission

Figure 1. Algorithms for basic ECG signal processing. Thetiming information produced by the QRS detector may be fed tothe blocks for noise filtering and data compression (indicated bygray arrows) to improve their respective performance. The outputof the upper branch is the conditioned ECG signal and relatedtemporal information, including the occurrence time of eachheartbeat and the onset and end of each wave.

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Wiley Encyclopedia of Biomedical Engineering, Copyright & 2006 John Wiley & Sons, Inc.

ate in a system for the analysis of micropotentials, as suchpotentials spectrally overlap the powerline interference.

2.1. Baseline Wander

Removal of baseline wander is required in order to mini-mize changes in beat morphology that do not have cardiacorigin, which is especially important when subtle changesin the ‘‘low-frequency’’ ST segment are analyzed for thediagnosis of ischemia, which may be observed, for exam-ple, during the course of a stress test. The frequencycontent of baseline wander is usually in the range below0.5 Hz; however, increased movement of the body duringthe latter stages of a stress test further increases thefrequency content of baseline wander (see Fig. 2). Patientsunable to perform a traditional treadmill or ergometerstress test may still be able to perform a stress test byeither sitting, running an ergometer by hand, or using aspecial rowing device. In such cases, baseline wanderrelated to motion of the arms severely distorts the ECGsignal.

The design of a linear, time-invariant, highpass filterfor removal of baseline wander involves several considera-tions, of which the most crucial are the choice of filter cut-off frequency and phase response characteristic. The cut-off frequency should obviously be chosen so that theclinical information in the ECG signal remains undis-torted while as much as possible of the baseline wanderis removed. Hence, it is essential to find the lowestfrequency component of the ECG spectrum. In general,the slowest heart rate is considered to define this parti-

cular frequency component; the PQRST waveform is at-tributed to higher frequencies. During bradycardia, theheart rate may drop to approximately 40 beats/minute,implying that the lowest frequency contained in the ECGis approximately 0.67 Hz (2). As the heart rate is notperfectly regular but always fluctuates from one beat tothe next, it is necessary to choose a slightly lower cut-offfrequency such as 0.5 Hz. If too high a cut-off frequency isemployed, the output of the highpass filter contains anunwanted, oscillatory component that is strongly corre-lated to the heart rate.

In certain situations, baseline wander becomes parti-cularly pronounced at higher heart rates such as duringthe latter stages of a stress test when the workloadincreases. Then, it may be advantageous to couple thecut-off frequency to the prevailing heart rate, rather thanto the lowest possible heart rate, to further improve base-line removal. Linear filtering with time-variable cut-offfrequency was initially suggested for offline processing ofECG signals and later extended for online use (3,4).

The other crucial design consideration is related to theproperties of the phase response and, consequently, thechoice of filter structure. Linear phase filtering is highlydesirable in order to prevent phase distortion from alter-ing various wave properties of the cardiac cycle such asthe duration of the QRS complex, the ST–T segment level,or the endpoint of the T wave. It is well-known that FIRfilters can have an exact linear phase response, providedthat the impulse response is either symmetric or antisym-metric; however, FIR designs result in high filter orders.

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Figure 2. (a) Electrocardiographic baseline wan-der because of sudden body movements. The am-plitude of the baseline wander is considerablylarger than that of the QRS complexes. (b) Aclose-up in time (10 � ) of the ECG signal framedin (a), the estimated baseline obtained by fitting acubic spline to the series of knots (indicated bydots), and the corrected ECG signal.

2 ELECTROCARDIOGRAM (ECG) SIGNAL PROCESSING

Forward-backward IIR filtering is a useful techniquethat exhibits the linear phase property. Although an IIRfilter meets a magnitude specification more easily with amuch lower filter order than does an FIR filter, it comeswith a nonlinear phase response. The use of forward-backward filtering remedies this disadvantage becausethe overall result is filtering with a zero-phase transferfunction. Implementation of such a filtering scheme in-volves three steps, namely, (1) processing of the inputsignal x(n) with an IIR filter h(n), (2) time reversal of thefilter output, and repeated processing with h(n), followedby (3) time reversal of the twice-filtered signal to producethe baseline-corrected output signal.

A useful low-complexity implementation of linear fil-tering involves sampling rate alteration (5). As the base-line wander to be removed is a narrowband component,filtering can be performed at a much lower sampling ratethan at the rate of the original ECG signal. The main stepsof this multirate approach are: (1) decimation of theoriginal signal, which includes antialising filtering, to alower sampling rate better suited to filtering, (2) lowpassfiltering to produce an estimate of the baseline wander, (3)interpolation of the estimate back to the original samplingrate, and (4) subtraction of the estimate from the originalECG so as to produce the baseline-corrected signal. Inaddition to offering low complexity, the sampling ratealteration technique has the advantage of easily accom-modating a time-variable cut-off frequency.

Yet another approach is to fit a polynomial to repre-sentative samples (‘‘knots’’) of the ECG followed by sub-traction of the polynomial. The fit is done by requiring thepolynomial to pass through knots usually being selectedwithin the isoelectric PQ segments. As the knots can onlybe located once QRS detection has been performed, thelocation of knots illustrates the feedback mechanism fromQRS detection to noise filtering displayed in Fig. 1. Poly-nomial fitting can be interpreted as time-varying filteringin which the heart rate is controlling the cut-off frequency.

2.2. Powerline Interference

Electromagnetic fields caused by a powerline represent acommon noise source in the ECG that is characterized by50 or 60 Hz sinusoidal interference, possibly accompaniedby a number of harmonics. Such narrowband noise ren-ders the analysis and interpretation of the ECG moredifficult, as the delineation of low-amplitude waveformsbecomes unreliable and spurious waveforms may be in-troduced (6). Although various precautions can be taken toreduce the effect of powerline interference, for example, byselecting a recording location with few surrounding elec-trical devices or by appropriately shielding and groundingthe location, it may still be necessary to perform signalprocessing to remove such interference. Several techni-ques have been presented for this purpose, ranging fromstraightforward linear, bandstop filtering to more ad-vanced techniques that handle variations in powerlinefrequency and suppress the influence of transients man-ifested by the occurrence of QRS complexes (5,7).

A major concern when filtering out powerline interfer-ence is the degree to which the QRS complexes influence

the output of the filter. The QRS complex acts, in fact, asan unwanted, large-amplitude impulse input to the filter.As linear, time-invariant notch filters are generally moresensitive to the presence of such impulses, powerlinefilters with a nonlinear structure may be preferable (8).In order to assure that a filter does not introduce unac-ceptable distortion, its performance should be assessed bymeans of simulated signals so that distortion can beexactly quantified.

3. QRS DETECTION

The presence of a heartbeat and its occurrence time isbasic information required in all types of ECG signalprocessing. As the QRS complex is that waveform that ismost easily discerned from the ECG, beat detection issynonymous to the detection of QRS complexes. The de-sign of a QRS detector is of crucial importance becausepoor detection performance may propagate to subsequentprocessing steps and, consequently, limit the overall per-formance of the system. Beats that remain undetectedconstitute a more severe error than do false detections; theformer type of error can be difficult to correct at a laterstage in the chain of processing algorithms, whereas,hopefully, false detections can be eliminated by, for exam-ple, performing classification of QRS morphologies.

A QRS detector must be able to detect a large numberof different QRS morphologies in order to be clinicallyuseful and able to follow sudden or gradual changes of theprevailing QRS morphology. Furthermore, the detectormust not lock onto certain types of rhythm, but treat thenext possible event as if it could occur at almost any timeafter the most recently detected beat. Several detector-critical types of noise and artifacts exist depending on theECG application of interest. The noise may be highlytransient in nature or be of a more persistent nature, asexemplified by the presence of powerline interference. Inthe case of an ECG recording with episodes containingexcessive noise, it may be necessary to exclude suchepisodes from further analysis. Figure 3 illustrates twotypes of noise that are particularly problematic in QRSdetection.

Most detectors described in the literature have beendeveloped from ad hoc reasoning and experimental in-sight. The general detector structure can be described bythe block diagram in Fig. 4 (9,10). Within such a detectorstructure, the purpose of the preprocessor is to enhancethe QRS complexes while suppressing noise and artifacts;the preprocessor is usually implemented as a linear filterfollowed by a nonlinear transformation. The output of thepreprocessor is then fed to a decision rule for detection.The purpose of each processing block is summarizedbelow.

The linear filter is designed to have bandpass charac-teristics such that the essential spectral content of theQRS complex is preserved, while unwanted ECG compo-nents such as the P and the T waves are suppressed (seeFig. 5). The center frequency of the filter varies from 10 to25 Hz and the bandwidth from 5 to 10 Hz. In contrast toother types of ECG filtering, waveform distortion is not a

ELECTROCARDIOGRAM (ECG) SIGNAL PROCESSING 3

critical issue in QRS detection. The focus is instead onimproving the SNR to achieve good detector performance.

The nonlinear transformation further enhances theQRS complex in relation to the background noise as wellas transforming each QRS complex into a single positivepeak better suited for threshold detection. The transfor-mation may consist of a memoryless operation, such asrectification or squaring of the bandpass-filtered signal, ora more complex transformation with memory. Not allpreprocessors employ a nonlinear transformation, butthe filtered signal is instead fed directly to the decisionrule.

The decision rule takes the output of the preprocessorand performs a test on whether a QRS complex is presentor not. The decision rule can be implemented as a simpleamplitude threshold procedure, but usually include addi-tional tests, for example, on reasonable waveform dura-

tion, to assure better immunity against various types ofnoise. The threshold is usually adapted to the most recentwaveform amplitudes so that gradual changes in ampli-tude can be tracked.

It is interesting to note that the above detector struc-ture can be derived from a model-based perspective byapplying maximum likelihood estimation to a statisticalmodel whose parameters describe the unknown occur-rence time y and amplitude a (5),

xðnÞ¼asðn� yÞ þ vðnÞ: ð1Þ

In this model, the observed signal x(n) is assumed to becomposed of the waveform of interest, denoted s(n), andadditive noise v(n), being a stationary, white Gaussianprocess. Although this model only accounts for a singleheartbeat, the resulting detector structure can still beused to process successive intervals of the ECG signal.

Detector performance is commonly measured in termsof the probability of a true beat being detected, denotedPD, and the probability of a false beat being detected PF.The probability of a missed beat PM is related to theprobability of detection through PD ¼ 1 � PM. These prob-abilities are usually estimated from the performancefigures that results from analyzing a database of ECGscontaining a large variety of QRS morphologies and noisetypes. The estimators are defined by ratios that includethe number of correctly detected QRS complexes ND, thenumber of false alarms NF, and the number of missedbeats NM [i.e., PF ¼NF=ðND þNFÞ andPD ¼ND=ðND þNMÞ]. As each probability is determinedfor each of the ECG recordings in the database, it iscustomary to compute a ‘‘gross’’ average of the estimatesin order to reflect the overall performance of the QRSdetector.

The numbers ND, NF, and NM can only be computedonce the database has been subjected to manual annota-tion. Such annotation is typically a laborious process,involving one or several skilled ECG readers, and leads

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QRS complex

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Figure 5. Power spectrum of the P wave, QRS complex, and Twave. The diagram serves as a rough guide to where the spectralcomponents are located; large variations exist between beats ofdifferent lead, origin, and subjects.

Preprocessor

Linear filtering

Nonlinear transformation

Decisionrule

x (n) �1 �2, . . ., Figure 4. Block diagram of a commonly usedQRS detector structure. The input is the ECGsignal, and the output y1; y2; . . . is a series ofoccurrence times of the detected QRS complexes.

Figure 3. Examples of noise being proble-matic in QRS detection caused by electrodemotion artifacts (top) and electromyographicnoise (bottom).


to every QRS complex being assigned its correct occur-rence time yi. A beat is said to have been detected whenthe difference between the estimated occurrence time yjand the annotation time yi is within a certain matchingwindow defined by Dy. A false detection is produced whenyj is located at a distance larger than Dy from any yi, and abeat is considered to have been missed when no detectionoccurs closer than Dy to yi (Fig. 6).

As indicated by its name, the QRS detector is designedto detect heartbeats, while not producing occurrence timesof the QRS complexes with high temporal resolution.Hence, it may be necessary to improve the resolutionusing an algorithm that performs time alignment of thedetected beats. Such alignment reduces, for example, theproblem of smearing that may occur when computing theensemble average of several beats.

4. WAVE DELINEATION

Once the QRS complex has been detected, the T wave canbe analyzed because ventricular repolarization alwaysfollows depolarization. Conversely, the P wave does notlend itself as easily to analysis because atrial and ventri-cular rhythms may be independent of each other. In the

vast majority of cases, however, atrial and ventricularrhythms are associated so that P wave detection may bebased on a backward search in time, beginning at the QRScomplex and ending at the end of the preceding T wave.

A method of wave delineation determines the bound-aries of each wave within the PQRST complex so that,with the resulting time instants, different wave durationscan be computed (see Fig. 7). Once a wave has beendelineated, other measures characterizing the wave,such as amplitude and morphology, can be easily com-puted. Such a method must also be able to detect when acertain wave is absent; this situation is commonly en-countered because, for example, only the R wave or the Swave is present in certain leads or pathologies.

The classic definition of a wave boundary is the timeinstant at which the wave crosses a certain amplitudethreshold level. Unfortunately, this definition is not well-suited for the common situation when the ECG containsbaseline wander, and, therefore, this definition is rarelyapplied in practice. Instead, many methods for wavedelineation exploit the change in slope that occurs at aboundary to avoid the problems because of low-frequencynoise. Hence, the first derivative of the signal is calculatedand analyzed with respect to zero crossings and extreme

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Figure 6. Comparison of the QRS detector out-put to the manual annotations, in this caseindicating that all beats are correctly detectedexcept the beat occurring at y6, which is missed.A noise wave is falsely detected at y6. Thematching window, with length Dy, is displayedfor the beat at y3 but is, of course, equallyapplicable to the other beats.

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-2Figure 7. Wave definitions of the cardiac cycle. Theonset and end of the P wave, the QRS complex, andthe T wave, respectively, are indicated with dottedlines.


values. This type of delineation is illustrated by Fig. 8where the aim is to find the end of the S wave; the otherwave boundaries of the PQRST complex can be found in asimilar way. In this example, the search for the endpointstarts when the steepest upslope of the S wave occurs andcontinues until the derivative of the signal falls below acertain threshold value. The time instant at which thelevel is crossed defines the QRS end. As the above searchprocedure is based on the assumption that each of thedifferent waves is present, it is necessary to first establishwhich waves are absent to ensure meaningful delineation.Such wave detection is usually done by analyzing thepattern of successive peak amplitudes and interpeak

distances of the differentiated signal in an interval posi-tioned around the QRS complex.

The threshold level that determines the position of awave boundary may be fixed and chosen with reference toa slope value that is representative of the boundary to bedetermined. Alternatively, the threshold may be related tosignal morphology so that its level is set to a certainpercentage of the maximum slope (11). The latter type ofthresholding is more suggestive of a cardiologist’s ap-proach to delineation because the boundaries of a large-amplitude wave with steep slopes and a low-amplitudewave with less steep slopes will occur at about the sameposition.

In noisy signals, wave delineation from the differen-tiated signal performs poorly because an already lowsignal amplitude at the wave boundary is disturbed bynoise. The performance can, to a certain degree, be im-proved by combining signal differentiation with lowpassfiltering to attenuate high-frequency noise. The cut-offfrequency of the lowpass filter may be fixed or, better,adapted to the spectral content of the wave to be deli-neated (12). For example, delineation of the QRS complexshould be based on a filter with a higher cut-off frequencythan the filter used to find the end of the T wave, reflectingthe fact that the T wave contains much less high-fre-quency components (see Fig. 9).

The threshold levels, or the shapes of the waveformtemplates, should be chosen such that the resultingdelineation agrees with those obtained by cardiologicalexpertise. Following training of the delineation method toobtain suitable parameter values, its performance shouldbe evaluated on a database with P, QRS, and T waveboundaries having been manually annotated (13,14). De-lineation performance is described in terms of the meanand standard deviation of the error between the bound-aries produced by the method and the experts (15,16). It is

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Figure 9. Wave delineation based on lowpass dif-ferentiated signals. The original signal (top) isdifferentiated and lowpass-filtered to yield theQRS onset and end (middle) and the T wave end(bottom). The threshold level that determines eachwave boundary is indicated by the horizontal line. Ahigher cut-off frequency of the lowpass differentiatorwas used for QRS complex delineation than for theT wave.

ECG

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Figure 8. Determination of the QRS end using slope informa-tion. The QRS end is the time at which the differentiated signalcrosses a threshold after the maximum slope has occurred. Thethreshold level is usually expressed as a percentage of themaximum slope.


important to realize that a zero value of the standarddeviation can never be attained because a certain disper-sion will always exist even among experts. However, amethod’s performance is judged as satisfactory when thedispersion is approximately on the same order as thatamong experts (17).

Wave delineation is particularly problematic whendetermining the end of the T wave, which is often char-acterized by a very gradual transition to the isoelectricline of the ECG, see, for example, the T wave in Fig. 9. Infact, its delineation is problematic even among cardiolo-gists, and differences between cardiologists may occasion-ally approach as much as 100 ms (17). Despite thesedifficulties, the end of the T wave is an extremely impor-tant boundary, required when computing the total dura-tion of ventricular depolarization and repolarization. As aresult of the importance of this measurement, severaltechniques have been developed for the purpose of ro-bustly determining the T wave end (18–20). Multiresolu-tion signal analysis of the ECG using the dyadic wavelettransform, in which the signal is analyzed at differenttime resolutions, has proven to be well-suited for T wavedelineation. By first determining a robust, but prelimin-ary, boundary position from a smooth approximation ofthe original signal, the position can be refined by analyz-ing the properties of better approximations in an intervalpositioned around the preliminary boundary. The wavelet-based approach can, with an appropriate choice of waveletfunction, be viewed as a filter bank of lowpass differentia-tors with varying cut-off frequencies. Evaluating the per-formance of the methods based on either lowpassdifferentiation or wavelet analysis, the latter method hasbeen found to produce T wave ends in better agreementwith those produced by cardiologists (21).

5. DATA COMPRESSION

As a wide range of clinical examinations involve therecording of ECG signals, huge amounts of data areproduced not only for immediate scrutiny, but also forstorage in a database for future retrieval and review. It iswell-known that the availability of one or several previousECG recordings improves diagnostic accuracy of variouscardiac disorders, including myocardial infarction. Today,such serial ECG comparison encompasses short-durationrecordings acquired during rest, but may in the futureencompass long signals, for example, acquired duringstress testing or ambulatory monitoring. Although harddisk technology has undergone dramatic improvements inrecent years, increased disk size is paralleled by the ever-increasing wish of physicians to store more information.In particular, the inclusion of additional ECG leads, theuse of higher sampling rates and finer amplitude resolu-tion, the inclusion of other, noncardiac signals such asblood pressure and respiration, and so on, lead to rapidlyincreasing demands on disk size. It is evident that efficientmethods of data compression will be required for a longtime to come.

Another driving force behind the development of meth-ods for data compression is the transmission of ECG

signals across public telephone networks, cellular net-works, intrahospital networks, and wireless communica-tion systems. Such data transmission may be initiatedfrom an ambulance or a patient’s home to the hospital andhas, among other things, been found to be valuable forearly diagnosis of an infarct.

An ECG signal exhibits a certain amount of redun-dancy, as manifested by correlation between adjacentsamples, the recurrence of heartbeats with similar mor-phology, and the relative resemblance between differentleads. Considerable savings can be achieved in terms ofstorage capacity and transmission time by exploiting thedifferent types of redundancy so that each sample can berepresented by fewer bits than in the original signal.Hence, the data compression algorithm should accountfor the fact that the signal contains recurrent heartbeats,often with similar morphology, and that the signal is,almost invariably, a multilead recording. Equally impor-tant, it must account for the fact that both small- andlarge-amplitude waveforms are present in the signal,carrying important diagnostic information, whereas theisoelectric line contains negligible information.

The overall goal is to represent a signal as accurately aspossible using the fewest number of bits, by applyingeither lossless compression, in which the reconstructedsignal is an exact replica of the original signal, or lossycompression, in which the reconstructed signal is allowedto differ from the original signal. With lossy compression,a certain amount of distortion has to be accepted in thereconstructed signal, although the distortion must remainsmall enough not to modify the diagnostic content of theECG. For both types of compression, it may be necessaryto perform noise filtering of the ECG signal before it issubjected to data compression.

The outcome of data compression is critically depen-dent on the sampling rate and the number of bits used torepresent each sample of the original signal. For example,a signal acquired at a low sampling rate contains lessredundancy than one acquired at a high rate; as a result,the compression ratio, defined as the bit size of theoriginal signal divided by the bit size of the compressedsignal, is lower for a signal acquired at a lower samplingrate. Other factors that influence the outcome of datacompression are the signal bandwidth, the number ofleads, and the noise level. For example, a signal sampledat a rate of 500 Hz but bandlimited to 50 Hz is associatedwith a better compression ratio than is a signal bandlim-ited to the Nyquist frequency of 250 Hz. Consequently, it isimperative that any comparison of performance for differ-ent compression methods is based on identical values ofthe system parameters.

Methods for data compression may be categorizedaccording to the following three main types of dataredundancy found in ECG recordings:

* Intersample or, equivalently, intrabeat redundancy isexploited by employing either direct or transform-based methods.

* Interbeat redundancy is manifested, within eachlead, by successive, similar-looking heartbeats.


Hence, their occurrence times must be determined bya QRS detector before interbeat redundancy can beexploited.

* Interlead redundancy is because of the fundamentalfact that a heartbeat is ‘‘viewed’’ concurrently indifferent leads. Therefore, waveforms exhibit inter-lead correlation that depend on the distance betweenelectrodes on the body surface.

It should be noted that many methods of data compressionhave been designed to solely deal with the first type ofredundancy, although methods that deal with all threetypes combined are becoming increasingly common. Theblock diagram in Fig. 10 presents the two main steps indata compression. In the first step, the redundancy of theoriginal signal is reduced so that a more compact signalrepresentation is obtained. The output data is then fed toan encoder whose purpose is to produce an efficientlycoded bit stream suitable for storage or transmission.

5.1. Direct Methods for Data Compression

Direct methods operate in the time domain by extracting aset of K ‘‘significant’’ samples x(nk) from the original signalx(n) such that

ðn; xðnÞÞ;n¼ 0; . . . ;N � 1 ! ðnk; xðnkÞÞ;

k¼ 0; . . . ;K � 1;ð2Þ

where KoN. The resulting subset of K samples is retainedfor data compression, and the other samples are dis-carded. Reconstruction of the samples between the sig-nificant samples is achieved by interpolation using thefollowing general expression:

~xðnÞ¼

xðnÞ; n¼n0; . . . ;nK�1;

fn0 ;n1 ðnÞ; n¼n0 þ 1; . . . ;n1 � 1;

..

. ...

fnK�2 ;nK�1ðnÞ; n¼nK�2 þ 1; . . . ;nK�1 � 1:

8>>>>>><>>>>>>:

ð3Þ

The first and last significant samples of the signal x(n) areusually chosen to be n0 ¼ 0 and nK�1 ¼N � 1, respectively.The interpolating function fnk�1;nk

ðnÞ usually has a poly-nomial form of low order, approximating the signal withzero- or first-order polynomials, for example, by a se-quence of plateaus or straight lines. First-order (linear)

interpolation has become especially popular because thesignal can be completely reconstructed from the set ofsignificant samples x(nk). Although more advanced inter-polating functions can be used (e.g., rational or trigono-metric functions), additional parameters need to be storedas side information to reconstruct the signal. As a result,improvements in performance may still be lost because ofthe additional cost of representing the interpolating func-tion.

The selection of significant samples can be viewed as an‘‘intelligent’’ subsampling of the signal in which the iso-electric segments are approximated by a small number ofsamples, whereas the QRS complex is much more denselysampled so that the essential information contained in theECG is preserved. A simplistic approach would be to selectthe significant samples from among the turning points ofthe signal (i.e., its peaks and valleys); however, the errorbetween the original and reconstructed signal may attimes be quite considerable. Therefore, the selection ofsignificant samples is usually based on a criterion assur-ing that the reconstruction error remains within a certaintolerance. The selection process can be performed sequen-tially so that the next significant sample is selected withreference to the properties of preceding signal properties.Alternatively, a larger block of samples can be processedat the same time so that significant samples are selectedwith reference to the enclosing signal properties. Althoughthe block-based approach can be expected to yield betterperformance, it is less suitable for real-time processing.

The performance of direct methods is particularlyinfluenced by the noise level of the ECG, as the numberof significant samples required to meet the maximal errortolerance increases as the noise level increases. Accord-ingly, poorer compression ratios are achieved at high noiselevels. Although direct methods work satisfactorily whenprocessing ECGs acquired during resting conditions, thevery idea of selecting significant samples can be ques-tioned in noisy recordings.

AZTEC and SAPA are two well-known examples ofdirect methods for data compression (22,23); several var-iations and improvements on these two methods havebeen suggested over the years (24,25).

5.2. Transform-Based Data Compression

Transform-based compression assumes that a compactsignal representation exists in terms of the coefficients of

Encoderintersampleredundancy

interlead redundancy

Side information

Storage or transmission

Data coefficients

Further processing

Noise filtering

QRSdetection

ECG

interbeat redundancy

Reduction of

Figure 10. Data compression of ECG signals.The output of the block performing redundancyreduction is a sequence of data coefficients. Theoutput may also include side information, which,for example, describes the set of basis functionsused for computing the data coefficients. Theencoder translates the input into an efficientlycoded bit stream.


a truncated orthonormal expansion,

x¼XNk¼ 1

wkuk; ð4Þ

where x denotes a column vector containing N ECGsamples, wk the coefficients, and uk the basis functions.The basic idea is to obtain an estimate of x by truncation ofthe complete series expansion in Equation 4 so that only Kout of the N terms are included. The coefficients w1; . . . ;wK

are retained for storage or transmission, hopefully provid-ing adequate signal reconstruction, whereas the remain-ing (N�K) coefficients, being near zero, are discarded.The coefficients wk are obtained by correlating x with eachof the basis functions (i.e., by computing the inner productwk ¼uT

kx). Hence, the subset of K coefficients constitutesthe information to be compressed, and from which thesignal is later reconstructed. If the basis functions are apriori unknown, the set of coefficients must be supple-mented with the samples of the required basis functions.Following data compression, the reconstructed signal ~xK

is obtained from

~xK ¼XKk¼ 1

wkuk: ð5Þ

In contrast to most direct methods, transform-basedmethods require that the ECG first be partitioned into aseries of successive blocks, where each block is subse-quently subjected to data compression. The signal may bepartitioned so that each block contains one heartbeat, and,therefore, QRS detection must always precede such com-pression methods. Each block is positioned around theQRS complex, starting at a fixed distance before the QRSthat includes the P wave and extending beyond the T waveend to the beginning of the next beat. As the heart rate isnot constant, the distance by which the block extends afterthe QRS complex is adapted to the prevailing heart rate.

A fixed number of basis functions are often consideredfor data compression, with the value of K being chosenfrom considerations concerning overall performance ex-pressed in terms of compression ratio and reconstructionerror. Although serving as an important guideline to thechoice of K, such an approach may occasionally produce anunacceptable representation of certain beat morphologies.As the loss of morphologic detail causes incorrect inter-pretation of the ECG, the choice of K can be adapted forevery beat to the properties of the reconstruction errorðx� ~xK Þ (26). For example, the value of K may be chosensuch that the RMS value of the reconstruction error doesnot exceed the error tolerance e or, more demanding, thatnone of the reconstruction errors of the entire blockexceeds e. It is evident that the value of K sometimesbecomes much larger than the value suggested based onconsiderations on overall performance; however, it some-times also becomes smaller. By letting K be variable, onecan fully control the quality of the reconstructed signal,while also being forced to increase the amount of side

information because one must keep track of the value of Kfor every data block.

A crucial question to address is which set of basisfunctions to choose for data compression. It is well-knownthat the Karhunen–Loeve (KL) expansion is optimal inthat it minimizes the MSE of approximation, and, there-fore, the KL basis functions have become popular (26–28).The basis functions are obtained as eigenvectors of thecorrelation matrix Rx that is determined from one orseveral datasets. The basis functions are labeled ‘‘univer-sal,’’ when the dataset originates from many patients, or‘‘subject-specific,’’ when the data originates from a singlerecording. Although it is rarely necessary to store ortransmit universal basis functions, subject-specific func-tions need to be part of the side information. The use ofuniversal KL basis functions is illustrated by Fig. 11.

The above-mentioned compression methods are de-signed to reduce intersample redundancy of the ECG,while not dealing with the fact that successive beats oftenhave almost identical morphology. A simplistic approachto dealing with interbeat redundancy is to use the pre-vious beat to predict the next, and to only code thedifference. By repeating the prediction for all beats, adifference signal is produced whose magnitude is muchsmaller than the original one, thus requiring fewer bits forits representation. A major drawback of the simple ‘‘pre-vious-beat’’ predictor is its vulnerability to noise, a prop-erty that can be improved by using a predictor based onaveraging of the most recent beats (29).

A fundamental assumption of the beat subtractionapproach is that the beats, used to predict the next beat,exhibit similar morphology. To ensure this similarity, it isnecessary to first categorize the beats according to theirrespective morphology so that several average beats canbe initialized. A straightforward approach to such beatcategorization (clustering) would be to consider the energyof the prediction error

Pn e

2i ðnÞ in a beat interval: A new

average beat is initialized if the energy exceeds a certainthreshold, unless the current beat matches an alreadyexisting average beat category.

As considerable correlation exists between differentECG leads, data compression of multilead ECGs wouldbenefit from exploring interlead redundancy rather thanjust applying the previously described methods to one leadat a time. Direct methods for single-lead data compressionhave turned out to be not easily extended to multileadcompression, although a few adaptations have been pre-sented. With transform-based methods, interlead correla-tion may be dealt with in two steps, namely, atransformation that concentrates the signal energy spreadover the total number of leads into a few leads, followed bycompression of each transformed lead using a single-leadtechnique (5).

5.3. Performance Evaluation

The compression ratio PCR is a crucial measure whenevaluating the performance of data compression methods.It is defined as the ratio between the number of bitsrequired to represent the original signal x(n) and thenumber of bits required to represent the compressed


signal ~xðnÞ. Another crucial measure is the bit rate PBR,defined as the average number of bits required per secondto represent the ECG, and is, in contrast to PCR, indepen-dent of sampling rate and word length. However, none ofthese two measures provide sufficient detail on the per-formance when lossy data compression is used becausethey do not reflect the distortion of the reconstructedsignal. Accordingly, an excellent PCR or PBR may beachieved at the expense of a severely distorted signal,and, therefore, an essential aspect of data compression isto define complementary performance measures that re-flect the accuracy with which the diagnostic informationin the original ECG signal is preserved.

The percentage root mean-square difference (PRD) is afrequently employed distortion measure that quantifiesthe error between the original signal x(n) and the recon-structed ~xðnÞ, defined by

PPRD ¼ 100 �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN�1

n¼ 0

ðxðnÞ � ~xðnÞÞ2,XN�1

n¼ 0

x2ðnÞ;

vuut ð6Þ

where it is assumed that the mean value of x(n) has beensubtracted prior to data compression. The measure PPRD

has become popular because of its computational simpli-city and the ease with which distortion can be comparedfrom one signal to another. However, PPRD has certainflaws that make it unsuitable for performance evaluation.For example, compression of ECGs with large-amplitudeQRS complexes results in less distortion than does com-pression of an ECG with small-amplitude QRS complexes,even if the squared error ðxðnÞ � ~xðnÞÞ2 is identical in bothcases. This disadvantage can, to a certain degree, bemitigated by replacing the energy normalization in PPRD

with a fixed normalization so that the modified measure,denoted PRMS, describes the error in absolute terms,

PRMS ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

XN�1

n¼ 0

ðxðnÞ � ~xðnÞÞ2:

vuut ð7Þ

This measure is somewhat more suggestive of diagnos-tic ECG interpretation where criteria are expressed asmillivolt wave amplitudes rather than in percentages ofsignal energy. However, care should be exercised whennoisy signals are compressed because PRMS then wouldrepresent the noise discarded by the compression method,as measured by the difference between x(n) and ~xðnÞ,rather than by the distortion of the ECG.

Performance is often presented as a rate distortioncurve where signal distortion is displayed as a functionof PBR. Such a curve is shown in Fig. 12 for transform-based data compression (based on the KL transform), withPRMS as the chosen distortion measure. With this type ofcurve, the operating point of a compression method can beeasily defined, specifying the bit rate at which acceptabledistortion of the reconstructed signal is achieved. By

0 0.5 1 1.5 2

-2

-1

0

1

Time (s)

Residual ECG

Am

plitu

de (

mV

)

Original & reconstructed ECG

0 10 20 30

-2

0

2

k

wk

Universal KLT

0 1 2 3 4Time (s)

KL

basi

s fu

nctio

n

λ1 = 0.465

λ2 = 0.247

λ3 = 0.080

λ4 = 0.046

λ5 = 0.039

λ6 = 0.024

Figure 11. Transform-based data compression usingthe KL basis functions derived from a huge databaseincluding thousands of ECGs from different subjects.The basis functions uk and associated eigenvalues lkare presented, as are the 30 largest coefficients of theoriginal ECG’s KL transform. The ECGs are recon-structed with K ¼8.

0 100 200 300 400 5000

5

10

15

20

P RM

S (

µV)

PBR (bits/second)

Figure 12. Rate distortion curves for data compression based onthe KL transform, where account is taken of the required sideinformation when calculating PBR. The results were obtainedfrom 10 minutes of ECG data, selected from the MIT–BIH data-base.


requiring the distortion to be low, for example, a PRMS ofonly 12 mV, it is tempting to believe that the diagnosticinformation in the reconstructed signal is preserved.However, both PPRD and PRMS suffer from an inability toreflect loss of diagnostic information; instead, all samplesare treated equally whether located in the QRS complex orin the uninformative isoelectric segment. Although theloss of a tiny Q wave in the reconstructed signal essen-tially goes unreflected, the absence of a Q wave representsan essential loss from a diagnostic point of view when, forexample, diagnosing myocardial infarction.

The weighted diagnostic distortion (WDD) measurePWDD is one of the few mathematically defined measuresthat addresses the limitations of distortion measuresbased on the error between samples of the original andreconstructed signal (30). The measure PWDD is compositebecause it involves various wave parameters essential toECG interpretation, especially wave amplitudes and dura-tions of the PQRST complex. Assuming that measure-ments of the kth ECG parameter have been obtainedfrom the original and reconstructed signals, denoted bkand ~bk respectively, a normalized error Dbk can be defined,

Dbk ¼jbk � ~bkj

maxðjbkj; j ~bkjÞ; ð8Þ

which is constrained to the interval 0oDbk � 1; it isassumed that bk and ~bk have nonzero values. Whenseveral beats are available for measurement, the resultingvalues of Dbk are averaged before further processing isdone. For a set of P different parameters on amplitude andduration, the WDD performance measure is defined as

PWDD ¼ 100 �XPk¼ 1

akðDbkÞ2

,XPk¼1

ak; ð9Þ

where the coefficients ak make it possible to weight theparameter measurement errors Dbk in relation to theiroverall significance. Such weighting can be used to em-phasize measurements of particular significance, such asST segment measurements in ischemia monitoring.

An important aspect of performance evaluation is, ofcourse, the choice of ECG database. As the performance ofa method depends on the noise level, the evaluationshould be based on data representative of the applicationin question. The amount of ectopic beats and arrhythmiasare other factors that, to various degrees, influence theevaluation outcome.

6. CLUSTERING OF BEAT MORPHOLOGIES

Feature extraction may be performed for the purpose ofcharacterizing the morphology of a QRS complex.Although the durations and amplitudes that result fromwave delineation contain important diagnostic informa-tion, additional features are required to reliably groupbeats with similar morphology into the same cluster. Oneapproach to feature extraction is to derive a set of ‘‘heur-istic’’ features that, for example, describe the area, polar-

ity, and slopes of the waves. Another, more robust,approach is to make use of the coefficients that resultfrom the correlation of each beat with either a set ofpredefined orthonormal basis functions or a set of QRStemplates. Based on the set of extracted features, cluster-ing of QRS morphologies can be performed. In its simplestform, clustering may be used to single out beats thatdeviate from the predominant morphology, which isusually that belonging to the normal sinus beat (see Fig.13). Once this is done, beats belonging to the ‘‘sinuscluster’’ can be subjected to, for example, ensemble aver-aging or heart rate variability analysis. In other situa-tions, reason to study the entire range of beat clustersexists. As clustering does not assign a label with aphysiological meaning to a beat, it may be necessary toclassify the beats according to their cardiac origin.

Clustering is based on a set of features, contained in thecolumn vector pi, which describe waveform morphologyand, possibly, also rhythm properties of the current beat.In its simplest form, pi contains time-domain samples ofthe QRS samples, and is often used in combination withthe cross-correlation coefficient ril as a measure of patternsimilarity (31–34),

ril ¼pTi ll

k pi k2k ll k2; ð10Þ

where 8 � 82 denotes the Euclidean norm. The columnvector ll defines the mean of the lth beat cluster (and iscommonly referred to as a ‘‘template’’ beat). The ECGsamples of the current beat are usually bandpass-filteredbefore clustering so that the influence of baseline wanderand EMG noise is reduced. A straightforward approach toclustering is given by assigning the ith beat to the clusterfor which the highest correlation coefficient is achieved,provided that it exceeds a certain minimum threshold; if itdoes not, a new cluster is created. More advanced ap-proaches to clustering have recently been presented thatmake use of artificial neural networks, see, for example,Refs. 35 and 36.

Using the cross-correlation coefficient as a measure ofsimilarity, it is easily shown that clustering becomesinvariant to changes in QRS amplitude. Amplitude invar-iance is acceptable in certain types of ECG analysis wherethe information in demand is restricted to the timing ofsinus beats. However, invariance to amplitude changesexceeding those induced by respiration is undesirablewhen the purpose is to average the sinus beats of a clusterfor noise reduction as required, for example, in high-resolution ECG analysis; averaging of similar-shapedbeats with widely differing QRS amplitudes produces anonrepresentative ensemble average.

The basis function representation, previously consid-ered for data compression, has also been considered forfeature extraction when clustering heartbeats, often ex-pressed in terms of the Karhunen–Loeve or the Hermitebasis functions (35–39). In such cases, the coefficients ofthe series expansion that correspond to the most impor-tant basis functions would define the feature vector pi.


Improved accuracy of the occurrence time is intimatelyrelated to the clustering process because the current beatpi can be optimally aligned in time to ll when similarity ismeasured. The availability of morphologic informationthrough ll may be used to improve the accuracy of thetime, originally determined by the QRS detector thatoperates at a lower temporal resolution (and determinedwithout considering the morphology of previous beats).When clustering is based on the cross-correlation coeffi-cient, the samples of pi are correlated to the mean of thecluster ll and shifted in time until the highest cross-correlation value is obtained; the resulting value is usedfor cluster assignment. It is important to realize thatomission of the time alignment operation leads to theinitiation of undesired clusters.

7. ECG SIGNAL PROCESSING IN APPLICATIONS

Numerous types of ECG analysis have been developedthat draw on the ECG signal processing so far presented.It is outside the scope of this text to provide a comprehen-sive description of such types of analysis. Instead, thisarticle is concluded by briefly mentioning two types ofanalyses that both exploit low-level activities of the ECG,aiming either at characterizing static properties of theECG (‘‘high-resolution ECG’’) or dynamic properties (‘‘Twave alternans’’).

7.1. High-Resolution ECG

For many years, the interpretation of resting ECGs wasbased on measurements derived from waves whose am-plitude were at least several tens of microvolts; waveswith smaller amplitudes were ignored because these werealmost always caused by noise. This limitation was, how-ever, removed with the advent of the high-resolution ECGwith which it became possible to detect signals on the

order of 1mV thanks to signal averaging techniques. Thehigh-resolution ECG has helped unlock novel informationand has demonstrated that signal processing for thepurpose of noise reduction is a clinically viable technique.The acquisition procedure is usually the same as for theresting ECG, except that the signal is recorded over anextended time period so that a sufficiently low noise levelis attained by averaging.

Different subintervals of the cardiac cycle have re-ceived special attention in high-resolution ECG analysis,and low-level signals have been considered in connectionwith (1) the bundle of His that depolarizes during the PRsegment (40,41), (2) the terminal part of the QRS complexand the ST segment where so-called ‘‘late potentials’’ maybe present (42–44), (3) intra-QRS potentials (45,46), and(4) the P wave (47,48). Of these four applications, theanalysis of late potentials has received the most wide-spread clinical attention. Late potentials may be found inpatients with myocardial infarction where ventriculardepolarization can terminate many milliseconds afterthe end of the QRS complex (Fig. 14). This prolongationis because of delayed and fragmented depolarization of thecells in the myocardium that surround the dead region(scarred tissue) caused by infarction; the conduction cap-ability of the bordering cells is severely impaired byinfarction. Many studies have demonstrated the impor-tance of late potentials when, for example, identifyingpostinfarct patients at high risk of future life-threateningarrhythmias, see, for example, Ref. 49.

The high-resolution ECG rests on the assumption thatthe signal to be estimated has a fixed beat-to-beat mor-phology. As the high-resolution ECG is often expected tocontain high-frequency components up to at least 250 Hz,the sampling rate is at least 1 kHz. It is essential that theoccurrence time of each beat (the ‘‘fiducial point’’) isaccurately determined from each individual beat before

0 2 4 6 8 10-7

-6

-5

-4

-3

-2

-1

0

1

2

31

1

2

2

4

4

5

5

6

6

7

7

9

9

3

3

8

8

Cluster #1

Cluster #2

Time (seconds)

Am

plitu

de (

mV

)

Figure 13. Clustering of an ECG that contains twodifferent beat morphologies. Cluster 1 contains the sinusbeats, whereas cluster 2 contains the two ectopic beats.


ensemble averaging to avoid smearing of low-amplitude,high-frequency components of the ECG.

Ensemble averaging is related to the following signalmodel in the ith beat xi is assumed to be additivelycomposed of a deterministic signal component s andrandom noise vi, which is asynchronous to cardiac activ-ity,

xi ¼ sþvi; i¼1; . . . ;M: ð11Þ

It is assumed that only sinus beats are modeled (i.e., beatsof ectopic origin have already been sorted out by means ofsome technique for morphologic clustering). Representingthe entire ensemble with the matrix X,

X¼ ½x1 x2 � � �xM�; ð12Þ

where each column vector contains one beat, an estimateof the signal s is obtained by computing the ensembleaverage,

s¼1

MXw; ð13Þ

where w denotes a weight vector whose elements are allequal to one. When the noise is uncorrelated from beat tobeat and with a standard deviation that remains constantthroughout the ensemble, the noise level is reduced by afactor

ffiffiffiffiffiM

p. In situations when the noise level varies over

time, it is instead preferable to use weighted averaging inwhich each weight of w is inversely proportional to thenoise level (5).

Once a low-noise ECG signal is produced by ensembleaveraging, the late potential components can be eluci-dated from the terminal part of the QRS complex and theST segment using linear, time-invariant highpass filter-ing. In order to avoid that filter ringing may obscure thelow-amplitude components, the ensemble average s isfiltered backward in time rather than forward as iscustomary. The detection of late potentials is commonlyaccomplished by first determining the time instant whenthe signal activity ends, involving a threshold procedurethat relates to the residual noise level of s (44); then, the

amplitude of the interval immediately preceding thedetermined endpoint must be sufficiently low for a detec-tion to occur.

7.2. T-Wave Alternans

Tiny beat-to-beat alternations in T wave morphology arerelated to myocardial ischemia and have been founduseful as a predictor of malignant ventricular arrhyth-mias that often lead to sudden cardiac death (50,51). Themorphologic alternations follow a flip-flop pattern inwhich every other T wave has the same morphology (seeFig. 15). The alternans is often a low-amplitude phenom-enon in the microvolt range; therefore, it cannot be easilyperceived by the naked eye from a standard ECG printout,but requires signal processing techniques for its detectionand quantification (52).

Similar to the detection of late potentials, it is crucialthat successive T waves are properly aligned in time sothat the alternans relates to underlying physiology ratherthan to inaccurate alignment. On the other hand, ensem-ble averaging cannot play a central role in detecting Twave alternans as such an operation would obliterate thealternating behavior. Of the several detection methodsthat have been devised, the most popular detectors arebased on the following statistical model of the T wave. At acertain predefined time instant within each T wave, theobserved amplitude x(i) is modeled by

xðiÞ¼Aþað�1Þi þ vðiÞ; i¼ 1; . . . ;M; ð14Þ

where i denotes beat index, M denotes total number ofbeats, A denotes T wave amplitude, and a denotes alter-nans amplitude (although it is 2a that has physiologicalsignificance because it describes the difference betweentwo beats). The additive noise v(i) is assumed to be a zero-mean, random process that is stationary and white. As theamplitude A does not convey any information on alter-nans, its influence is typically removed from x(i) bysubtracting the mean value �x of xð1Þ; . . . ; xðMÞ so that thecorrected signal yðiÞ¼ xðiÞ � �x is instead analyzed.

By applying statistical detection theory to the model inEquation 14 under the assumption that the noise v(i)

X

X

Z

Y

Y

Z

0 200 400 600 800Time (ms)

360 400 440 480 520Time (ms)

0

10

20

30

40

Am

plitu

de (

mic

rovo

lts)

(a) (b)

Figure 14. (a) The high-resolution ECG ob-tained by signal averaging the orthogonal X, Y,and Z leads. (b) The terminal part of the QRScomplex and the ST segment (i.e., the intervalshaded gray in (a), is magnified 10 times inamplitude to better display the small undula-tions known as late potentials).


obeys a Gaussian probability density function, it can beshown that the optimal detector performs a correlationbetween y(i) and the alternating pattern (� 1)i, for exam-ple:

TG ¼XMi¼ 1

yðiÞð�1Þi !2

: ð15Þ

The M successive T waves are judged to contain alternanswhen the decision statistic TG exceeds a certain thresholdvalue. Interestingly, the detector in Equation 15 can beinterpreted in terms of power spectral analysis because TG

is exactly the periodogram computed for the highestnormalized frequency at 0.5. In fact, one of the mostpopular detectors was heuristically developed from theobservation that alternans is manifested by an increase inspectral power at 0.5 (53); alternans was detected whenthe power at this frequency exceeded a certain factor ofthe surrounding spectral power.

The Gaussian detector in Equation 15 is sensitive tothe presence of outliers in y(i) caused by, for example,baseline wander and ectopic beats. By assuming insteadthat the noise v(i) obeys a Laplacian probability densityfunction (i.e., with heavier tails than the Gaussian func-tion), the optimal detector becomes more robust to im-pulsive noise. In the Laplacian detector, the followingdecision statistic is compared with a threshold (52),

TL ¼XMi¼ 1

ðjyðiÞð�1Þij � jyðiÞð�1Þi � ajÞ; ð16Þ

where a denotes the maximum likelihood estimator of thealternans amplitude, being defined by

a¼medianðyð1Þ � ð�1Þ; yð2Þ � 1; . . . ; yðMÞ � ð�1ÞMÞ: ð17Þ

It is evident from Equation 16 that the Laplacian detectorputs less emphasis on large-amplitude values in y(i) thandoes the Gaussian detector in Equation 15, replacing thesquaring operation with absolute values. Moreover, thealternans amplitude a is robustly estimated by computingthe median of the signal yðiÞð�1Þi.

Although the above detectors are designed to process asingle interval, they can be easily extended to processintervals defined by a sliding window with the detectionprocedure repeated in each new interval. With the slidingwindow approach, a series of successive alternans ampli-

tudes can be produced, thereby providing means forcharacterizing the morphology of the ‘‘alternans wave-form.’’

Using simulated ECG signals, the Laplacian detectorhas been found to perform better than the Gaussian one(52,54). In general, performance assessment is difficult tostudy on ECG recordings because manual annotation of Twave alternans episodes cannot be performed because oftheir low amplitude. However, the use of simulated signalshas been found valuable because the presence and extentof T wave alternans can be controlled in detail.

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