AuthorMarkus Hoglinger

SubmissionInstitute of SignalProcessing

Thesis SupervisorUniv.-Prof. Dr. MarioHuemer

Assistant Thesis SupervisorDI Carl Bock

November 2016

JOHANNES KEPLERUNIVERSITY LINZAltenbergerstraße 694040 Linz, Austriawww.jku.atDVR 0093696

ECG Preprocessing

Bachelor’s Thesis

to confer the academic degree of

Bachelor of Science

in the Bachelor’s Program

Electronics and Information Technology

Abstract

Electrocardiography is a well-established method to monitor and record heart activity.The electrocardiogram (ECG) is obtained by measuring the difference in potential be-tween two points on the body surface. However, surface measurements include varioustypes of noise. The challenge of ECG preprocessing is to filter and minimize these noisecomponents, therefore making it easier to diagnose various heart disorders. In orderto create such methods, within this work the most important noise sources, baselinewandering, frequency noise, muscle noise and interference with impulse character aremodelled. Subsequently denoising methods were implemented to cancel out the mod-elled noise components.To evaluate each method, the signal-to-noise ratios (SNR) of the original and filteredsignals were calculated. We showed that the so called morphological filtering works bestfor baseline wander and impulsive noise whereas bandstop filtering leads to good resultswhen dealing with narrow-band frequency noise. Finally the modelling and denoisingmethods were integrated into an existing Matlab GUI.

Keywords: ECG preprocessing, noise modelling, denoising

Kurzfassung

Elektrocardiogramme (EKG) ermoglichen die Untersuchung unserer Herzaktivitat. Dabeiwerden Spannungsunterschiede zwischen zwei Stellen auf der Haut gemessen. Auf-grund der Messung direkt auf der Haut treten allerdings viele verschiedene Storsig-nale auf. Die Aufgabe der EKG Vorverarbeitung ist es, diese Storungen zu filtern undzu minimieren, um das Erkennen von Herzerkrankungen zu erleichtern. Um Metho-den zur Entstorung der Signale zu entwickeln, ist es hilfreich zunachst die wichtigstenStorquellen, Schwankung der Grundlinie, frequenzabhangige Storungen, Muskelzitternund Storungen mit Impuls-Charakter zu modellieren. Anschließend werden Methodenzur Unterdruckung dieser modellierten Storsignale entwickelt.Um die Ergebnisse auswerten zu konnen wurde das Signal-Rausch-Verhaltnis (SNR) desoriginalen und des gefilterten Signals berechnet. Es kann gezeigt werden, dass die so-genannte morphologische Filterung die besten Ergebnisse bei Grundlinienschwankungenund Storungen mit Impuls-Charakter liefert, wahrend fur Storungen mit einem schmalenFrequenzband ein Bandstopp-Filter eine gute Losung ist. Die entwickelten Methodenzur Modellierung und zur Storunterdruckung wurden abschließend in eine vorhandeneMatlab GUI integriert.

Schlagworter: EKG Vorverarbeitung, Storsignal-Modellierung, Entstorung

Contents

1. Introduction 2

2. Theoretical Background 42.1. Function of the heart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2. Leads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1. Limb leads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2. Precordial Leads . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3. Abnormalities of the ECG wave . . . . . . . . . . . . . . . . . . . . . . . 8

3. Methods 103.1. Noise Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1.1. Baseline Wandering . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1.2. Frequency Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.1.3. Muscle Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1.4. Impulsive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133.1.5. Respiration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.1.6. Noise Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2. Denoising . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.1. Baseline Wandering . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2.2. Frequency Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.3. Impulsive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.2.4. Muscle Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3. Evaluation of the denoising methods . . . . . . . . . . . . . . . . . . . . 21

4. Results 22

5. Discussion 265.1. Baseline Wandering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.2. Frequency Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.3. Impulsive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275.4. Muscle Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Appendix A. Signal details 29

1

1. Introduction

Motivation:Cardiovascular diseases are the world’s leading cause of death. In 2012, 31% of all globaldeaths resulted from cardiovascular problems [1]. Electrocardiography is the most com-mon way to monitor heart activity. Various heart disorders can be detected by analysisof electrocardiogram (ECG) signal abnormalities. Chapter 2 explains the theoreticalbackground of the ECG, in order to provide a solid foundation for any future work.For an accurate and early detection of heart problems a clean ECG reading is of greatimportance. As the electrodes are sensitive to minimal electrical changes of the skin,internal or external sources can easily produce noise, which may lead to false interpreta-tions. Especially random noise, caused for example by muscle disturbances is very hardto cancel. Hence ECG preprocessing is a major challenge in order to eliminate noise andproduce a cleaner, more easily interpretable ECG. Therefore the aim of this work is tomodel different types of noise and then creating methods for denoising them. The reasonfor the artificially modelled noise is that this makes it possible to evaluate the imple-mented methods for denoising by calculating its signal-to-noise ratio (SNR) for example.

Objectives:Within this work we aim to develop new methods for adding several typical noise typessuch as baseline wandering, frequency noise, impulsive noise and muscle noise to ar-tificially generated ECG. Subsequently filtering methods should allow us recreate theclean ECG signal. By calculating the SNR we can evaluate the success of the developedmethods.The goal is to obtain a graphical user interface (GUI) allowing to add artificial noisefilter it and subsequently evaluate these denoising methods simply by clicking buttons.

ECG denoising algorithms - A reviewBaseline WanderMany methods have been used in literature to eliminate baseline wander. One of themis ensemble averaging. This approach is sufficient when the ECG signal remains ap-propriately constant from beat to beat, but this is not the case in many real-worldECG recordings. Another method is polynomial interpolation, where linear interpola-tion introduces significant distortions but a third order approximation called cubic splineachieves better results [2]. Another possibility is a digital narrow-band linear-phase fil-ter [3]. This method can be implemented in real time, but has two problems. First, thefilter is restricted to an FIR filter with a long impulse response and therefore a largenumber of coefficients. The second problem is that the spectrum of the ECG and base-line wander usually overlap. Consequently it is not possible to completely remove thebaseline wander with a linear filter without distorting ECG components. [4]

2

Frequency NoiseThere are many possible methods to get rid of this kind of noise. One is the so calledwavelet coefficient threshold based hyper shrinkage function as described in [5]. Thesubtraction procedure is another effective cancellation method. [6]Impulsive NoiseFor removing noise with impulsive character, different practices are widely used. Oneof them are median filters as described in [7]. This is the classical approach to removeimpulsive noise. A median filter is implemented as a window of predetermined length,which slides sequentially over the signal.Muscle NoiseMuscle noise normally has white Gaussian noise characteristics, hence it is a big challengeto find methods to minimize these usually short lasting interferences.One approach is Wiener filtering. It is a well developed and popular class of optimalfilters, which uses available signal and noise characteristics. Wiener filter theory is basedon the minimization of the difference between the filtered output and the desired output.The Wiener filter coefficients are calculated with

w = R−1xx · rxy, (1.1)

where Rxx is the autocorrelation matrix of the noisy signal and rxy is the cross-correlationvector of the noisy signal and the desired signal [8].

Importance:In this work the different noise sources are artificially modelled and then added to theECG. We always know which part of the signal is noise and which part is the clean ECG.Therefore the algorithms for filtering single noise types can be better evaluated.

Outline and Contribution:The work consists of 5 chapters:Chapter 2 provides the theoretical background of the ECG. Section 2.1 focuses on thefunction of the heart and the origin of the electrical impulses. Section 2.2 explains theplacement of the leads for the measurement of the impulses and section 2.3 describespossible abnormalities of the ECG.In Chapter 3 methods for noise modelling (Section 3.1) and denoising (3.2) for differentnoise types are presented.Chapter 4 presents the results obtained for denoising different noise sources.Chapter 5 concludes this thesis by discussing the results.

3

2. Theoretical Background

2.1. Function of the heart

The cardiac muscle is composed of two main cell types, cardiomyocytes, which generateelectrical potentials during contraction, and cells specialized in the generation and con-duction of the action potentials. At rest, cardiomyocytes are polarized with an electricalmembrane potential of about −90mV . Excitation by an external stimulus can trigger arapid reversal of the electrical potential of working myocardial cells (depolarization). [9]Figure 1 shows the wiring diagram of the heart. Electrical impulses are generated in theSino-Atrial (SA) node. As the SA node fires, which can not be seen in the ECG signal,electrical impulses travel through the right and left atrium. As a consequence, the twoupper chambers of the heart contract. In the ECG signal this process is represented asthe P-Wave shown in Figure 2. Next the impulse travels to the atrio-ventricular (AV)node, which is placed above the ventricles. The AV-node is the only electrical connec-tion between atrium and ventricle and here the propagation of the electric signal getsdelayed. This is reflected in the PR-interval in Figure 2. Subsequently, the electricalimpulse travels through both ventricles, leading to contraction as represented by theQRS complex in Figure 2. Since the muscle of both ventricles is bigger compared to theatria, the amplitude of the QRS complex is higher than the one of the P-wave. Dur-ing relaxation of the muscle the ECG shows the ST segment and T wave in Figure 2 [10].

Figure 1: The wiring diagram of the heart (Source [10]).

4

Figure 2: Single ECG wave of a heart in normal sinus rhythm (Source [11]).

The length and height of the various parts of the ECG wave give information about thecondition of the patient’s health.For example, if the PR interval is very short, depolarization might have accidentallybeen initiated by a cell close to the AV node, or there is abnormally fast conductionfrom the atria to the ventricles. The length of the QT interval can be influenced bydrugs which would lead to ventricular tachycardia, resulting in a higher than normalresting rate. [10]

2.2. Leads

The electrical signal generated by the heart is detected by electrodes placed on the sur-face of the body. The ECG recorder compares the different electrical activities in theelectrodes and creates a so-called lead.

Today a standard ECG consists of 12 leads, each of which is determined by the placementand orientation of the electrodes on the body. This is necessary because the heart isa 3-dimensional organ and therefore has to be viewed from different angles in order torecreate the full signal.In Figure 3 the electrodes for a 12 lead ECG are spread as follows:

� 2 on the arms

� 2 on the legs

}These provide the basis for the six limb leads(Sec. 2.2.1)

� 6 across the chest, forming the precordial leads (Sec. 2.2.2)

5

Figure 3: Placement of the electrodes for a 12 lead ECG (Source [12]).

2.2.1. Limb leads

The six limb leads record the heart in a frontal vertical plane. This can be pictured asa circle on the body as it is shown in Figure 4 and 5.To produce this six leads the electrodes on the arms and legs can be marked positiveand negative, depending which lead you want to observe. The angle of the lead can beillustrated by drawing lines from the negative to the positive electrode(s) as shown inFigure 4 and 5.

Figure 4: Standard Limb Leads (Source [12]).

6

Figure 5: Augmented Limb Leads (Source [12]).

3 standard limb leads

� Lead I: right arm negative → left arm positive ⇒ Angle: 0°

� Lead II: right arm negative → legs positive ⇒ Angle: 60°

� Lead III: left arm negative → legs positive ⇒ Angle: 120°

3 augmented limb leads

In this case one electrode is chosen to be positive, all others are negative. The angle isnow specified between the median of the negative electrodes and the positive one.

� Lead aVL: left arm positive ⇒ Angle: -30°

� Lead aVR: right arm positive ⇒ Angle: -150°

� Lead aVF: legs positive ⇒ Angle: 90°

Each lead views the heart from its own particular angle of orientation. [12]Leads I, II and aVL provide information about the left lateral surface of the heart, IIIand aVF about the inferior surface and aVR about the right atrium.

2.2.2. Precordial Leads

These six electrodes are arranged across the chest to build the six precordial leads asseen in Figure 6. To obtain these six leads, one electrode is made positive and the bodyacts as common ground. This is done successively for all electrodes. They are positionedas follows.

� V1 is placed right of the sternum in the fourth intercostal space.

� V2 is placed left of the sternum in the fourth intercostal space.

� V3 is placed between V2 and V4.

� V4 is placed in the fifth intercostal space in imaginary line, that extends downwardover the trunk from the midpoint of the clavicle.

7

� V5 is placed between V4 and V6.

� V6 is placed in the fifth intercostal space in the line leading from the axilla downmidway between ventral and dorsal surfaces of the body.

The precordial leads view electrical forces moving anteriorly and posteriorly [12].These six leads view the heart in a horizontal plane, where V1 and V2 provide informa-tion about the right ventricle, V3 and V4 about the septum between the ventricles andV5 and V6 about the anterior and lateral walls of the left ventricle.

Figure 6: Precordial Leads (Source [12]).

2.3. Abnormalities of the ECG wave

When interpreting an ECG signal each section and possible abnormalities provide infor-mation about the underlying physiological condition.

P-wave

The most common abnormality of the P-wave is its change of shape as the heart rhythmchanges. Additionally, the P-wave exhibits a sharp peak instead of the usual wave whenthe right atrium is enlarged. Conversely, an enlargement of the left atrium manifests ina broad and split P wave. [10]

QRS-complex

When the depolarization has spread through the ventricles by an abnormally slow path-way the QRS-complex is widened. There are also other reasons for widening, like Wolff-Parkinson-White syndrome described in [13]. An enlargement of either ventricle resultsin a higher QRS-complex due to the increased electrical activity. [10]

8

ST-segment

The ST segment is normally at the same level as the segment between the T wave andthe next P wave. In abnormal signals, the ST-segment may be depressed or elevated.The reason for an elevation is mainly an acute myocardial injury resulting from eitheran infarction or an inflammation of the fibrous sac surrounding the heart. Depressionof the ST-segment is mostly a sign of ischaemia, i.e a restriction of blood flow to tissuesor organs causing a shortage of oxygen and glucose. [10]

T-wave

Although in some leads, like in aVr or in V1 and sometimes also in III and V2, theT-wave can be inverted, it can also be a sign of abnormalities like myocardial infarctionor ventricular enlargement. Another reason for T-wave deformation is the bundle branchblock. This is caused by injury to the bundle branch, which forces the electrical impulseto use muscle fibres instead, resulting in a deceleration of the electrical movement anda deformation of the T wave. A bundle branch block can also be diagnosed when theQRS-complex is prolonged. [10]

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3. Methods

3.1. Noise Modelling

Since noise can be generated by multiple sources, we differentiate between differenttypes of noise. In order to create filter methods for single sources, we have to know thecharacteristics of the noise we want to create a filter for. Therefore it is an importanttask to create single noise models where we can test and improve the noise cancellingmethods. The most important sources in ECG processing and their models are describedin the following:

3.1.1. Baseline Wandering

Baseline wandering is a type of slow frequency noise which adds to the ECG signal,resulting in a varying baseline. This noise is caused by changes in the impedance betweenthe electrode and the patient’s skin. These changes might be caused by movement,breathing or by perspiration, leading to a change of distance between the source of thesignal, the heart, and the electrodes. The ST-segment is especially affected by this kindof noise which is particularly relevant in exercise testing.The frequency components of the baseline wander usually lie below 0.5 Hz but, in caseof stress tests, this limit can be higher. Thus, these components can be in the samerange as low frequency ECG components like the ST segment or the T-wave. [4]This type of interference can be modelled by adding a single sine shaped half-wave tothe ECG signal,

xn = A · sin(2π · f · t). (3.1)

The frequency f of this function is determined by the startpoint and endpoint enteredby the user. It is also possible to vary the signal-to-noise ratio (SNR) of the signal byincreasing or decreasing the amplitude A of the noise signal. Furthermore the shape ofthe baseline wandering can be changed by manually dragging points placed on the halfwave. An exemplary ECG signal is shown in Figure 7.

3.1.2. Frequency Noise

Many noise sources have known characteristics regarding their frequency. By adding asinusoid with either constant or varying frequency within a given range these sourcescan be shaped easily. In this work the chirp-function was used to model the frequencyvariations. The chirp-function in MATLAB generates samples of a swept-frequencycosine signal

x(t) = A · sin(2 · π · f(t)). (3.2)

10

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

ampl

itude

/mV

Figure 7: Baseline Wander, manually modelled

The following are the possible sweep-methods:

� linearf(t) = f0 + βt (3.3)

with β beingβ = (f1 − f0)/t1 (3.4)

� quadraticf(t) = f0 + βt2 (3.5)

with β beingβ = (f1 − f0)/t21 (3.6)

� logarithmicf(t) = f0 × βt (3.7)

with β being

β =

(f1f0

) 1t1

(3.8)

f0 . . . frequency at the beginning of the noisef1 . . . frequency at the end of the noiset . . . time instances of the noise vectort1 . . . end of noisy signal

These sweep methods allow to increase or decrease the frequency of the noise. It is alsopossible to vary the SNR by changing the amplitude of the added noise sinusoid.In Figure 8 we modelled an ascending linear chirp between 40 Hz and 60 Hz. Becausethe difference between 40 Hz and 60 Hz can hardly be seen in Figure 8, Figure 9 showsthe frequency spectrum of the signal. Figure 9 clearly shows that the added noise islimited between 40 Hz and 60 Hz.

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0 0.5 1 1.5 2 2.5 3

time /s

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

ampl

itude

/mV

Figure 8: Frequency noise between 40 Hz and 60 Hz.

0 10 20 30 40 50 60 70 80 90 100

frequency /Hz

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

|Y(f

)|

Figure 9: Frequency spectrum of an ecg signal with frequency noise between 40 Hz and60 Hz.

Powerline Interference

An important occurance of this type of noise is the powerline interference, which has afrequency of 50 Hz. It is a significant source of noise during bio-potential measurements.It degrades the signal quality and overwhelms small features that may be critical forclinical monitoring and diagnosis. [14]Power lines and other surrounding equipment produce electromagnetic fields. Duringrecording of an ECG signal, the way of the signal between patient and ECG recordercan not be completely shielded. Therefore these fields produce significant interferences,which can be modelled with a sinusoid. The frequency spectrum of the power lineinterferences is quite narrow and centred around the frequency of the power supply.

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3.1.3. Muscle Noise

Muscle disturbances occur when skeletal muscles contract, the patient moves or becauseof shivering due to inappropriate temperature of the environment. The main problemwith these interferences is the spectral overlap between the ECG and the muscle noise.Modelling muscle disturbances is quite difficult as it appears at random and thereforehas no exact deterministic description and can only be characterised by stochastic terms.In practice, either white Gaussian noise or databases for noise models are used to addmuscle disturbances to the ECG signal. For adding them from databases see section3.1.6.In this section we modelled muscle disturbances by adding white Gaussian noise atrandom positions to the ECG signal with user-defined starpoint, length and amplitudeof the noise. One example is shown in Figure 10

0 1 2 3 4 5 6 7 8 9 10 11

time /s

-0.5

0

0.5

1

1.5

2

ampl

itude

/mV

Figure 10: ECG signal with muscle noise of length 2s and 4s respectively

3.1.4. Impulsive Noise

Muscle noise can not be described with white Gaussian noise only, because sometimesit displays impulse character too. Additionally impulsive noise may be produced bydiathermy, which is a form of heating tissue, when using surgical devices or in occupa-tional therapy [15].These impulses have a short duration and a high peak, and can therefore be shaped asa triangle function with adjustable height and width, which is added to the signal. Thetriangle is created by using linear time vectors, and is modelled with the function

x(i) =

{k · i+ d1 for i ≤ duration

2

−k · i+ d2 for i > duration2

(3.9)

where k and d depend on the duration and location of the impulse.In Figure 11 we added five example impulses to the signal.

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0 2 4 6 8 10 12-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Figure 11: ECG signal with 5 impulses of height 1 and width 0.02s

3.1.5. Respiration

During breathing, the chest electrodes shift in position, changing the mutual positionbetween heart and electrodes. This results in varying amplitudes of the QRS-complexes.We reproduced this variation by amplitude modulation of the ECG signal, as shown inFigure 12.

0 2 4 6 8 10 12-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Figure 12: ECG signal with respiratory noise.

3.1.6. Noise Data

Another method to model noise was implemented in this work by adding noise vectorsgiven from a database such as the MIT-BIH noise stress test database [16], [17]. Therecordings showing baseline wander, electrode motion artefacts and muscle noise can bedownloaded by the user and then added to the ECG signal with this method. Beforeadding the noise to the signal, the amplitude of the added vector has to be adapted tothe signal.The MIT-BIH Noise Stress Test Database does not just provide noise-only vectors butalso noisy ECG signals from real patient recordings.

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3.2. Denoising

Denoising is used during preprocessing of the input signal. Since real-world ECG sig-nals are often disturbed by noise and strongly depend on the individual patient, it ismandatory to perform denoising to get a robust recognition model. In section 3.2.1 -3.2.4 we describe denoising for methods baseline wander, frequency interference, musclenoise and impulsive noise.

3.2.1. Baseline Wandering

In this work baseline wander was removed by morphological filtering, which is an effec-tive non-linear signal processing method and keeps the shape information of the signal ofinterest well. [18]. Structuring elements are the basic concept of mathematical morphol-ogy and are used to interact with a given signal, with the purpose of drawing conclusionson how this shape fits or misses the shapes of the signal. They have a certain form (suchas point, line, circle, etc.) and by using a structuring element to operate on a signalthe information of a signal (shape, size, etc) can be extracted. In this work a linearstructuring element was used.There are two basic morphological operators, erosion

(fΘk)(n) = minm=0...M−1

f(n+m)− k(m); n = (0, 1, . . . , N −M) (3.10)

and dilation,

(f ⊕ k)(n) = maxm=0...M−1

f(n−m) + k(m); n = (M − 1,M, . . . , N − 1) (3.11)

with f(n) being the signal sequence and k(m) the linear structuring element with thewidth M. The single operations are used on a signal with baseline wander in Figure 13.

Opening,

(f ◦ k)(n) = (fΘk ⊕ k)(n) (3.12)

and closing,

(f • k)(n) = (f ⊕ kΘk)(n) (3.13)

are derived operators defined in terms of erosion and dilation and are used to suppresspeaks and pits. Figure 14 shows that opening is used to suppress peaks and closing tosuppress pits. (Note: Suppressing the pits only influences the Q- and S-waves)

15

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-2

0

2

4

ampl

itude

/mV

original signal

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-2

0

2

ampl

itude

/mV

erosion

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-2

0

2

ampl

itude

/mV

dilation

Figure 13: Erosion and dilation used on a signal with baseline wander.

0 1 2 3 4 5 6 7 8 9 10

time /s

-2

0

2

4

ampl

itude

/mV

original signal

0 1 2 3 4 5 6 7 8 9 10

time /s

-1

0

1

2

3

ampl

itude

/mV

opening

0 1 2 3 4 5 6 7 8 9 10

time /s

-2

0

2

4

ampl

itude

/mV

closing

Figure 14: Opening and Closing used on a signal with baseline wander.

16

The morphological filters can remove certain peaks and pits of the signal, which have aspecific width by combining opening and closing operations. The removed part of thesignal is related to the structuring element. The used combinations are Opening/Closing,

OC(f(n)) = (f ◦ k • k)(n), (3.14)

and Closing/Opening,

CO(f(n)) = (f • k ◦ k)(n) (3.15)

and consequently Opening/Closing - Closing/Opening

OC CO = (OC + CO)/2 (3.16)

In order to avoid the distortion of ECG waveform, the steps, illustrated in Figure 15,were used to extract the baseline drift:

Figure 15: Block diagram for correcting baseline drift (Source [18]).

(1) First the QRS-complex is filtered out by using an Opening/Closing - Closing/Open-ing filter on the original signal f0.fb = OC CO(f0, k1) with k1 being the first structural element, where the width is0.11 · Fs, with Fs being the sampling frequency of the ECG signal (Value is takenfrom [18])

(2) Second the signal fb is processed through OC CO operation to remove the P-waveand T-wave. The result is then an estimate of the baseline drift fc.fc = OC CO(fb, k2) with k2 being the second structural element, where the width is0.27 · Fs (Value is taken from [18])

(3) Last the baseline is subtracted from the original signal resulting in a ECG withcorrected baseline [18],

fbc = f0 − fc. (3.17)

17

These steps are illustrated in Figure 16.

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-2

0

2

ampl

itude

/mV original ecg

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-2

0

2

ampl

itude

/mV ecg without QRS-complex

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-2

0

2

ampl

itude

/mV baseline of ecg without QRS-complex, T-, and P-wave

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-1

0

1

2

ampl

itude

/mV ecg with corrected baseline

Figure 16: ECG signals during the process of baseline correction.

3.2.2. Frequency Noise

Powerline interference as an example of frequency noise has a central frequency of 50 Hzwith possible variations in a certain range in either direction. In case that the frequencyrange of the noise does not influence the frequency range of the ECG signal one effectivemethod to filter this kind of noise is a simple bandstop filter. This allows to remove allsignal components in the range around the centre frequency of the noise. In this worka Chebyshev Type II Bandstop Filter was used with the specifications shown in Figure17 and Table 1. The advantage of a bandstop filter compared to a low-pass filter is thatpossible signal frequencies higher than those of the frequency noise don’t get filtered outand therefore the signal does not get distorted as much as it would with a low-pass filter.

Figure 17: Filter Specifications of a Bandstop Filter.

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The variables in Figure 17 have been chosen as described in Table 1 with f0 being thecentral frequency and ±∆f describing the frequency range of the noise.

Fpass1 f0 −∆f − 1Fstop1 f0 −∆f − 0.5Fstop2 f0 + ∆f + 0.5Fpass2 f0 + ∆f + 1Apass1 0.5Apass2 0.5Astop 60

Table 1: Filter Parameters used for frequency noise cancellation.

The magnitude response of the filter is shown in Figure 18.

Figure 18: Magnitude Response for attenuating frequencies of 50Hz ± 5Hz

The weakness of this method is that the clean ECG has frequency components, forexample such as those of the QRS complex, lying within the stopband of the filter whenused for filtering powerline interference with 50 Hz (Figure 19). Therefore the QRScomplex is disorted when filtered with a bandstop filter. One possible solution of thisproblem, which was also used in this work, is to preserve the QRS-complex, filter theremaining signal, and then add the complex back to the filtered signal.

Figure 19: FFT of clean ECG Signal

19

3.2.3. Impulsive Noise

In this work morphological filtering as described in section 3.2.1 was applied. Due to thesmall width of the impulses, other linear structural elements, with width of 0.012 ·Fs and0.008 · Fs respectively, had to be used so that all peaks smaller than the QRS-complexget filtered out. (Values resulted of manual optimization)

3.2.4. Muscle Noise

The method for filtering muscle noise used in this work is the empirical mode decompo-sition (EMD). The aim of the EMD is to decompose the signal into a sum of intrinsicmode functions (IMF). An IMF is defined as a function with equal number of extremaand zero crossings or at most differed by one. Its envelopes, which are defined by all thelocal maxima and minima, are symmetric with respect to zero. [19]Before the EMD can be applied one difficulty is to get the noisy parts only. This mustbe done because there is a difference in the amount of IMF and their shape betweenclean and noisy signal parts. The first IMF of a noisy part for example contains mostof the high-frequent noise components and therefore has to be removed from the signal.If this would be performed for clean signals too they would get distorted. To determinethe on- and offset of the noisy parts a method based on the maximal overlap discretewavelet transform and a subsequent envelope building was applied as shown in Figure20.

0 500 1000 1500 2000 2500 30000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Figure 20: Signal envelopes with two different windows for thresholding

For each noisy part the EMD can then be applied. For this purpose the signal is splitup in its intrinsic mode functions by performing the following steps as described in [20]:

1. Find all the local maxima Mi, (i = 1, 2, ...) and minima mk, (k = 1, 2, ...) in thesignal x(t).

2. Compute the corresponding interpolating signals M(t) := fM(Mi, t) and m(t) :=fm(mk, t). These signals are the upper and lower envelopes of the signal.

3. e(t) := (M(t) + m(t))/2 building the mean function of the upper and lower enve-lope.

20

4. Subtract e(t) from the signal, x(t) := x(t)− e(t).

5. Repeat step 1 to step 4 until the signal remains nearly unchanged (e(t) becomesnegligible small).

6. Once we obtain an IMF, ϕ(t), remove it from the signal x(t) := x(t) − ϕ(t) andreturn to step 1 if x(t) has more than one extrema (neither a constant nor a trend)to start with the next IMF.

During this process the number of extrema should decrease when going from one IMF tothe next, and the whole decomposition is expected to be completed with a finite numberof IMFs. If this is not the case the EMD has to be terminated.As the first IMFs contain the high frequency noise components and the QRS-complexusually lies in a similar frequency range, it is important to preserve the QRS-complexin these IMFs. This is achieved by applying the envelope function with two differentwindows on all the IMF’s, similar to detecting the noisy parts of the signal.After that all the modes with signal components are added back together to form thefiltered ECG signal.

3.3. Evaluation of the denoising methods

One goal of signal processing is to improve the signal-to-noise ratio (SNR). In this workwe used it to compare and interpret the produced results. The SNR can be calculatedby the following formula,

SNR = 10log(PSignal

PNoise

) (3.18)

or,

SNR = 20log(Urms,Signal

Urms,Noise

). (3.19)

The root mean square (RMS) is given by

Urms =√u2 =

√1

T

∫ t0+T

t0

u2 dt. (3.20)

Calculating the SNR this way is only possible with simulated ECG signals because therethe clean signal and also the added noise is known which is essential for 3.18 and 3.19.

21

4. Results

We applied denoising methods shown in section 3.2 on 5 different ECG examples pernoise source. The results are shown in Table 2 - Table 5. Figure 21 visualizes theprocesses of modelling and then filtering baseline wander.

0 5 10 15

time /s

-1

0

1

2

3

ampl

itude

/mV

ECG with baseline wander

0 5 10 15

time /s

-0.5

0

0.5

1

1.5

2

ampl

itude

/mV

Filtered ECG signal

Figure 21: ECG signal with modelled baseline wander.

It shows an ECG signal with added baseline wander created as described in subsection3.1.1. After performing morphological filtering with implemented baseline correction aspresented in 3.2.1, the result is also shown in Figure 21. In this example, the SNR wasimproved from 1.2910 dB to 32.5157 dB.

Baseline wander

#Signal

length (s)Noise

length(s)Noise

amplitudeNoisy SNR

(dB)Denoised SNR

(dB)SNR Improvement

(dB)1 7 3 1 4.2235 32.0854 27.86192 7 3 3 1.0465 23.8043 22.7578

3 1034

1-1

1.3613 28.7156 27.3543

4 2 1 1 4.1805 31.4560 27.27555 22 11 1 3.8986 42.6245 38.7259

Table 2: SNR measurement of ECG signal with baseline wander using morphologicalfiltering for denoising.

22

Frequency Noise

# *Noisy SNR

(dB)

SNR withoutQRS preserving

(dB)

SNRImprovement

SNR withQRS preserving

(dB)

SNRimprovement

1 25.9084 17.7677 -8.1407 60.3313 34.42292 25.9150 9.1303 -16.7847 51.5068 25.59183 8.6291 17.7164 9.0873 56.8910 48.26194 25.9324 8.6183 -17.3141 52.6916 26.75925 14.0748 30.2694 16.1946 64.1992 50.1244

Table 3: SNR measurement of ECG signal with frequency noise using a bandstop filterfor denoising.* Signal details in Appendix A

Figure 22 shows the results of modelling an ECG signal with frequency noise and thefiltering with a bandstop filter. Table 3 shows the SNR measurements of ECG signalswith frequency noise.

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-1

-0.5

0

0.5

1

1.5

2

ampl

itude

/mV

ECG with frequency noise

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-1

-0.5

0

0.5

1

1.5

2

ampl

itude

/mV

Bandstop filtered ecg signal

Figure 22: ECG signal with frequency noise with a center frequency of 50 Hz ± 5 Hz

23

Impulsive Noise

#Signal

length (s)Impulseheight

Impulseamount

Noisy SNR(dB)

Denoised SNR(dB)

SNR Improvement(dB)

1 7 2 2 19.7375 49.2577 29.51022 7 1 15 14.2296 42.0132 27.78363 7 4 5 4.9321 25.0902 20.15814 1 1 10 9.1211 26.1656 17.04455 20 1 10 26.9682 49.0528 22.0846

Table 4: SNR measurement of ECG signal with impulsive noise using morphologicalfiltering for denoising.

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-1

-0.5

0

0.5

1

1.5

2

ampl

itude

/mV

ECG with impulsive noise

0 2 4 6 8 10 12 14 16 18 20 22

time /s

-1

-0.5

0

0.5

1

1.5

2

ampl

itude

/mV

Filtered ECG signal

Figure 23: ECG signal with 5 impulses with height 1 mV and witdh 20 ms.

In Figure 23, 5 impulses were modelled and morphological filtering was used to filter outthese impulses. Table 4 shows the SNR measurements of ECG signals with impulsivenoise.

24

Muscle Noise

#Signal

length (s)Noise

length(s)Noise

amplitudeNoisy SNR

(dB)Denoised SNR

(dB)SNR Improvement

(dB)1 7 2 0.2 29.1059 35.5210 6.41512 7 6 0.1 25.5369 32.6855 7.14863 16 2 0.1 43.0826 49.5351 6.4525

4 20

324

1.5

0.10.30.050.2

27.4377 30.5703 3.1326

5 10 5.5 4 3.8340 6.4072 2.5732

Table 5: SNR measurement of ECG signal with muscle noise using the empirical modedecomposition for denoising.

0 5 10 15 20 25

time /s

-0.5

0

0.5

1

1.5

2

ampl

itude

/mV

ECG with muscle noise

0 5 10 15 20 25

time /s

-0.5

0

0.5

1

1.5

2

ampl

itude

/mV

Filtered ECG signal

Figure 24: ECG signal with two parts with muscle noise.

In Figure 24 the modelling of muscle noise and the effectiveness of the EMD is shownwhen it is applied on a signal with two noisy parts. Table 5 shows the SNR measurementsof ECG signals with muscle noise.

25

5. Discussion

5.1. Baseline Wandering

Table 2 shows different examples of baseline wander and their interference elimination.The examples differ in the length of the signal as well as the amplitude and the lengthof the noise. It can be observed that short signals like #4 can not be denoised as well aslong signals like #5. Although it must be said that when comparing different examplesit is difficult to draw statistical conclusions, because of the different signal and noisecomponents.The used method of morphological filtering presents good results, as the value of SNRimprovement of around 30 dB is in the desirable range, consequently we are able torecreate the original signal in a nearly perfect shape.The maximum reachable SNR of this method would be around 48 dB depending on thelength of the signal, due to signal distortions caused by the filtering method. This valuewas obtained when applying the morphological filtering on a clean ECG wave. Theresults show that this method enables good ECG interpretation.

5.2. Frequency Noise

To show the influence of QRS preserving introduced in section 3.2.2, results of both,with and without QRS preserving, have been presented in Table 3.In general, the SNR becomes worse without QRS preserving. This happens becausesignal components of the QRS complex are in the range of the bandstop filter andthereby get distorted and shifted in time as shown in figure 25. By calculating theremaining noise through subtraction of the original from the filtered signal, the timeshifting produces erroneous noise and therefore resulted in a worse SNR.When enlarging the interval in which the frequency of the noise varies, exemplified in#2 of Table 3, even more signal components were distorted by filtering. Similar, buteven worse effects were observed when the centre frequency of the noise was decreasedto 40 Hz as done in #4. When we increased the centre frequency to 100 Hz, as donein #5, less signal components got distorted and so the SNR improvement enhanced,even without QRS-preserving. The reason for this is that the ECG signal has far lessfrequency components around 100 Hz.The performance of the used method was significantly improved by preserving the QRScomplex which is reflected in the values of the SNR improvement. This indicates that themethod by itself provides useful results, and that only signal components with frequenciesin the range of the bandstop filter have to be handled separately.The maximum value of SNR for a bandstop at 50 Hz ± 5 Hz is around 61 dB dependingon the length of the signal. The denoised SNR in this work around up to 60 dB show

26

0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52

time /s

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

ampl

itude

/mV

Noisy SignalFiltered Signal

Figure 25: Time shifting due to the bandstop filter without QRS preserving

that the bandstop plus QRS-preserving result in a nearly perfectly reconstructed ECGwave.

5.3. Impulsive Noise

In Table 4, the SNR improvements of ECG signals with impulsive noise are presentedfor different signal lengths as well as for different numbers and amplitudes of impulses.As long as the width of the impulses stayed below the width of the shortest ECGcomponent, the QRS-complex, morphological filtering increased the SNR significantly.Even if many impulses were added to the signal or the amplitude of the impulse exceededthe signal amplitudes, this method still produced good results.It is also important to note that the quality of the SNR improvements depended on theposition of the impulses, which were distributed randomly. If an impulse was right onthe QRS-complex, for example, this complex was distorted and the SNR improvementbecame less. However, when it occured on a low frequent section like the ST-segment,the SNR improved significantly.Table 2 as well as Table 4 illustrate, that the method of morphological filtering led tosatisfying results in ECG preprocessing.Due to the use of morphological filtering the SNR values were similar to the baselinewander denoising. Higher SNR values are impossible to reach, because the peaks ofQRS-complexes have similar widths to the impulses and would therefore be filteredaway.

5.4. Muscle Noise

As mentioned above, muscle noise is the most difficult one to denoise. This is reflectedby comparing the SNR improvement in Table 5 to that of other noise sources. Althoughit must be mentioned that different noise types cannot really be compared regardingtheir SNR. Muscle noise for example usually has a short duration and therefore theSNR before filtering is higher and thus has less space for improvement. As muscle

27

noise exhibits random characteristics, there is a lack of methods to regain the shape ofthe original signal. As there is no deterministic mathematical description of the noise,methods for filtering muscle noise can only improve the SNR in a small scale. The SNRof the filtered signal depends on the length and amplitude of the white Gaussian noiseas shown by the first three results in Table 5.Many short noisy parts make the SNR improvement of the method worse as shown inthe example #4. The detection of start- and endpoint is not exact enough and thereforethe empirical mode decomposition modifies the signal at the start- and endpoint.The extreme example #5 showed denoising results when the noise amplitude is higherthan the signal amplitudes. As there was no real improvement, we concluded that thismethod has limits at high noise amplitudes.In summary we showed that EMD is an effective method when it comes to improvingECG signals disturbed by muscle noise. The decomposition of the signal in its intrinsicmode functions allows the cancellation of high frequency components of the ECG signal.

Because of this work it is now possible to manually model different noise types and add itto the ECG generated via an existing ECG generator. Therefore methods for cancellingout single noise types can be implemented and evaluated, which was also done in thiswork.

28

A. Signal details

#Signal

length (s)Noise

amplitude

Frequencyof the noise

(Hz)

Frequencyfluctuation

(Hz)

Ascending (up)or descending(down) chirp

chirpmethod

1 7 0.1 50 5 up linear2 7 0.1 50 10 up linear3 10 0.3 50 5 down quadratic4 7 0.1 40 5 down logarithmic5 15 0.2 100 10 up quadratic

Table 6: Signal details for the 5 example ECG signals with frequency noise in Table 3

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