The Philosophy Of Electrocardiogram

Published Date: 02 Nov 2017

CHAPTER 2

This chapter highlights the literature related to this research. Initially, a brief introduction

of sleep is mentioned followed by detailed discussion of Sleep Apnea. Later,

Philosophy of Electrocardiogram has been discussed. Time to frequency domain transformation

techniques have been discussed in fourth section. The fifth part describes the

diagnosis techniques in literature followed by associated limitations.

2.1 Sleep

“Sleep that knits up the ravelled sleave of care,

The death of each day’s life, sore labour’s bath,

Balm of hurt minds, great Nature’s second course,

Chief nourisher in life’s feast”[6]

The foregoing quote highlights the vital nature of sleep as perceived byWilliam Shakespeare.

Sleep is one of the most basic and indispensable aspect of life. In humans, it

covers almost one third of total life time. It provides physical and mental relaxation

during which a person becomes inactive and partially or totally unaware of the environment.

But it is not just a rest from consciousness rather it is a complex and dynamic

process being researched under the umbrella of somnology.

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2.1.1 Definition and Recognition

Before the nineteenth century, sleep was considered to be a form of revokable death

[2]. It was assumed that sleep is basically a short time death that after sometime turns

back to life again. It was analogized with death because mental, physical and emotional

sufferings appear to cease while sleeping and arise again when waken-up. Surprisingly,

it was not only a famous myth but the text books of 1800s also presented the same

notion of sleep [2].

In 1830, Dr. Robert MacNish defined sleep as; “Sleep is the intermediate state

between wakefulness and death: wakefulness is regarded as the active state of all the

animals and intellectual functions and death as that of their total suspension” [7].

Twentieth century brought a new milestone for understanding the phenomenon of

sleep when it was discovered that brain remains active during sleep. In 1928, the first

EEG was introduced by a Germen doctor when he placed the electrodes on skull and

recorded the electrical activity of the brain waves. Following this discovery, further

advancements were made for measuring the very minute nocturnal voltage changes

produced by brain waves [2].

From a behavioral point of view, sleep is a behavioral state that is reversible in

nature and own visceral detachment and apathy towards the surroundings. Sleep is a

complex and dynamic blend of physiological and behavioral processes. Closed eyes,

behavioral repose, postural decumbent etc are the commonly considered features of

sleep. Although there may be anomalies like teeth grinding, talking or walking etc in

one’s sleep patterns. Similarly like other life processes, sleep also faces ailments and

trouble that are researched in special branch of science known as somnology.

2.1.2 Sleep Architecture

The theoretical description of normal sleep is structurally organized in two types, nonrapid

eye movement sleep (NREM) and rapid eye movement sleep (REM). Depending

upon the relative depth of sleep, NREM sleep is further divided in 4 stages namely stage

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1, 2, 3 and 4. All of these stages have their own characteristic features in terms of eye

movement, muscle tone and brain waves feature [8]. The brain activity is monitored and

sleep stages are classified by using EEG. Over an episode of sleep, REM and NREM

sleep follow alternative pattern, cyclically, as depicted in Fig. 2.1. Although, the exact

functionality of these cycles are yet not known but irregularity or skipping of one or

more stages is known to be associated with sleep ailment [9]. For example, patients

suffering from narcolepsy directly enter into REM sleep instead of following the pattern

as highlighted in Fig. 2.1.

Figure 2.1: Sleep stages over a period of sleep (Hypnogram) - [10]

An episode of sleep is such organized that a person initially fall asleep in stage 1 of

NREM sleep later progressed to stage 2 and subsequently followed by stage 3 and 4.

After all the 4 stages of NREM sleep, the phase of REM sleep starts. Interestingly, REM

sleep does not last for the rest of the sleep rather the sleep stages keep on swinging, as

depicted in Fig. 2.1. The ratio of REM and NREM sleep is about 20-25% to 75-80%,

respectively [10]. Normally, the REM sleep increases as the sleep episode progresses

ad it reaches to maximum in the last one third of sleep. With the progression of sleep

stage 2 of NREM sleep dominates and sometimes stage 3 and 4 completely vanishes.

Physiological details of Sleep Stages

NREM sleep The NREM sleep is usually subdivided in four stages defined along

one measurement axis of Electroencephalogram (EEG). The pattern of NREM sleep is

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commonly considered similar to high voltage slow waves. Fig. 2.2 depicts the EEG

patterns of all the 4 stages of NREM sleep.

Figure 2.2: EEG patterns of NREM sleep - [10]

Stage 1 sleep NREM Sleep at stage 1 offers the entering point to the sleep (exception

to infants, patients of narcolepsy and neurological disorders.). This stage acts as

transitional stage in sleep cycling. Person sleeping in this stage usually gets interrupted

with noise. Stage 1 constitutes about 2-5% of sleep. Transition from rhythmic alpha

waves to mixed frequency low voltage waves can be observed in stage 1 shown in Fig.

2.2. Alpha waves are associated with wakefulness and have the characteristic frequency

of 8-13Hz. [10][8]

Stage 2 sleep Stage 2 constitutes about 45-50% of the total sleep episode. In

order to wake up an individual from stage 2, relatively stronger stimuli is required as

compared to stage 1. The EEG wave for this stage is composed of mixed frequency and

relatively low voltage activity. Sleep spindles and K-complexes can also be seen in Fig.

2.2. In stage 2 of Fig. 2.2, an arrow marks the k-spindle while two sleep spindles have

also been highlighted by an underline.

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Stage 3 and 4 Stage 3 and 4 are collectively known as Slow Wave Sleep (SWS).

Stage 3 lasts for only a few minutes and contributes about 3-8% of total sleep episode.

Increased high-voltage and slow wave activity can be observed in stage 3 demonstration

of Fig. 2.2. Stage 4 is the last stage of NREM sleep. This stage contributes about 10-

15% of net sleep episode. Increased amounts of high voltage and slow wave activity, as

can be observed in Fig. 2.2, are the characteristics of this stage.[10]

REM sleep Desynchronized brain wave activity, muscle atonia and bursts of rapid

eye movements are the characteristics features of REM sleep [10]. EEG of REM sleep

shows a saw-tooth wave form, theta activity and slow alpha activity [8]. In the initial

cycles, REM sleep may last for 1-5 minutes but gradually its length progressively increases

as the sleep episode advances [10]. Mostly, dreaming is related to REM sleep

[8]. REM sleep is a mysterious state, as the brain cells use a great deal of energy and

EEG pattern shows great similarity between wakefulness and REM sleep [2].

2.1.3 Sleep Ailments

Sleep is a complex state that has recently been given serious importance in research. An

excellent amount of night sleep can increase productive capacities of a person while a

poor sleep makes a person exhausted and nonproductive. Different types of sleep fulfill

different needs. For example, it is believed that REM sleep is the time of memory stockup

in our brain. Similarly, SWS is required to wake-up fresh and energetic. Increase

and decrease in the total amount of sleep, fluctuations in different sleep stages, unusual

breaking of sleep cycles, interruption in brain activity etc can cause different types of

sleep ailments.

Sleep disorders are very common and there is a great upsurge of research interest

in this area over the past few years. Sleep disorders affects one’s performance, safety

and quality of life. Sleep loss is itself a medical condition, to be taken seriously and

medicated.

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2.2 Sleep Apnea

2.2.1 Preamble

The term “apnea” has a Greek origin and literally means absence of sleep. From a

clinical stand point, it refers to a sleep ailment during which the patient faces episodes

of very less or no breathing. This disease owns a very silent nature that means it usually

stays hidden from the general physicians as it has a rather complicated diagnosis

procedure (to be discussed in section 2.2.7).

2.2.2 Discovery and Definitions

“The Posthumous Papers of the Pickwick Club”, is one of the famous novel by Charles

Dickens, back in 1837. In this novel he planted a character of Joe and described him

as “A fat and red-faced boy, (often) in a state of somnolency and constantly snoring”

[11]. With this description of Joe, Dickens provided one of the very early description of

a person suffering from Sleep apnea. The medical sciences did not start observing and

understanding this disease for about 120 years after Dickens, a wonderfully accurate

observer [2].

In twentieth century, one of the key milestone in the history of sleep disorders occurred

in Europe, when sleep apnea was discovered by Gastaut, Tassinari, and Duron

(in France) and by Jung and Kuhlo (in Germany). Both of these research groups published

their findings in 1965 [12]. Although the phenomenon of sleep apnea has also

been observed by the scholars earlier, but the foregoing is the most clear recognition

and more importantly the description paved the path to the today’s philosophy of sleep

disorders.

From a clinical and research stand point, sleep apnea is a sleep-breathing disorder

and the symptoms generally are the combination of snoring, episodes of breathing

cessation, sever day time sleepiness and fatigue etc [2].

An episode of apnea is considered to occur when a person do not breath for more

then ten seconds, during his sleep [3]. The occurrence time of an episode may vary.

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The longest apnea event seen is of 2 minutes length [13].

An occasional episode of apnea is quite common. In order to consider a person as a

sleep apnea patient AASM has provided a criteria that if a person has 5 or more apnea

events per hour he is considered a patient of sleep apnea otherwise normal [5].

2.2.3 Epidemiology

In the last two decades, several epidemiological studies have been performed to determine

the prevalence of sleep disordered breathing in different parts of the world. In

1993, Young et. al., studied the prevalence of sleep disordered breathing in American

population and discovered that 25% male and 19% of female population is suffering

from obstructive sleep apnea [14]. In another study by Bixler et. al., 17% of American

men were patients of sleep apnea in 1998 [15]. Duran et. al. performed a similar epidemiological

study, in 2001, on Spanish population and discovered that 26% of Spanish

man and 28% of Spanish women suffer from sleep apnea [16]. In 2001, Ip. et. al., discovered

that 8.8% of Chinese men face sleep apnea [17]. He extended his research to

Chinese women in 2004 and discovered that about 3.7% of Chinese females also suffer

from sleep apnea [18]. A similar study was performed on Korean population in 2004 by

Kim et. al. and statistics marked that 27% of Korean men and 16% of Korean women

are patient of sleep apnea [19]. For the determination of sleep apnea in Indian men,

a study was performed by UdWadia et. al., in 2004. This study revealed that 19.5%

of Indian men are victim of Sleep apnea [20]. In another study on Indian population,

Sharma et. al. quote that 19.7% of Indian men and 7.4% of Indian women face sleep apnea

[21]. In 2007, a study was conducted in Malaysia by Kamil et. al. and 8.8% males

while 5.5% females were clinically suspected of Sleep apnea (out of the population of

1161 adults) [22].

This disease is highly prevalent in in overweight or obese people, however, elderly

people are also at a risk. As an overall estimate across many countries, as mentioned

earlier individually, almost 3-7% of adult man while 2-5% of adult female suffer from

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sleep apnea [23]. Male community suffers more than female in a ratio of about 2:3 [24].

2.2.4 Risk Factors

There are a number of risk factors that can contribute to prevalence of sleep apnea. A

few of them are highlighted in this section.

Obesity

Obesity is considered to be a major contributor of anatomical alterations of whole body

in general and upper airway in particular causing it to collapse during the course of

sleep by increasing adiposity over and around the pharyngeal pathway. It also becomes

a factor of decrease in the natural volume of lungs because of which posterior grip on

the upper airway is decreased causing collapse [25]. A study on middle aged Europoid

subjects it was found that if body mess index (BMI) is increased by one fold, sleep

apnea prevalence sharply increases by four folds, showing the high association between

obesity and sleep disordered breathing [14].

In a study it is shown that if body weight is reduced by 10%, AHI is subsequently

decreased by 26% [26]. A study on the patients of severe obesity (BMI > 40) revealed

that sleep apnea was present amongst them for about 40-90% [27]. It is clear from the

epidemiological studies that obese subjects are highly at risk of sleep apnea and in order

to well treat and control the faster prevailing epidemic, reduction in weight should be

the maiden choice.

Age

Statistical studies reveal that risk of sleep apnea increases after the age of 65 years

which is estimated to be about 10% [28]. In another report it is discovered that 6% of

people between the age of 50-70% years suffer from sleep apnea [29]. It has also been

reported that in the age group of 40-98 years old, about 11% of women and 25% of

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men suffer from sleep disordered breathing and have an AHI > 15, which is certainly

alarming [30]. Increased decomposition of body fat, especially in the parapharyngeal

area, changing in the body structures and lengthening of the soft palate are blamed for

sleep disordered breathing in elderly people [31].

Alcohol consumption and Smoking

Smoking is generally considered dangerous for health. In case of sleep disordered

breathing it has shown to be a great risk factor by increased snoring and disrupted

sleep [32], [33]. Wisconsin Sleep Cohort Study proves that smokers are at greater risk

of sleep apnea as compared to people who never smoke [34]. Smoking severely affects

the airway, destroy the structure of upper airway causing easy collapse while sleeping.

Experiments have revealed that alcohol reduces the output to the upper airway from respiratory

motor hence introducing hypotonia of the phalangeal muscles causing collapse

[35] [36]. Alcohol consumption also increases rates of traffic accidents in sleep apnea

patients as compared to normal drinkers [37].

Craniofacial Issues

Craniofacial refers to skull and facial structures. Sometimes abnormalities in these

structures also leads to sleep disordered breathing. It is because of the fact that abnormalities

in these structures may alter or affect their functionalities and increase probability

of collapse during sleep. Imaging studies have marked many differences in craniofacial

structures of normal and sleep apnea patients. Some of these abnormalities include

enlarged tongue, soft palate, wrongly positioned hyoid bone, decreased posterior narrow

space, retrognathia and tonsils etc [38]. In non-obese patients of OSA, craniofacial

issues plays an important role in diagnosis [39]. Two studies are available in literature

on Chinese subjects suffering from sleep apnea. Both of these studies have consistent

results proving the role of craniofacial abnormalities in collapse of pharyngeal tissues

[39] [40].

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Genetics

Genetics and family history also plays an important role in development of sleep apnea

in a patient. Studies have shown that people who are having blood relations with sleep

apnea patients are very much suspected of having sleep apnea themselves too [41] [42].

Family obesity history may also be a reason for inheriting sleep apnea.

The suspected locus for sleep disordered breathing has been found in the defined region

of Apolipoprotein E (APOE) [43]. APOEe4 is famous for cardiovascular diseases.

A study highlights the fact that e4+ subjects develops sleep disordered breathing more

then e4- subjects [44]. It probably links to the cardiovascular affects of sleep apnea.

Further investigations are required in this area in order to develop better understanding

of role of genetics in sleep apnea development.

2.2.5 Health Hazards

Sleep apnea can be responsible for a number of problems. Because of a large number

of sleep apnea episodes, the oxygen supply to the brain reduces time after time, each

night this process is repeated again and again which directly impairs the brain functions.

Because of the persistent disruption of sleep and time to time fall in oxygen level,

patients of sleep apnea suffer from headaches, fatigue, memory losses, impotence, difficulty

in understanding, reduced learning capabilities, day time sleepiness and sexual

dysfunction etc. The permanent jet lag like day time sleepiness not only causes lake

of concentration on work but overall it affects ones professional career causing further

complex social and financial issues [3].

The day time sleepiness is one of the causes of automobiles accidents. Sleep apnea

is also one of the factor behind high blood pressure and heart disease. Basically, as the

muscles of the body relaxes during sleep the blood pressure eventually decreases. But

the research has shown that blood pressure of a sleep apnea patient increases after each

episode of sleep apnea [3].

According to a statement issued by American Sleep Apnea Association, the in-

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creased blood pressure is due to the fact that the blood oxygen level falls during sleep

apnea so in order to cover this potential crises more blood flows to fulfill the deficiency

[5].

During an episode of sleep apnea, oxygen level in the blood drops eventually causing

the heart to work harder in order to provide oxygen to the brain. Normally, the blood

oxygen level in around 90%, if it falls beyond 85 it put a strain on the heart subsequently

causing heart failure. If the oxygen saturation falls below 60% heart arrhythmia may

occur. In a research conducted at Stanford University by Dr. Markku Partinen and

Christian Guilleminault, blood pressure, heart disease and brain circulatory disease are

more prevalent in sleep apnea patients as compared to others in a ratio of 2, 3 and 4

times respectively [].

In another study conducted in Australia discovers that sleep apnea increases risk of

heart attack by almost 25 times than the other without sleep apnea.

2.2.6 Pathogenesis

An episode of sleep apnea occurs when collapsible upper pharyngeal airway obstructs

during sleep. The upper airway is quite complicated yet vital structure. It has its due

physiological role in sneezing, breathing, swallowing, coughing, yawning, vomiting,

speaking and singing. These jobs requires efficient movement that, certainly, has to

be performed in a confined space of throat. Some of these cases requires synergistic

mechanism while the other needs antagonist action. Therefore, a well coordinated and

highly sophisticated control of brain is required in order to fulfill the jobs of upper

airways. Mouth, soft palate, pharynx, nose and nasal fossae are the major components

of upper airway. These anatomic components are composed of small bony segments

connected together with soft tissues and muscles. The formalistic limits of pharyngeal

tissues keep on overlapping forming continuum [45].

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2.2.7 Diagnosis

Correct diagnosis of a disease is the most critical yet vital for the timely cure and treatment.

The detection of sleep ailments is further critical as it involves the sleep time

monitoring of the patients that is not only expensive but troublesome. Fig. 2.3 highlights

several methods of sleep apnea detection.

Figure 2.3: Sleep Apnea detection Methods in a nut-shell -

Traditional Diagnosis

The gold standard for sleep apnea detection is by means of nocturnal Polysomnography.

This technique was introduced in 1980s. Polysomnography, as the name indicates,

involves a set of different physiological signals achieved through different sets of electrodes

placed at multiple distinctive locations of patient’s body. Polysomnography has

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to be performed simultaneously and continuously, using a polygraph, in a specialized

sleep laboratory in the presence of qualified personnel. Polysomnography helps in diagnosis

of common sleep disorders [46]. A minimum of 12 different physiological signals

are needed, including sleep signals, respiratory effort signals, cardiovascular signals,

muscle movement signals and brain signals [1]. The signals are mentioned in table 2.1.

The signals that are marked as C are the compulsory signals while the others (marked

as O) depends upon individual situation of the patients. The laboratory personnel has

to record patient’s situation from time to time in the form of notes.

The minimum number of signals that are sufficient for characterization of sleep have

been mentioned in full detail in “Manual of Standardized Terminology, Techniques and

Scoring System for Sleep Stages of Human Subjects” [47]. A minimum of 1 EEG lead

is required whose electrodes can either be placed at C3-A2 or C4-A1, following the

10-20 system of EEG skull electrodes placements. It is recommended to have a spare

lead also connected for emergency cases where the primary lead face any failure during

nocturnal recording environment. Two EOG (Electrooculogram) leads (ROCT (Right

Outer cantus) and LOCT (Right Outer cantus)) are also required in order to record the

eye movements. EMG lead is to be placed at the chin, as the chin muscles provide best

depiction of muscles tone in general [1]. A set of these recordings provide necessary information

for sleep scoring. In case of detection for sleep disordered breathing, oronasal

airflow, respiratory movements and blood gases study is also needed. Pulse oximetry is

used to determine the state of blood gases. Pneumotachograph (with closed face mask)

is the gold standard for quantitative requirement of airflow [5]. Esophageal pressure

transducer records the respiratory efforts by the subject [48]. Pneumotachograph and

Esophageal pressure transducer lacks the due comfort level and may disturb the sleep

of patient. Because of this reason, normally, less disturbing methods are preferred for

example pressure transducers. Although these are not very accurate but does not disturb

the patient much. Inductive plethysmography or piezo elements (less accurate) are

used for recording the respiratory effort by the subject. These respiratory recordings

helps in determining the sleep disordered breathing (for example apnea/hypoapnea).

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A microphone or a room microphone is used to record the snoring level which helps

in determining the upper airway obstruction. Fig. 2.4 presents a typical example of

polysomnographic recording. It has been recorded in a sleep laboratory following the

exact standards of Polysomnography. In this example, 30second epoch is shown. The

EEG signal shows that its just the beginning of the sleep. The start of signal (EEG)

shows alpha waves (typical for start of sleep) followed by theta waves. There is a slow

eye movement shown in signals LOC and ROC. Respiration is also smooth [1].

Figure 2.4: An exemplary chunk of Polysomnographic recording -

Modern Diagnosis

Due to the troublesome procedure of the traditional diagnosis and high costs, research

directions are turning towards signal processing based sleep apnea detection. There are

few signals that, some-way or the other, get affected by disruption in breathing caused

by sleep apnea. The features from these signals are extracted using different signal processing

techniques and used in sleep apnea detection. As depicted in Fig. 2.3, several

researchers have deployed signals like EEG, SpO2 and ECG signals both individually

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and in combination of each other for developing a signal processing based solution to

sleep apnea detection. We have used ECG signal as it is a very common test and home

monitoring of ECG is also possible these days. As summarized in Fig. 2.3, there are

a number of signal processing techniques in literature that have been incorporated for

sleep apnea detection previously, like Fourier transform, wavelet transform etc. We

have used a specific combination of Discrete wavelet packet transform for our proposed

solution. Before proceeding to different modern diagnostic schemes, an overview of

ECG and different signal processing techniques is mandatory to be mentioned.

2.3 Philosophy of Electrocardiogram (ECG)

2.3.1 History and Basics

An electrocardiogram is a non-invasive diagnostic tool used to record the electrical

activity of the heart by the help of electrodes placed over human body. The action

potentials of the excitable cardiac cells are responsible for variations in voltage captured

by ECG. A series of waves manifest the heartbeat in ECG and their morphological

patterns and schedule of appearance and disappearance serves as diagnostic measures

highlighting the heart’s electrical activity [49].

The biggest milestone in the history of Electrocardiogram was the proof of electrical

pulse generation by each heart beat in a living organism as provided by Carlo

Matteucci, Professor of Physics at the University of Pisa, in 1838. He cut a nerve of a

frog and twitch the frog at legs. An electrical activity was observed when the leg was

twitched proving the stimulus to be in the form of electrical pulses. This device was

named as “Rheoscopic frog” [50]. The maiden ECG recording on a human subject was

made in 1880s by Augustus Waller [49]. Later in 20th century, a Dutch physiologist

Willem Einthoven deployed a string galvanometer to invent a recording device having

the capability to measure human body potentials from the skin. The credit for ECG

electrodes placement sites also goes to Willem Einthoven. His marked sites are in use

till now. In 1924, he also received Nobel Prize in physiology and medicine for his re-

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markable contributions in discovery of Electrocardiogram. Since then ECG has become

a vital clinical tool [49].

Today ECG has advanced further from a laboratory test to a more mobile and dynamic

tool for example Holter ECG that can be performed anywhere. Signal processing

techniques are becoming an essential tool for extracting important information from

the ECG signal, going beyond the limits of so-called visual analysis. The importance

of ECG has been further strengthen by the discoveries of veiled information in wave

patterns, beat-to-beat variations and cardiac micro-rhythms. These facts have opened

countless windows for the research in ECG signal processing [49]. As this is an old

area of research, so it is often assumed that all of the aspects of ECG signals have already

been discovered. But actually there still remain complicated research problems

that are being incrementally solved with the development of signal processing tools

like filtering, pattern recognition, and classification. Moreover remarkable advances in

computational power and memory capacity over the last couple of decades have also

supported the viable solutions to many troublesome problems associated with ECG signal

processing [51].

2.3.2 Electrical Activity of Heart - An Overview

Heart is a vital organ of human body, failure of its functionality is definition of death. It

is muscular in nature and owns the responsibility of pumping oxygenated blood (from

lungs) to the body. The job of pumping the blood throughout the body is done by

the help of action potentials generated. The mechanical job of circulation of blood

throughout the body relies on the internal electrical activity of heart [52]. In rest position

the cardiac muscle cells are polarized where the cell nucleus is negatively charged

as compared to the surroundings. The polarization is dependent upon the concentration

of different ions, like potassium and sodium either sides of cell membrane. In case

of a stimuli, these ions move changing their concentration which subsequently results

in depolarization. These depolarization and depolarization are responsible for nerve

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impulses and muscle contractions. There are few special cells in heart that owns the capability

of spontaneous depolarization. These special cells exist in sinoatrial node (SA)

of the heart and are responsible for cardiac rhythm. The depolarization of these cells

adjust the heart rate and cause the SA muscles to contract which in turn pump the blood

into ventricles before polarizing back. The electrical pulse generated by depolarization

of SA node, simultaneously, passes to atrioventricular (AV) node, depolarize it’s cells,

causes the ventricles to contract, subsequently pumping the blood into pulmonary and

systematic circulation. The next phase is then re-polarization of ventricle and the whole

process repeats again [52].

2.3.3 Signal Morphology

ECG is used to monitor and record the electrical activity of heart. The basic components

of an ECG signals are:

_ Waves: Signal that starts and ends at the baseline is considered an individual wave

_ Complexes: Two or more waves together form a complex, e.g QRS complex

_ Segments: Straight/flat or an isoeletric line is called segment

_ Intervals: A wave or a complex connected to a segment is known as interval

Fig. 2.5 shows that there are a total of 5 waves in an ECG signal. The description of

some basic cardiac components is as under.

P-wave The normal ECG signal starts with a P-wave. The P-wave depicts the arterial

depolarization. It is usually symmetric. Normally, ECG P-wave is 0.08 to 0.11 seconds

in duration having an amplitude of 0.2 to 0.3mV [53].

PR segment Following the P-wave there is a small pause (straight line) that indicates

the electrical current passing through the AV node [53].

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PR interval The PR interval starts from the beginning of the P-wave and end before

the QRS complex. This interval depicts the supra-ventricular electrical activity before

the activation of Purkinje fiber system and bundle of His [53].

QRS complex The QRS complex in the ECG waveform, represent the ventricular

depolarization [53].

Q-wave Q-wave is maiden negative deflection and represents initial phase of the

depolarization of the ventricular myocardium [53].

R-wave R-wave is the ECG wave with maximum positive deflection and so the

most prominent wave in the ECG signal. It represents the early ventricular depolarization

[53].

S-wave It is the second negative deflection of ECG signal and represents late ventricular

depolarization [53].

As all of the three waves highlights different stages of ventricular depolarization so

normally they are treated and analyzed as a complex i-e; QRS complex [51].

ST segment The time between vetricular depolarization and re-polarization is represented

by ST segment, in an ECG signal. The point where the QRS complex ends, is

known as “J point”. It may be above or below the isoelectric line. The placement of

J point is dependent on certain physiological aspects. The ST segment begins at the J

point and ends before the T wave starts. Normally it is of 0.12 seconds or less.

T-wave T-wave is a positive deflection representing ventricular re-polarization. It

symbolizes rest and recovery phase for the heart activity. Normally it has an amplitude

of 0.5mV and lasts for about 0.20 seconds.

QT interval It is the biggest interval that starts from the QRS complex and ends at

the end of the T-wave. It represents the cycle of ventricular depolarization and repolarization.

It lasts for about 0.38 seconds.

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RR interval As the name indicates, RR interval the time difference between the Rwave

of two consecutive ECG signal episodes. It represents cardiac cycle or Heart rate.

The heart rate with respect to time is called heart rate variability.

Fig. refecg highlights all the discussed terminologies.

Figure 2.5: ECG signal - [?]

2.4 Transform Notion -An Overview

This section briefly highlights the basic theory of Fourier and wavelet transform, in

order to build a bridge between fundamental theories of transformation and our basis

of selection. Initially, Fourier and Wavelet transforms are briefly discussed followed by

their due comparison leading to the point of our selection hypothesis.

2.4.1 Fourier Transform

Probably, Fourier transform is the most commonly used tool in the field of signal processing.

In one line, it can be defined as a tool to reveal the frequency domain information

of a time domain signal (x(t)). In 1807, Joseph Fourier discovered that any

periodic signal can be represented as a weighted sum of sine and cosine series [54]. But

unfortunately this great finding could not be published as some of his contemporaries

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had some uncompromising objections [55]. About 15 years later Fourier published his

book “The analytical theory of heat” and presented his discovery in an extended form

by mentioning that aperiodic signals can be represented as integrals of sines and cosines

series [56]. This integral is what known as Fourier transform.

Fourier transform of a signal, x(t) can be expressed as:

X(f) = (x; ei2_ft) =

Z 1

ô€€€1

x (t) eô€€€i2_ftdt (2.1)

This was a representation of an analogue signal but the signals (assume xk) obtained

through data accusation, like in our case ECG signal, are generally sampled at certain

discrete interval _t, where the total time can be considered as _T. The frequency

domain such signals can be represented as :

DFT(f) =

1

N

NXô€€€1

k=0

xkei2_fnk_T (2.2)

Eq. 2.1 and 2.2 depicts that Fourier transform is basically between the time series

x(t) or xk with a series of template functions (sine and cosine functions). The similarity

between the signal and template functions is measured and average frequency information

of the entire period is expressed as the result of Fourier transformation [55].

2.4.2 Wavelet Transform

The maiden wavelet : Haar

Historically, the first link to the wavelets can be traced in early twentieth century when

a PhD scholar of University of Gottingen studied theory of orthogonal function systems

and mentioned his discovery in his dissertation in 1909. Later his research mapped its

path to the development of Haar wavelet, on his name “Alfred Haar”[57]. It was used for

illustration of such functions which can be decomposed into several orthogonal blocks.

Moreover it has also been used for image compression [58].

Apart from the contributions of several individuals, like Elias M. Stein [59], Norman

25

H. Ricker [60] and John Littlewood, Richard Paley [61], till 1970, the biggest milestone

in the advancements of wavelet transform is credited to Jean Morlet who devised the

scaling and shifting technique of the analysis window function while working on an

oil company based project related to acoustic echoes [62]. Morlet developed an analysis

scheme where he changed the width of the window by stretching or squeezing the

function window while keeping the frequency constant [62]. He named this technique

as “wavelets”, opening the door of the new era of wavelet transformations. Although

Morlet followed the same idea as haar but the first theoretical description of the wavelet

based breakdown and reconstruction of a signal is first crafted by a joint venture of

Morlet and Alex Grossmen [63]

Wavelet definition and description

The term “wavelet” refers to an oscillating wave that has a fixed life time and posses

the ability to describe the time frequency plane. Usually the wavelets are purposefully

crafted to adapt certain characteristics in order to make them useful in special signal

processing situations. The wavelets, denoted by (t), are considered very useful for the

analysis of non-stationary signals [54]. Mathematically, wavelets have all the energy

concentrated in time and represent a function of zero average:

Z 1

ô€€€1

(t) dt = 0 (2.3)

The wavelets provides flexibility for extracting time and frequency information

because of the concept of mother and daughter wavelets. The function (t), as described

in Eq. 2.3 is confined in a finite interval and termed as `‘mother wavelet”. The

“daughter wavelet” , u;s(t), is the dilated (by a scale parameter a) and translated (by a

factor b) version of the `‘mother wavelet”. Mathematically,it can be represented as:

a;b(t) =

_

t ô€€€ b

a

_

(2.4)

26

Wavelets provide the liberty to choose the size of the analysis window that can suit

the situation of signal processing under consideration in time or frequency domain.

Hence, depending on the signal to be analyzed, different scaling and translation of the

mother wavelet (the daughter wavelets) can be used. The wavelet transform is principally

the convolution of the signal to be transformed with that of the daughter wavelets

in the whole range defined by the signal [54][64] .

Continuous wavelet transform -An Overview

Continuous wavelet transform (CWT) performs mapping of a time series (a univariate

function in time) into a dual variable function (time and frequency dependent), while

providing highly redundant information. CWT is basically an integral transformation.

In principle, CWT essentially follows the definition of wavelet transform whereby, a

convolution of the signal to be analyzed is done with the scaled wavelet. using Eq. 2.4

the wavelet transform of continuous signal can be represented as:

T(a; b) = W(a)

Z 1

ô€€€1

x (t) _

_

t ô€€€ b

a

_

dt (2.5)

where asterisk represents that the complex conjugate of the wavelet function is deployed.

It is mandatory while dealing with complex wavelets. W(a) is weighting function

which is responsible for energy conversation. In other words, W(a) ensures that

wavelets at each scale posses same energy [54][64]. Generally, W(a) is taken 1/

p

a.

Considering W(a) to be 1/

p

a, the wavelet transform can be written as:

T(a; b) =

1

p

a

Z 1

ô€€€1

x (t) _

_

t ô€€€ b

a

_

dt (2.6)

Eq. 2.6 represents the CWT of the signal x(t). It shows that the product of wavelet

and the signal are integrated over the whole range of signal, more precisely it is convolution.

The normalized wavelet function, in terms of wavelet energy can be represented

as [54]:

27

a;b(t) =

1

p

a

_

t ô€€€ b

a

_

(2.7)

The transform integral may be written as:

T(a; b) =

Z 1

ô€€€1

x (t) _

a;b(t)dt (2.8)

Wavelet transform representation can be made further compact by representing it as

inner product.

T(a; b) = hx; a;bi =

Z 1

ô€€€1

x (t) _

a;b(t)dt (2.9)

Mexican Hat wavelet, Morlet wavelet, Gaussian wavelet, Frequency B-spline wavelet,

Shannon wavelet and harmonic wavelet are few commonly used wavelets for performing

CWT [54].

Discrete Wavelet Transform

As the name indicates, discrete wavelet transform deploys discrete values of translation

and scaling parameters. Eq. 2.7 represents the wavelet function with continuous values

of dilation and translation. A natural approach to the discretization may be by using

logarithmic discretization of a and b, where b can be dependent on a. In other words, at

each discrete location b is proportional to a, i-e,

a ) amo

b ) nboamo

(2.10)

Hence, Eq. 2.7 can be re-written as:

m;n(t) =

1

p

amo

_

t ô€€€ nboamo

amo

_

(2.11)

28

m and n are the control parameters for dilation and translation respectively. amo

represents

fixed dilation step where ao > 1 and the location parameter, bo > 0. Moreover,

changes in bo are directly related to amo

because 4b = boamo

.

Using Eq. 2.11, Eq. 2.6 can be written as:

T(m; n) =

Z 1

ô€€€1

x (t)

1

am=2

o

ô€€€

aô€€€m

o t ô€€€ nbo

_

dt (2.12)

Similarly, Eq. 2.9 leads to:

T(m; n) = hx; m;ni (2.13)

Tm;n represents DWT given on scale location grid of index m,n. Tm;n provides the

values of wavelet coefficients or detail coefficients.

The most commonly used base wavelets for discrete wavelet transform includes

Haar wavelet, Daubechies wavelet, coiflet wavelet, symlet wavelet, meyer wavelet,

biorthogonal and reverse biorthogonal wavelets. Among all of the so-far developed

base wavelets, Haar wavelet is considered the most simplified wavelet [54][64].

Dyadic Grid

Common choices for ao and bo are 2 and 1 respectively. This choice is known as dyadic

grid arrangement. Substituting these values in Eq. 2.11 leads to:

m;n(t) =

1

p

2mo

_

t ô€€€ no2m

2mo

_

(2.14)

Dyadic grid wavelets are generally selected to be orthonormal. They also posses

unit energy normalization. Mathematically,

Z 1

ô€€€1

m;n(t) _ _

m0;n0(t) =

8>><

>>:

1; if m = m0; n = n0

0; otherwise

(2.15)

Hence, the product of each wavelet with it’s translated/ dilated counterpart is zero,

29

eliminating the redundancy. Moreover, they have also been normalized to unit energy.

Using Eq. 2.14, DWT can be written as [54],

T(m; n) =

Z 1

ô€€€1

x(t) m;n(t)dt (2.16)

The signal x(t) can be represented in terms of wavelet coefficients, Tm;n,

x(t) =

X1

m=ô€€€1

X1

n=ô€€€1

Tm;n m;n(t) (2.17)

Scaling Function and Multi-Resolution Concepts

Orthonormal dyadic discrete wavelets are linked with scaling function and dilation

equation. scaling function is responsible for smoothing of the signal. It has the same

form as wavelets [54]. Mathematically,

_m;n(t) = 2ô€€€m=2_(2ô€€€mt ô€€€ n) (2.18)

Scaling function posses the property,

Z 1

ô€€€1

_0;0(t) dt = 1 (2.19)

where _0;0(t) = _(t). Generally, _(t) is named as father wavelet or scaling function.

The scaling function owns orthogonality with respect to translation with itself

but this property does not hold with respect to dilation of itself [54]. Approximate

coefficients can be achieve by convolving the scaling function with the signal. mathematically:

Sm;n =

Z 1

ô€€€1

x(t)_m;n(t) dt (2.20)

Approximate coefficients at certain m are known as the discrete approximation of

the signal at the specific m. A continuous approximation of x(t) can be obtained by

30

adding the scaling function at the scale m, factored by approximate coefficients, i.e,

xm(t) =

X1

n=ô€€€1

Sm;n_m;n(t) (2.21)

where xm(t) is a smoother version of x(t), at certain level m. It is noticeable that

the resemblance of xm(t) with x(t) is dependent upon the index level m, i.e, if m !

ô€€€1 ) xm(t) ! x(t). x(t) can be represented in terms of approximation (Sm;n) and

detailed coefficients (Tm;n),i.e,

x(t) =

X1

n=ô€€€1

S0;n_0;n(t) +

X1

m=ô€€€1

X1

n=ô€€€1

Tm;n m;n(t) (2.22)

The signal details at m can be encapsulated as,

dm(t) =

X1

n=ô€€€1

Tm;n m;n(t) (2.23)

where as,

X1

n=ô€€€1

S0;n_0;n(t) = xm0(t) (2.24)

Hence, by using Eq. 2.23 and Eq. 2.24 in Eq. 2.22,

x(t) = xm0(t) +

X1

m=ô€€€1

dm(t) (2.25)

Similarly,

xmô€€€1(t) = xm(t) + dm(t) (2.26)

Eq. 2.26 represents that addition of a signal detail at index m with approximation at

same scale gives signal approximation at an increased resolution, i.e, at index m ô€€€ 1.

This concept is refereed as Multi resolution scheme [54][64].

Scaling and Wavelet Equation

Scaling equation depicts scaling function in terms of shift and contraction, i.e,

31

_(t) =

X

k

ck_(2t ô€€€ k) (2.27)

where k is the integer showing shift along time axis and ck is the associated scaling

coefficient. Integrating Eq. 2.27 leads to:

X

k

ck = 2 (2.28)

However, in order to provide an orthonormal system,

X

k

ckck+2k0 =

8>><

>>:

2 if k0 = 0

0 otherwise

(2.29)

The same coefficients are also used in wavelet equation but with alternative signs

and reverse order, i.e,

(t) =

X

k

(ô€€€1)kc1ô€€€k_(2t ô€€€ k) (2.30)

The reason behind this choice is to maintain orthonormality between (t) and its

scaling counterpart _(t) [54]. For finite number of scaling coefficients Nk,

(t) =

X

k

(ô€€€1)kcNkô€€€1ô€€€k_(2t ô€€€ k) (2.31)

In order to make Eq. 2.31 more compact, bk can be introduced as reconfigured

coefficients where;

bk = (ô€€€1)kcNkô€€€1ô€€€k (2.32)

Using Eq. 2.32 in Eq. 2.31 leads to,

(t) =

NXkô€€€1

k=0

bk_(2t ô€€€ k) (2.33)

From Eq. 2.18 and Eq. 2.27,

32

_m+1;n(t) =

1

p

2

X

k

ck_m;2n+k(t) (2.34)

Similarly,

m+1;n(t) =

1

p

2

X

k

bk_m;2n+k(t) (2.35)

Fast Wavelet Transform

For scale index m+1 Eq. 2.20 can lead to the definition of approximate coefficients as:

Sm+1;n =

Z 1

ô€€€1

x(t)_m+1;n(t) dt (2.36)

Using Eq. 2.32 in Eq. 2.36 leads to,

Sm+1;n =

Z 1

ô€€€1

x(t)

"

1

p

2

X

k

ck_m;2n+k(t)

#

dt (2.37)

Eq. 2.37 can be re written as,

Sm+1;n =

1

p

2

X

k

ck

_Z 1

ô€€€1

x(t)_m;2n+k(t)

_

dt (2.38)

In the light of Eq. 2.20, the bracketed part of eq. 2.38 can be written as:

Sm;2n+k =

Z 1

ô€€€1

x(t)_m;2n+k(t) dt (2.39)

Using Eq. 2.39 in Eq. 2.38 yields,

Sm+1;n =

1

p

2

X

k

ckSm;2n+k =

1

p

2

X

k

ckô€€€2nSm;k (2.40)

Hence, the approximation at scale index m+1 can be generated using scaling coefficient

at previous scale. Similarly, wavelet coefficients, (t), can be find from approximate

coefficients at the previous scale by utilizing bk. Mathematically,

33

Tm+1;n =

1

p

2

X

k

bkSm;2n+k =

1

p

2

X

k

bkô€€€2nSm;k (2.41)

It is clear from Eq. 2.40 and Eq. 2.41 that if Sm0;n at specific scale m0 is known,

then through iterative approach of using Eq. 2.40 and Eq. 2.41, all the approximate

and detailed coefficients at the scales larger then m0 can be extracted. Interestingly,

underlying continuous signal x(t) is not required. Sm0; n is enough for this purpose

[54][64].

Filter Banks

Eq. 2.40 and Eq. 2.41 represents multi-tire decomposition algorithm. It provides an

easier way as compared to laborious convolution of equations. Eq. 2.40 and Eq. 2.41

can be utilized in the form of repeated iterations whereby they acts as highpass and

lowpass filters, respectively. Fig. 2.6 and 2.7 depicts the high pass and low pass filters

respectively [54].

- HPF - Sm;2n+k Tm+1;n

Figure 2.6: High-pass Filter

- LPF - Sm;2n+k Sm+1;n

Figure 2.7: Low-pass Filter

The vectors that contains the sequences 1=

p

2ck and 1=

p

2bk represents the filters.

1=

p

2ck is low pass filter that allows low frequency while blocks HF components, hence

provides a smoother version of the signal [54][64]. On the contrary, 1=

p

2bk acts as a

34

highpass filter and stores the signal details. In the light of above discussion Eq. 2.26

can be written as:

xmô€€€1(t) =

X

n

Sm;n_m;n(t) +

X

n

Tm;n m;n(t) (2.42)

DWT of Discrete Signal

In order to fit for wavelet MRA, the discrete signal should be the approximation at scale

m=0, Hence,

S0;n =

Z 1

ô€€€1

x(t)_(t ô€€€ n)dt (2.43)

Eq. 2.40 and Eq. 2.41 can be used to generate Sm;n and Tm;n at scale m > 0.

S0;n has finite length N. Itterative procedure is adopted to achieve the required level of

decomposition [54]. In the begining, S1;n and T1;n are extracted from S0;n.

S1;n =

1

p

2

X

k

ckS0;2n+k (2.44)

T1;n =

1

p

2

X

k

bkS0;2n+k (2.45)

Similarly in the next step S2;n and T2;n are computed as,

S2;n =

1

p

2

X

k

ckS0;2n+k (2.46)

T2;n =

1

p

2

X

k

bkS0;2n+k (2.47)

The iterative procedure depicted by Eq. 2.44 to Eq. 2.47 can be continued till

the desired level of decomposition is achieved. The maximum achievable level is M,

where N = 2M. Hence, 1 < m < M and 0 < n < 2Mô€€€m ô€€€ 1. At level M, only one

approximate, SM;0 and 1 detailed coefficient TM;0 is left.

35

The wavelet transform Vector

After the full decomposition of the signal, the wavelet transform vector can be written

as:

WM = (SM; TM; TMô€€€1; TMô€€€2; :::::::::; Tm; ::::::::T2; T1) (2.48)

where Tm represents sub-vector containing Tm;n at scale index m. It is not compulsory

to do the complete decomposition rather it can be stopped at any index level m0,

the transformation vector would be [54]:

Wm0 = (Sm0 ; Tm0 ; Tm0ô€€€1; Tm0ô€€€2; :::::::::::::T2; T1) (2.49)

where 1 6 m0 6 M ô€€€ 1.

2.4.3 Discrete Wavelet Packet Transform

Wavelets provide a dynamic range of possibilities to analyze the signal. A well known

and highly useful modification to the basic wavelet transform is the wavelet packet

transform. The only difference between the DWT and DWPT is that in DWPT the detailed

coefficients are also filtered again like the approximate coefficient. This filtering,

although increases the memory usage and time consumption but provides high resolution

for high frequencies which is not possible in DWT. Fig. 2.8 and Fig. 2.9 depicts the

difference between DWT and DWPT. In Fig. 2.8 it is obvious that only the approximate

coefficients (As) are re-filtered in case of DWT while the detailed coefficients are intact.

Fig. 2.9 clearly marks the splitting of both the approximate and detailed coefficients for

better high frequency resolution.

36

Figure 2.8: DWT Coefficients filtration algorithm -

Figure 2.9: DWPT Coefficients filtration algorithm -

37

2.4.4 Comparison of Fourier andWavelet Transforms

Fourier transform has the capability to mention the different frequency contents involved

in a signal. However, it does not mention if the frequency content vary with

time or remain present throughout the period of a signal. Hence the temporal structure

of a signal cannot be studied using FT. This limitation of time-frequency localization

lead FT to be an inappropriate tool for non-stationary signals. A natural solution to this

problem lies in windowing. A window of certain length which can glide over the time

axis to provide time localized Fourier transform. This extension of Fourier transform is

known as short time Fourier transform (STFT) [65].

In order to overcome the fixed window size limitation of STFT, CWT provides flexible

window size where dilation (by a scale parameter s) and translation (by a factor b)

are continuously possible. As a result of continuous iterations, CWT provides highly redundant

information. Although, in some application, redundancy is useful (for example

in case of signal demising) but other applications may need optimized use of memory

and computational time (for example image compression) [54]. Discrete wavelet transform

utilizes parameter discretization and provides reduced redundancy yet providing

acceptable signal information.

DWT suffers with the problem of low resolution in high frequency region, as the

highpass filter contents are not further filtered in DWT. DWPT filters both approximate

and detailed coefficients, providing high resolution in both low frequency and high

frequency regions.

Figure 2.10: Time-Frequency plane of FT -

38

Figure 2.11: Time-Frequency plane of STFT -

Figure 2.12: Time-Frequency plane of WT -

The time-frequency localization of FT, STFT and WT is depicted in Fig .2.10, Fig

.2.11 and Fig .2.12 respectively. It can be seen that Fourier transform does not provide

time localization but owns a very good frequency localization. Although, STFT

do provide time-frequency localization but it has fixed windowing that limits its usage.

Wavelet approach progressively narrows the window size highlighting the timefrequency

localization in quite a better way.

2.5 Related Work

Many signal processing techniques have been deployed for inexpensive and non-invasive

diagnosis of sleep apnea. This section highlights different methods available in literature.

39

2.5.1 Multiple physiological signal Based Techniques

Several researchers have deployed different physiological signals to diagnose sleep apnea.

Since EEG is a tool to reflect mental activity of an individual, few reaserchers have

deployed EEG to study the brain status during sleep in normal and abnormal(apnea)

cases. Derong Liu et. al [66] have used EEG signal and eye-pupil study to diagnose

sleep apnea. Their scheme is 91% accurate. Azim et. al. [67] have proposed an idea

of diagnosing sleep apnea using a combination of EEG and EMG signals. Studying

different bands of frequency in EEG signal, ucer et. al. [?] have diagnosed sleep apnea

with an accuracy of 63.5%. Apart from ECG, SpO2 signal has also been researched

for diagnosis of sleep apnea. Almazaydeh et. al. [68] have used SpO2 signal (obtained

through pulse oximetery). They have deployed neural network approach to predict sleep

apnea. The accuracy of this scheme turned to be 93.3%. Suzuki et. al. have developed

a sensor based hardware to capture variation in photoplethysmography waves during

sleep. The accuracy of this scheme is less then that of SpO2 based techniques. Apart

from the mentioned physiological signal an extensive research is on-way for diagnosing

sleep apnea using ECG signal.