Snoring Analysis on Full Night Recordings based in the Energy

and Entropy in PSG Basal Studies

Tiago Marc¸al

, Jos´e Bas´ılio Sim˜oes

, Jos´e Moutinho dos Santos

, Agostinho Rosa

and Jo˜ao Cardoso

Instrumentation Centre, University of Coimbra, Physics Department 3004-516, Coimbra, Portugal

Centro de Medicina do Sono, Centro Hospitalar e Universit´ario de Coimbra, Coimbra, Portugal

LaSEEB, Technical University of Lisbon, Lisbon, Portugal

Keywords:

Snoring, Shannon’s Entropy, Pulse Energy, Sleep, Sleep Disorders, Obstructive Sleep Apnea Syndrome,

Acoustic Analysis.

Abstract:

Snoring is a widely occurring problem in our society and it is highly associated with pathologies like Ob-

structive Sleep Apnea Syndrome (OSAS) being, usually, one of the ﬁrst symptoms to appear. Economically,

OSAS has a great impact since sleep disorders affect the daily performance of people in their professional

activities. The extensive study of snoring evidences may be useful to improve the knowledge of associated

pathologies, such as OSAS or others, at an early state. In this work, we study full night sound recordings

of patients undergoing polysomnography (PSG) procedures. Recordings are ofﬂine processed to characterize

time series of snoring events through the record length and correlated with the PSG data. The main goal of the

proposed algorithms is to understand the behaviour of the full night sound recording and to identify snoring

event patterns that may help and reﬁne the diagnostics process. To achieve this goal, the relationship between

the energy and the entropy was studied, for each respiratory event, in both snoring and non-snoring cases.

Recordings are ofﬂine processed to characterize time series of snoring events through the record length and

correlated with the PSG data. In the future, the relationship between these two physical variables can be used

to predict the clinical evolution between a simple snorer patient and a patient with OSAS.

1 INTRODUCTION

Sleeping is a natural process in the life of a human

being and its importance is well known in several pro-

cesses of the human biology, such as memory consol-

idation, blood pressure regulation, learning motor se-

quence and normal immune function (Barkoukis and

Avidan, 2007)(Shneerson, 2005). This process is dy-

namic and throughout the life, sleep patterns change

in a natural way (Shneerson, 2005).

However, there are some changes in sleep patterns

induced by either pathological factors or drugs. Sleep

disorders are a common problem in our society af-

fecting both men and women, especially elderly, as

well as children (Pevernagie et al., 2010) (Spicuzza

et al., 2009) (Grunstein et al., 2001) (Ye et al., 2009)

(Launois et al., 2007). One of such disorders is the

Sleep Apnea Syndrome (SAS). SAS has a high impact

in the quality of life and in the world economy (Leger

et al., 2012) (Wittmann and Rodenstein, 2004). SAS

can be obstructive (OSAS), central (CSAS) or both.

OSAS is much more common than CSAS and it is

highly linked with snoring.

Snoring is the result of the mechanical vibration

of the anatomical structures of the upper airway and

usually precedes almost all the others OSAS symp-

toms (Banno and Kryger,2007). It is a complexsignal

since it changes between different people and it may

change throughout the same night in the same per-

son. Factors like route of breathing, site of narrowing,

sleep stage and sleep position contribute to changes in

the features of snoring (Pevernagie et al., 2010). Ac-

cording to (Beck et al., 1995) there are 2 basic dom-

inant patterns in snoring: the simple-waveform and

the complex-waveform. The second one is character-

ized by ”a repetitive, equally-spaced, train of sound

structures, each composed of a few oscillations, start-

ing with a large deﬂection which is followed by a

decaying amplitude wave.”. The ﬁrst one is char-

acterized as follows: ”In the time domain, simple-

waveform snores have a quasi-sinusoidal pattern and

almost no secondary internal oscillations within the

periodic wave.”.

Since snoring is highly linked to OSAS, our work

221

Marçal T., Basílio Simões J., Moutinho dos Santos J., Rosa A. and Cardoso J..

Snoring Analysis on Full Night Recordings based in the Energy and Entropy in PSG Basal Studies.

DOI: 10.5220/0004245202210227

In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2013), pages 221-227

ISBN: 978-989-8565-36-5

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

focuses its goal in the study of this condition. Previ-

ous works demonstrated differences in acoustic prop-

erties between simple snorers patients and patients

with OSAS in the sound power spectrum (Fiz et al.,

1996). The ﬁrst step is the determination of the en-

ergy of a full night sound recording in patients with

polysomnographic basal studies, splitting the sound

recordings in small segments of settable length (be-

tween 0.01s and 1s). The second step is the determi-

nation of the entropy for every respiratory event, with

or without a snoring signal. Entropy is a measure of

the disorder of a system. In information theory, the

concept of entropywas ﬁrst explored by Claude Shan-

non and it measures the uncertainty associated with

a random variable (Yadollahi and Moussavi, 2006)

(Zhang et al., 2009).

In the end, a relationship between the energy and

the entropy of all the respiratory events detected by

the algorithm was established.

2 METHODS

2.1 Data Acquisition

Full night sound recordings took place at the Centro

de Medicina do Sono of the Centro Hospitalar e Uni-

versit´ario de Coimbra with clinical supervision of MD

J. Moutinho dos Santos and the collaboration of his

clinical team.

Prior to each data acquisition, the patient is given

an informed consent. To the development of this

work 36 patients agreed to participate (22 men and

14 women). The arithmetic mean of their ages was

50.83 years with a standard deviation of 12.66 years.

Sound acquisitions are performed with a commer-

cial recording device in order to bypass developing

times and because such instruments provide the best

sound quality and noise immunity while still being

portable (Zoom, 2012). The instrument has 2 inde-

pendent channels with near-Lambertian spatial sen-

sitivity (directional microphones) which signiﬁcantly

reduces ambient sounds and other stray noises present

on the exam location. The recordings are stored on an

SD card and afterwards downloaded to a processing

workstation for analysis.

Each full night recording stores an uncompressed

16 bit single channel with at 44.1KHz sampling rate.

Due to the used acquisition conﬁguration, there is an

upper limit of 6h45m to the record length of a data

taking session. This is indeed compatible with the

PSG protocol and doesn’t represent a limitation to

data availability.

The use of a non-contact microphone may add

some challenges to this work since the source and the

destination of the sound do not have the same relative

position and distance throughout the night. In fact,

there are some works pointing their goals to this issue.

One of such works was developed by (Herzog et al.,

2009). Its investigation team used 4 non-contact mi-

crophones and 2 contact microphones. Non-contact

microphones were at different distances and at dif-

ferent relative positions from the source. The results

show an independence relationship between intensity

(% of maximum intensity) and the position of the non-

contact microphones since the intensity proﬁle is al-

most the same throughout all the studied frequencies

for all the non-contact microphones. Although there

is a suggestion that the recording took place with the

patient in the supine position there isn’t a clear evi-

dence if the sleeping position was controlled. If not,

the results can be biased, because different sleeping

positions mean different distances between the source

of the sound and the microphones. Another conse-

quence of studying different sleeping positions is the

sound reﬂection on the wall of the room, different for

each one.

Since this research work only used one acquisition

device, the best place to acquire sound was just above

the head of the patient. This choice should minimize

sound losses due to the different sleeping positions

adopted throughout the night. The sound acquisition

support was placed behind and above the bed to keep

the vertical distance, around 0.7m, between the bed

and the microphone. This support has 3 degrees of

freedom to allow a correct orientation of the acquisi-

tion device to the sound source. An infrared is used

to check the orientation (Figure 1).

2.2 Data Processing

To develop this work it was used a high-level pro-

gramming language, MATLAB, working in a com-

puter with the following features: Operating System:

Windows 7 (64 bits), Central Processing Unit: i7-

3610QM 2.3GHz, RAM: 6GB.

Energy calculation was the ﬁrst step in sound pro-

cessing. In this study, the full night sound recording

was split in smaller pieces of data with length of 0.1s.

Since the frequency acquisition was 44100Hz, each

energy calculation contained 4410 sound samples. To

calculate the energy of each set of 4410 sound sam-

ples, the mathematical equation implemented in the

algorithm was:

E(x) =

∑

i=1

(1)

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222

Figure 1: Data acquisition setup.

The variable x

represents the amplitude of the i

sound sample. The energy distribution, stored in an

array with a length of one tenth of the length of the

original data sound ﬁle, was ﬁltered. The ﬁltering

process started with a convolution between the energy

array and the [1 0 -1] array. The result of this high-

pass ﬁltering was an array with elements in R. To

avoid working with negative values the absolute val-

ues were taken and then a moving average ﬁltering

was applied. Each energy element was average by its

10 nearest neighbors to remove low amplitude peaks.

With the purpose of detecting each respiratory

event, a Gaussian ﬁt was applied to the ﬁltered data.

To perform the Gaussian ﬁt, a 4 second sliding win-

dow with a time step of 0.5 seconds was chosen to try

to get one respiratory event each time. On the other

hand, a smaller window could be ineffective to res-

piratory events detection. The Gaussian ﬁt does not

start at the beginning of the array but only 10 minutes

after the sound recording starts and it goes until the

end of the ﬁltered energy array. The 10 minutes de-

lay was implemented to ignore the ﬁrst minutes where

the patient was still awake. It was usual the patient

awakes in the middle of the study and, therefore, all

the results inside these time periods must be consid-

ered as interference. During the Gaussian ﬁt process,

the algorithm calculates the center of mass, R, of the

current window to know where the respiratory event

is most likely to be:

R =

∑

i=1

(2)

M =

∑

i=1

(3)

In (2) and (3) m

and r

represents, respectively,

the i

element of the energy ﬁltered subset and of the

time subset. Since the sliding window has a duration

of 4 seconds and each energy value represents 0.1s

then R is calculated for 40 points, k, each time.

The Gaussian function template to the ﬁt process

had one variable, x, and 3 parameters to be calculated,

a, b and c. The algorithm used the following Gaussian

function, F(x):

F(x) = a.e

−(

x−b

)

(4)

When the ﬁtting process is ﬁnished, the algorithm

calculates the maximum of the Gaussian function,

(4). Throughout the window sliding process, the al-

gorithm tried to ﬁnd each respiratory event and store

it.

With the respiratory events detected, the ﬁnal al-

gorithm step was to ﬁnd the entropy of each one in

the sound ﬁle. In information theory, a very common

formula is given by the Shannon’s Entropy, H(x):

H(x) = −

∑

i=1

p(x

)log

p(x

) (5)

If a probability of an event was 0, p(x

) = 0, then

the entropy of such event was 0:

0.log

0 = 0 (6)

Every time the sound recording device made an

acquisition, such data was stored in a signed variable

of 16 bits. The sample space, Ω, in a variable of

16 bits is a set of 65536 possible outcomes, l, each

one representing an elementary event, x

. To know

the probability of each event, a data acquisition pro-

ﬁle was calculated, for each sound ﬁle, to know how

many times each event occurred. The calculation of

the Shannon’s Entropy was performed for the neigh-

borhood of each respiratory event. The length of the

neighborhood was T = 3.1s. For a neighborhood of

length T and a respiratory event at time t, then the

Shannon’s Entropy would be calculated with samples

between



t −

t +



. Finally, the Shannon’s En-

tropy was calculated with a logarithm of base 2. The

maximum energy value, E

, around each detected

respiratory event with time t was determined using a

time span of 1s [t − 0.5 t + 0.5]. In the end, the plot

between E

and entropy was taken.

In the development of this data processing tool,

other features have been created as a background sup-

port or as a different parallel processing path (Figure

SnoringAnalysisonFullNightRecordingsbasedintheEnergyandEntropyinPSGBasalStudies

223

Figure 2: Algorithm workﬂow.

2). The alternative parallel processing path used a set

of conditions, e. g. calculation of the energy’s quan-

tile to 25%, 50% and 75%, to ﬁnd only snoring events.

The results achieved allow a proﬁle of snoring distri-

bution during the sleep and a proﬁle of the time space

between 2 consecutives snoring events. This last pro-

ﬁle allows the user to select a time span and see where

such snoring events occur during the night. Another

feature in the algorithm allows the user to select an-

other time span in the energy plot and either appears

a list with the times of the respiratory events or a list

with the times of the snoring events of such time span.

If the selected data type is respiratory events, there

is the possibility to listening an individual event and

classify it as breath, snore or interference.

3 RESULTS

Each full night sound recording had near 2GB of data.

Such amount of data was huge and not easy to han-

dle in an ordinary computer. Even if a computer has

enough RAM memory to load this amount of data it

would be unwise because it would affect its perfor-

mance. On the other hand, if the algorithm picked

up a suitable time span to calculate the energy, no

respiratory event would be lost and higher amplitude

signals would be distinguish even better than lower

amplitude signals because of the energy’s deﬁnition,

∑

i=1

. A good time span, not too big to lost respi-

ratory events and not too little to get a small energy

array, was required and the time chosen was 0.1 sec-

onds. An example of the energy array of a full night

sound recording, for a time span of 0.1 seconds, is

available in Figure 3 and in Figure 4.

Figure 3: Sound energy of a full night sound recording with

y-axis in linear scale.

In Figure 4 it is possible to identify some oscil-

lations in the baseline of the signal energy. The ﬁrst

half of the energy distribution is very different from

the second half. Even within the ﬁrst half of the en-

ergy distribution the baseline is not stable, with peri-

odic oscillations between 2 values. Both values are

higher than the energy baseline of the second half.

In signal acquisition is very difﬁcult to have a sig-

nal without interference. In this work several inter-

ference sources may exist. The most common ones

are coughing, changingbed sleep position, road trafﬁc

and sleep technicians talking with patients or resolv-

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224

Figure 4: Sound energy of a full night sound recording with

y-axis in log scale.

ing data acquisition problems. Another interference

sources are poor weather conditions, like heavy rain

or strong winds, air conditioning (AC) and capno-

graph. In Figure 4 the source of interference is most

likely to be the AC. Performed tests to evaluate the

functional behaviour of the AC show a similar pro-

ﬁle. In the ﬁrst half of the energy distribution, AC

switches between the working and the idle mode. In

the second half the AC was shut down since the en-

ergy baseline achieve even lower values. An example

of a recording free of interference from an AC system

is available in Figure 5.

Figure 5: Full night energy proﬁle when AC is always off.

Computing the energy of a signed signal shifts its

baseline from near zero to a higher value since all en-

ergy values are non-negative. Before the implementa-

tion of a Gaussian ﬁt, pre-processing techniques must

be implemented to have an energy signal with a base-

line near zero around the respiratory event. Since the

Gaussian function has near zero values for points far

enough of the expected value, µ, a ﬁltering process

was developed in the algorithm. The ﬁltering process

developed can be split in two steps. In the ﬁrst one, a

convolution was implemented to shift the baseline to

values nearer to zero. The second step implements a

moving average ﬁlter to reduce or even eliminate low

level amplitude signals. Figure 6 shows the energy

distribution before, in a blue line, and after ﬁltering,

in a red line.

After the ﬁltering process, the algorithm applied

Figure 6: Sound energy before (blue line) and after (red

line) ﬁltering and respiratory events detection (dark dots).

the Gaussian ﬁt to the ﬁltered data and it tried to ﬁnd

the time location of all the respiratory events. The

Gaussian ﬁt was very accurate and it found almost all

the respiratory events and its maxima. Figure 6 shows

how the algorithm performed in the detection of such

events, dark dots.

With a set of data identifying the respiratory

events of a full night sound recording, the algorithm

applied the deﬁnition of the Shannon’s Entropy to

calculate the entropy of each respiratory event in

its neighborhood. The Shannon’s Entropy is calcu-

lated using the original data from the full night sound

recording.

Figure 7: Relationship between energy and entropy for pa-

tient 1 to 12.

Figure 8: Relationship between energy and entropy for pa-

tient 13 to 24.

The relationship between energy and entropy for

all the patients from this research may be seen in Fig-

SnoringAnalysisonFullNightRecordingsbasedintheEnergyandEntropyinPSGBasalStudies

225

Figure 9: Relationship between energy and entropy for pa-

tient 25 to 36.

ure 7, Figure 8 and Figure 9. In Figure 10 it is possible

to see the relationship between entropy and energy for

2 different patients. The red proﬁle shows an exam-

ple of a patient with a medical diagnosis of snoring.

The blue proﬁle shows an example of a non-snoring

patient.

Figure 10: Relationship between energy and entropy of

each respiratory event for a non-snoring patient (blue) and

for a snoring patient (red).

Figure 11: Relationship between energy and entropy while

AC is off (green) an on (red) switching between working

and idle state.

The interference of the AC during data acquisition

can be analyzed in Figure 11. Although there are de-

viations in the data distribution, the trend line of the

relationship between both variables it is not affected.

The relationship between the energy and the en-

tropy of a respiratory event seems to have an upper

limit, a vertical asymptote function. This limit is jus-

tiﬁed by (5). For a chosen logarithm base, the en-

tropy is only a function of the probability of an event,

H(x) ∝ p(x

). So, whatever the energy value, the max-

imum entropy is achieved when the number of differ-

ent events in the neighborhood of a respiratory event

is equal to the number of different events of an entire

full night sound recording.

4 CONCLUSIONS

The relationship between both variables for a full

night data recording suggests the existence of a trend

line. Although the paper does not introduce a mathe-

matical equation of such trend line, Figures 7, 8 and

9 show a common behaviour. For low entropy values

an almost horizontal line represents quietly respira-

tory events. Such respiratory events are non-snoring,

meaning a normal breath from the patient. It is pos-

sible to see a high density in this area of the plot in

Figure 10, especially in the blue proﬁle.

In the case of a non-snoring patient the trend line

should be an equation of the type y = b, with b the

best representative value of all the energies of the res-

piratory events. Figure 10, blue proﬁle, is an example

of a non-snoring patient accordingly with the medi-

cal opinion. There isn’t a perfect horizontal trend line

but almost all the points are below the energy value

of 0.1. The points missing the equation y = b repre-

sents interference generated during the recording and

also snores. Despite the classiﬁcation as a non-snore

patient it doesn’t mean the patient doesn’t snore. It

means the patient doesn’t snore or he snores just a lit-

tle bit.

As quietly respiratory events start to be replaced

by loud respiratory events, a snoring event, the energy

also increases. The increase in energy induces an in-

crease in the disorganization of the normal breathing.

As a consequence entropy increases.

Although there is a clear trend line in the plots

entropy vs. energy, some dots miss such relationship.

Such deviations can be explained by the interference

and by the Gaussian ﬁt process. During the night, the

patient can change their sleeping position, can cough

or the sleep technician can go to the bedroom. On

the other hand, the Gaussian ﬁt can ﬁnd some false

respiratory events.

In the future, the relationship between energy and

entropy can be used by the physicians to understand

the development of OSAS. Since OSAS means a total

or partial obstruction of the upper airways, the mo-

ment when the muscle re-acquire tonus to let the air

go into the lungs can give useful information about

BIOSIGNALS2013-InternationalConferenceonBio-inspiredSystemsandSignalProcessing

226

the disorganization of the process.

Further work must be developed to understand

data distribution and its variability in the plots entropy

vs. energy. A second feature to be explored in these

plots is the slope of a mathematical equation repre-

senting each data set. To know how fast and earlier in

time the curve starts to rise can reveal new useful in-

formation. These information may bring new insights

in the study of snoring and OSAS.

ACKNOWLEDGEMENTS

A special acknowledge to the sleep technicians Clara

Santos, Conceic¸˜ao Travassos, Liliana Sousa, L´ucia

Batata, Mafalda Ferreira and Mar´ılia Rodrigues for

their support in the development of this work.

There is, also, an acknowledgement to be done to

all the patients who helped the development of this

work. Without their authorization to collect data it

would be impossible this work achieve its goal.

The development of this work was supported by

the Portuguese Foundation Fundac¸˜ao para a Ciˆencia

e a Tecnologia through the reference identiﬁcation

SFRH/BD/66442/2009.

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