Discrete Wavelet based Features for PCG Signal Classification using

Hidden Markov Models

Rima Touahria

1,3

, Abdenour Hacine-Gharbi

and Philippe Ravier

LMSE Laboratory, University of Bordj Bou Arréridj, Elanasser, 34030 Bordj Bou Arréridj, Algeria

PRISME Laboratory, University of Orléans - INSA CVL, 12 rue de Blois, 45067 Orléans, France

ETA Laboratory, University of Bordj Bou Arréridj, Elanasser 34030 Bordj Bou Arréridj, Algeria

Keywords: PCG Signal, Features Extraction, Discrete Wavelet Transform, Wavelet Cepstral Coefficients, MFCC

Coefficients, Hidden Markov Model, Classification.

Abstract: This paper proposes the use of several features based on Discrete Wavelet Transform as novel descriptors for

the application of classifying normal or abnormal phonocardiogram (PCG) signals, using Hidden Markov

Models (HMM). The feature extraction of the first descriptor called “DWE” consists in converting each PCG

signal into a sequence of features vectors. Each vector is composed of the energy of the wavelet coefficients

computed at each decomposition level from an analysis window. The second descriptor “LWE” consists in

applying the logarithm of DWE features, while the third descriptor “WCC” applies the DCT on the LWE

features vector. This work aims to find the relevant descriptor using PCG Classification Rate criterion. This

is achieved by implementing a standard system of classification using the HMM classifier combined with

MFCC features descriptor. Each class is modeled by HMM model associated to GMM model. Several

experiences are carried out to find the best configuration of HMM models and to select the optimal mother

wavelet with its optimal decomposition level. The results obtained from a comparative study, have shown that

the LWE descriptor using Daubechies wavelets at order 2 at level 7, gives the highest performance

classification rate, with a more compact features representation than the MFCC descriptor.

1 INTRODUCTION

Before the 19th century, physicians used the ear as a

way to listen to the sound emitted by heartbeats in

order to identify heart operation state, which can be

useful for diagnosing heart disease. This method of

"immediate hearing" on the chest or the back is a very

rudimentary approach for physicians having led to

dissatisfaction with it. In 1816 Isaac invented a

medical instrument called the "stethoscope", which is

an exciting and practical new method of bedside

examination. This instrument is widely used to

diagnose heart disease (Hanna & Silverman, 2002).

Despite its approval, this requires a long-term

practice and several years of clinical experience is

necessary and is difficult to obtain. This led doctors

and researchers to develop techniques for helping

cardiac auscultation. This need gave birth to

electronic stethoscopes, which have the advantage of

being able to record, store and replay the sounds in

https://orcid.org/0000-0002-7045-4759

https://orcid.org/0000-0002-0925-6905

better conditions, for diagnostic purposes (Jiang &

Choi, 2006) (Moukadem, Dieterlena, Hueberb, &

Brandtc, 2013).

The heart sound signal of a normal heartbeat has

two sounds. The first heart sound, a lub of "lub-dub"

(S1), corresponds to the systolic period. The second

heart sound, a dub (S2) of "lub-dub", corresponds to

the diastolic period. These sounds are caused by the

closing and opening of valves inside the heart

(Kumar, et al., 2006). A normal heartbeat sound has

an out of rhythm "lub ... dub...". Doctors can find

heart additional or abnormal sounds from listening to

sound with rhythm “lub-lub…dub, lub…dub-dub”

(Gomes & Pereira, 2012) (Raza , et al., 2019).

The classification phase usually comprises three

steps: pre-processing, feature extraction and

classification model. First, pre-processing is an

important step in the data mining process for

eliminating noise and cleaning the heartbeat signal,

and this is done using a band pass filter. The

334

Touahria, R., Hacine-Gharbi, A. and Ravier, P.

Discrete Wavelet based Features for PCG Signal Classiﬁcation using Hidden Markov Models.

DOI: 10.5220/0010343003340340

In Proceedings of the 10th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2021), pages 334-340

ISBN: 978-989-758-486-2

extraction of characteristics is an essential stage, from

which the classification system is carried out; this

step transforms each heartbeat sound signal into to

sequence of vectors. The choice of characteristics is

essential and is done by the system designer

following many considerations: the main motivation

is to choose features as discriminatory as possible;

also the greater the number of characteristics, the

more complex the classification system and the

longer the learning time, which makes the real-time

implementation more difficult. Several studies related

to classification and pattern recognition have been

introduced in the past using techniques such as

wavelet transform (WT), Mel-Frequency Cepstral

Coefficients (MFCC), ensemble empirical mode

decomposition, multi-fractal decomposition and

Shannon energy (Chen, et al., S1 and S2 heart sound

recognition using deep neural networks, 2016) (Chen,

Yang, & Ho, S1 and S2 Heart Sound Recognition

Using Deep Neural Networks, 2017) (Gupta,

Palaniappan, Swaminathan, & Krishnan, 2007)

(Alajarin, 2007). In many studies, Hidden Markov

Models (HMM) were used for PCG modelling and

analysing, in conjunction with short-time Fourier

transform coefficients (STFT). The mel-scaled WT

were used to classify signals of heart sounds in

(Wang, Lim, Chauhan, Foo, & Anantharaman, 2007).

Conjunction of signal amplitude and MFCC

coefficients with HMM were used in (Chauhan,

Wang, Lim, & Anantharaman, 2008) and the same

idea were also applied using DFT and principal

component analysis in (Saracoglu, 2012).

In this study, we propose to apply a feature

extraction method based on Discrete wavelet

Transform (DWT), mostly inspired by research in

speech processing (Didiot, Illina, Fohr, & Mella,

2010) and in electrical appliances identification

(Hacine-Gharbi & Ravier, 2018). This method can

extract three descriptors called respectively DWE

(Discrete Wavelet Energy), LWE (Log Wavelet

Energy) and WCC (Wavelet Cepstral Coefficients).

The DWE descriptor extraction consists to convert

each PCG signal into a sequence of features vectors

obtained each one by computing the energy at each

level of dyadic wavelet decomposition from an

overlapping analysis window. The LWE descriptor

applies the logarithm on the features of DWE

descriptor, while the WCC descriptor applies DCT

transform on the features of LWE descriptor. The aim

of this work is to investigate the relevance of these

descriptors by comparing them with the traditional

MFCC descriptor for the task of PCG signals

classification, in terms of classification rate and

complexity.

The remainder of this paper is organized as

follows. In Section 2, we discuss sound classification,

features extraction approaches and we introduce the

proposed approach and detail each algorithm step.

Experimental results and discussion are presented in

Section 3. We end up by a conclusion and

perspectives concerning future work.

2 CLASSIFICATION OF PCG

SIGNAL

2.1 Dataset

In order to test our methods, we used the PASCAL

Classifying Heart Sounds Challenge database

(Bentley, Nordehn, Coimbra, Mannor, & Getz, 2011).

Database comprises 176 recordings for heart sound

segmentation. More details about the challenge

dataset can be found in (Liu, et al., 2016). During

evaluation, we use only 621 cardiac cycles (beat)

including 204 pathological cardiac cycles. This

extraction and recording is carried out using the

PRAAT software. For each version of the signal, a

labelling file is created in text format, containing the

transcription of the signal in a sequence of labels.

These labels are the normal and abnormal classes

Each beat belongs either to the normal class (label

‘N’) or to the pathological class (label ‘AN’). Each

PCG signal was then resampled to 16000Hz.

Table 1 summarizes the distribution of the

training and testing sets composing the PASCAL

database.

Table 1: Distribution of the testing and training record

numbers of the PASCAL database.

Classes Normal Abnormal

Numbe

417 204

Test/Train 121/296 58/146

2.2 Proposed Feature Extraction

Method

In order to classify the heart sound components, many

authors have proposed the use of the MFCC descriptor

(Rahmandani, Nugroho, & Setiawan, 2018) (Nilanon,

Yao, Hao, & Purushotham, 2016) (Numan, et al.,

2019). This last descriptor is a perceptual

representation of the power spectrum of a sound

signal. It is obtained by taking the Discrete Cosine

Transform (DCT) of the logarithmic power spectrum

on a nonlinear mel-scale of frequency by using the

Discrete Wavelet based Features for PCG Signal Classiﬁcation using Hidden Markov Models

335

following frequency transformation (Wu, Kim, &

Bae, 2010):

𝑀𝑒𝑙



𝑓



 2595𝑙𝑜𝑔



1 

𝑓

700



(1)

The features extraction operation from PCG

signals requires the computation of 39 dimension

vectors per frame including static features and energy

with their dynamic features. When MFCC is used,

acceptable results for clean heart sounds are obtained.

However, the results are sensitive to the recording

frequency and the performance is not as good in a

noisy environment. This is based on the results of

many studies (Numan, et al., 2019) (YaseenSonG &

Kwon, 2018) (Li, et al., 2019), whereby the latter

indicates that the new extracted feature is more

suitable and shows stronger anti-interference ability

for heart sound signals representation than that of the

MFCC. The results show a remarkable classification

performance in detecting the noisy class accurately. At

least, the MFCC feature vectors require high

dimensionality computation.

To overcome this limitation P. Wang et al. have

proposed to replace the MFCC by the mel-scaled WT.

This method applies the wavelet transform to the mel-

spectrum of the phonocardiogram (Wang, Kim, &

Soh,2005). Their suggested method has produced

encouraging results compared with those obtained

achieved using the MFCC.

Many other wavelet features can be further

computed from discrete wavelet coefficients, namely

Discrete Wavelet Energy (DWE), Log Wavelet

Energy (LWE) and Wavelet Cepstral Coefficients

(WCC), as depicted in Figure 1.

Figure 1: block diagram describing the process of wavelet

cepstral coefficient (WCCs), discrete wavelet energy

(DWE) decomposition-based calculus and log wavelet

decomposition-based energy (LWE) features extraction

with Hamming windowing.

The idea of using DWE, LWE and WCC as the

feature set for a PCG classification system comes from

the success of wavelet cepstral coefficients for speaker

identification (Lei & Kun, 2016) and also because

PCG and speech are both acoustic signals. Our

acoustic analysis approach consists in extracting the

DWE, LWE and WCC descriptors for short-term

feature extraction with low dimensionality of the

features vectors. The LWE descriptor consists in

calculating the log of the energy of the wavelet

coefficients at each decomposition level without DCT

transform in order to keep the interpretation of a

descriptor representing energies in frequency bands.

The flowchart of DWE, LWE and WCC extraction

method used in this paper is shown in Figure 1. The

whole procedure was carried out in the four steps

given as follows:

Step 1: Preprocessing: this step goes through the

following operations (Nabih-Ali, EL-Sayed,

El-Dahshan, Ashraf, & Yahia, 2017):

 The PCG data is segmented into 20ms-

overlapping frames, with 10ms overlap

between them.

 Hamming window is applied on these

20ms portions.

Step 2: CWT is the continuous version of WT

which principle remains similar when going

to the DWT discrete version. However, the

application of DWT requires that the scales

used by the wavelet and their positions are

sampled down by a factor of two (or up for the

inverse DWT). This is called the dyadic scale.

In practice, DWT is simply computed by

using a filter bank for constructing the multi

resolution time-frequency plane. The filter

bank is achieved using a half-band low pass

filter and a half-band high pass filter. In the

iterative wavelet decomposition procedure,

the low-frequency coefficients are called the

approximations (𝑎



), while the high-

frequency coefficients are called the details

(𝑑



The DWT coefficients 𝑎



𝑛 and 𝑑



𝑛 are

calculated, at each level 𝑗, by the following formula:

𝑎





𝑛



𝑎





𝑙2𝑛





𝐿



𝑙



for

𝑗

1,… ,𝑝

(2)

𝑑





𝑛



𝑎





𝑙2𝑛





𝐻



𝑙



(3)

where the analyzed signal is of length N2



. The

notations 𝐿 and 𝐻 represent the low-pass and high-

pass filters, respectively.

As a result of this step, we obtain a feature vector,

which is called Discrete Wavelet decomposition-

based calculus Energy (DWE) and which is evaluated

as:

𝐷𝑊𝐸𝑑



 𝑑



𝑛



for

𝑗

1,… ,𝑝









(4)

ICPRAM 2021 - 10th International Conference on Pattern Recognition Applications and Methods

336

𝐷𝑊𝐸𝑎



 𝑎



𝑛











(5)

The number of samples is 𝑁



𝑁/2



at each

level 𝑗, which means that this number is reduced by a

factor 2 at each iteration from (1 to 𝑝.

Step 3: The previous step allows the calculation of

another descriptor called LWE. This last is the

log of energy at each level of dyadic

decomposition. It writes:

𝐿𝑊𝐸𝑑



𝑙𝑜𝑔 𝑑





𝑛







for

𝑗

1,…,𝑝









(6)

𝐿𝑊𝐸𝑎



𝑙𝑜𝑔 𝑎



𝑛











(7)

Step 4: The previous step finally allows further

computation of WCCs, which are the results of

the application of the inverse discrete cosine

transform (DCT) on the logarithmic values of

energies. This homomorphic analysis has the

effect of making the obtained coefficients less

correlated with each other.

Previous results described in (Hacine-Gharbi &

Ravier, 2018), in the field of electrical appliances

identification, showed that the WCC performed good

results, in terms of appliance identification rate.

2.3 Hidden Markov-based

Classification System

The classification system design of heartbeat sound is

divided into two phases, the training and testing

phases as shown in Figure 2. Therefore, we split the

dataset (Bentley, Nordehn, Coimbra, Mannor, & Getz,

2011) into two sets with a proportion of 70% for

training and 30 % for testing data. The two phases

require feature extraction step, which consists in

dividing each signal in overlapped windows and

converting each window into features vector.

Figure 2: Flow chart outlining the procedure of the

proposed classification system.

Hence, this step converts each signal into a sequence

of features vectors.

In the training phase, the data are learned by

modelling the signals of each class by a HMM model

associated with GMM (Gaussian Mixture Model)

model. The feature extraction techniques are applied

in order to produce input data to the system for class

learning.

In the testing phase, the temporal signal is

transformed into a sequence of feature vectors which

are used as input data for the HMM classifier.

Finally, the evaluation of the implemented system

is done by using the decision results given by the

classifier knowing the ground truth given by the

expert notations. Appropriate statistics will be used

for this performance evaluation task.

2.4 Performance Evaluation

The overall performance of the PCG signal

classification was evaluated by the computation of

classification rate (CR) given by the Accuracy value

𝐴𝑐𝑐



 provided by the HMM Toolkit library

software (HTK) (Young, Kershaw, Odell, & Ollason,

1999) and is calculated as follows (Young, Kershaw,

Odell, & Ollason, 1999):

𝐴

𝑐𝑐





𝐻

𝑁

(8)

where N is the total number of PCG signals given

at the input of the classifier, and H is the number of

the PCG signals correctly classified.

3 EXPERIMENTAL RESULTS

3.1 Experiments

Each heartbeat is modeled by a N



HMM. Each

state is modeled by a GMM with N



Gaussians

of frame size of 20ms. The implementation of the

system is carried out using the HTK library (Young,

Kershaw, Odell, & Ollason, 1999). The performance

of this classification is performed in terms of CR.

The following section, which is structured in two

parts, presents the experimental results. In the first

part, we compare the performance of the new features

to that of other features. In a second part, we carry out

an experiment to select the optimal mother wavelet

for the best previous descriptor and decomposition

level.

Discrete Wavelet based Features for PCG Signal Classiﬁcation using Hidden Markov Models

337

3.2 Results and Discussion

3.2.1 Comparative Study between Different

Features

Table 2 shows the best possible classification results

with optimal number of states and optimal number of

Gaussian components N



when varying the

States from 2 to 12 and varying the N



from 1

to 96 (taking 8 values of N



1,2,3,6,12,24,48,96). The features vector was

computed with sliding Hamming windows of 20ms

and 50% of overlapping (Nabih-Ali, EL-Sayed, El-

Dahshan, Ashraf, & Yahia, 2017).

By observing the results of each column, we can

find that the best performance is achieved when the

optimal number of states is set to 10 for the feature

descriptor (LWE) with CR of 92.74%. Using the

MFCC features, the baseline algorithm yielded the

poorest CR of 87.71 % with the configuration of 39

dimensional feature vector. In the light of these

results, we can conclude that the model, which uses

LWE features, obtained higher CR with respect to the

other wavelet features and the MFCC descriptors.

Table 2: Comparison of ACC

_HTK

(%) for different features

extractions descriptors techniques using Daubechies (db2)

at level 7 for the hmm optimal number of states (Lekram &

Abhishek, 2014). The features number is given for each

descriptor.

MFCC

(39)

DWE

(8)

LWE

(8)

WCC

(8)

𝐍

𝐒𝐭𝐚𝐭𝐞𝐬

9 8 10 8

𝐍

𝐆𝐚𝐮𝐬𝐬𝐢𝐚𝐧𝐬

2 2 3 3

𝐀𝐜𝐜

𝐇𝐓

𝐊

%

87.71 88.27 92.74 89.94

3.2.2 Optimal LWE Parameterization

Window Duration. Table 3 shows the CR results for

different window duration values. The Db 2 wavelet

and a decomposition level 7 are considered in this

experiment for the classification system (Lekram &

Abhishek, 2014). By analyzing the results in Table 3,

we can find that the maximum CR (Acc

HTK

) in each

column is achieved when the window size equals

20ms, the best CR of 92.74% was reached in this

table. Therefore, it is desirable to select a window

duration of 20ms.

Table 3: Acc

HTK

(%) for different combinations of the

window size.

Wind. size 60ms 50ms 40ms 30ms 20ms

𝑨𝒄𝒄

𝑯𝑻𝑲





87.71 88.27 88.83 89.39 92.74

Wavelet Family and Decomposition Depth. In this

part, the smoothness and the impact of the wavelet

family on the CR

is evaluated. This study intended to

define the optimal mother wavelet with its optimal

decomposition level. In the present work, the

following wavelet families are considered:

 the Daubechies family with orders going

from 1 to 8: Db1, Db2, ..., Db8;

 the Coiflets family with orders going from 1

to 5: Coif1, Coif2..., Coif5;

 the Symlets family with orders going from 1

to 8: Sym1, Sym2, ..., Sym8.

We used the optimal system configuration

identified in the previous studies, which is composed

of ten HMM states, where each state is represented by

a three Gaussian mixture.

The results are given in Table 4, where the highest

CR value of 92.74% was achieved when using

Daubechies wavelet of order 2 and a decomposition

level of 7.

Table 4: Comparative results between different kinds of

wavelet families. The table shows the Acc

HTK

values for the

optimal decomposition level as well as the optimal order for

each wavelet family.

Daubechies Symlet Coiflets

level 7 2 6

order 2 2 1

𝐀𝐜𝐜

𝐇𝐓

𝐊

%

92.74 89.94 89.39

Table 5 also gives the detailed results of AccHTK

for the best Daubechies wavelet family when

changing levels and orders. The Table gives some

credit to our study because of the high variability

observed in Acc

HTK

values between the lowest of

72.07% and highest value of 92.74%.

Table 5: Acc

HTK

(%) of LWE for different Daubechies

orders and different decomposition levels.

12345 6 7 8

db1 86.03 86.03 86.59 85.47 81.01 87.15 85.47 87.15

db2 87.15 89.94 86.03 85.47 86.03 87.71 92.74 90.50

db3 84.36 85.47 86.03 77.65 78.77 83.80 87.71

db4 79.89 82.68 82.12 77.09 81.56 81.56 85.47

db5 72.0

79.89 80.45 77.65 79.89 79.33

db6 76.54 78.77 85.47 82.12 83.80 86.03

db7 79.89 83.80 85.47 82.68 84.92 84.92

db8 78.77 83.24 87.15 83.24 87.71 82.68

Moreover, results were obtained with the Coiflets

and Symlets wavelet families by following the same

experimental protocol. The order 2 at level 2 showed

the best performance within the Symlet family with

CR of 89.94%. Finally, the order 1 at level 6 showed

ICPRAM 2021 - 10th International Conference on Pattern Recognition Applications and Methods

338

the highest performance within the Coiflets family

with CR of 89.39%.

As a conclusion, from the experiments carried out,

the LWE descriptors, obtained using Daubechies and

Symlets wavelets at low orders and high

decomposition levels (order 2 with level 7 and order2

with level 2, respectively), gave the best CR values.

On the other hand, taking Coiflets wavelets, the best

results were obtained at order 1 with level 6 and the

performance dropped of about 0.99%.

4 CONCLUSIONS

In this study, three features descriptors called DWE,

LWE and WCC, based on discrete wavelet transform

are proposed for the classification of normal and

abnormal PCG signals using HMM classifier.

Different experiments have been carried out to find

the best configuration of the HMM classifier and to

select the optimal wavelet mother with its

decomposition level. The results have shown that the

combination of HMM model of 10 states associated

to GMM of 3 Gaussian components, with LWE

descriptor computed on analysis window of 20 ms

duration using the mother wavelet Db2 with

decomposition level 7 presented the highest

performance level with CR of 92.74%. The results

demonstrate the relevance and the efficiency of LWE

descriptor compared to the MFCC, WCC and DWE

in terms of CR and compact feature representation.

In future works, we are planning to evaluate the

reference system on a larger database. The LWEs will

also be tested under different noise conditions in

order to observe their robustness towards noisy PCG.

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