Journal of Signal and Information Processing, 2011, 2, 232-237
doi:10.4236/jsip.2011.23032 Published Online August 2011 (http://www.SciRP.org/journal/jsip)
A Time-Frequency Approach for Discrimination of
Heart Murmurs
Sepideh Jabbari, Hassan Ghassemian
School of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran.
Received May 29th, 2011; revised July 18th, 2011; accepted July 26th, 2011.
ABSTRACT
In this paper, a novel fram ework based on a time-frequ ency (TF) approach is proposed for detection of murmurs from
heart sound signal. First, a high-resolution TF algorithm, matching pursuit, was used to decompose each heart beat
into a series of TF atoms selected from a redundant dictionary. Next, representative components of murmurs were iden-
tified by clustering the selected a toms of all th e beats into a finite numb er of clusters. Then, Wign er-Ville distrib ution of
the representative components was used to generate a set of 8 features which were fed to a classifier. Experiments with
a dataset consisting of heart sounds from 35 normal and 35 pathological subjects showed a classification accuracy of
95.71% in dist i ng ui shing murmur s fr o m n or mal heart sounds.
Keywords: Phonocardiogram (PCG), Murmur, Matching Pursuit (MP), Time-Frequency Atom, Clustering
1. Introduction
Mechanical activity of the heart is evaluated by ausculta-
tion and analysis of phonocardiogram (PCG) signal,
which is a recording of heart sounds. PCG provides val-
uable information on the structural integrity and function
of heart valves. Heart sounds normally consist of two
regularly repeated thuds, known as S1 and S2 for every
heat beat. An underlying pathology such as diseased
valves produces some additional and abnormal sounds
which are called murmurs. The automatic detection of
murmurs has been widely considered for several decades
because of the human auditory limitations in distin-
guishing them from normal heart sounds [1].
PCG is highly nonstationary signal with multicompo-
nent nature and identification of its components can be
performed by a nonstationary signal analysis tool such as
time-frequency (TF) analysis methods [2]. Short-time
Fourier transform (STFT) is one of the existing tech-
niques that tackles the nonstationarity of the PCG signal
by segmenting it into stationary parts [3,4]. Wavelet
transform (WT) was used to obtain TF decomposition of
PCG signals in previous studies [5,6]. It does not require
the fixed data window needed for STFT; however, even
wavelet bases are not well suited to exact TF representa-
tion of PCG components whose localizations in time and
frequency vary widely. Some researchers performed
analysis of PCG by using Wigner-Ville distribution (WV-
D) [7]. A major drawback of the WVD is presence of
cross-term artifacts caused by aliasing when analyzing
multicomponent signals such as PCG. A true nonstation-
ary TF technique would be one that can give an accurate
parametric display of PCG characteristics with satisfac-
tory TF resolution, cross-term suppression, and without
segmentation requirements. The parameters of decom-
posed components could be later used to extract crucial
features for identification of murmurs. In this paper, we
achieve this goal using a cross-term free high-resolution
method, matching pursuit (MP) algorithm. MP is a signal
decomposition method whereby a signal is decomposed
into a linear combination of TF components (atoms) that
are selected from a redundant dictionary [8].
Figure 1 represents the architecture of our proposed
framework for heart murmur detection. PCG signal from
an electronic stethoscope is processed along with a si-
multaneously recorded electrocardiogram (ECG) stream
as a reference signal. First, preprocessing stage is carried
out consisting of filtering, down sampling, and beat seg-
mentation. Next, all the beats are decomposed into a se-
ries of TF atoms using the MP algorithm and a redundant
Gabor-type dictionary. Each selected atom is described
by a set of parameters including the amplitude, position
in time, scale, frequency, and phase. Groups of atoms
with similar morphology of parameters are then isolated
into clusters. For each cluster, atoms are merged together

A Time-Frequency Approach for Discrimination of Heart Murmurs233
Figure 1. Block diagram of the propose d schem e .
based on the mean values of their parameters to create a
single representative atom. Also, a prototypical beat cor-
responding to the beats of the analyzed PCG can be con-
structed by synthesizing these representative atoms. MP-
based TF decomposition (MPTFD) of the PCG signal is
obtained by taking the WVD of the resulted atoms. Fea-
tures are derived from the MPTFD followed by classifi-
cation using a MLP-based classifier.
The paper is organized as follows. In Section 2, theory
of the utilized method for murmurs detection is intro-
duced and our data set of typical murmurs is described.
The obtained results on murmurs detection are presented
in Section 3 and conclusion in Section 4 is the final part
of this paper.
2. Materials and Methods
2.1. Matching Pursuit
In the MP method, a discrete-time signal

x
n is de-
composed into a sum of TF atoms selected from a re-
dundant dictionary
 
1
M
mm
m
x
nagne


n
(1)
where



2
πcos 2π
mm
np s
mm
gn efnp
mm

 


 

 (2)
and

m
g
n is a Gabor-type TF atom which has good
time-frequency localization. The scale factor m
s
is used
to control the width of the th atom, and the latency
parameter controls the temporal placement. The
parameters m
m
m
p
f
and m

are frequency and phase, re-
spectively and the amplitude factor m is the expansion
coefficient. The collection of atoms with all possible
combinations of scaling, translations, modulations, and
phase-shifting, forms a redundant dictionary. The first
part in (1) denotes the sum of TF atoms till
a
M
itera-
tions of the MP algorithm, and the second part is the re-
sidue to be decomposed in the subsequent iterations. At
first iteration the signal is projected over the dictionary of
atoms and the best correlated atom that can model the
maximum possible function of the signal energy is se-
lected. The selected atom is then subtracted from the
signal to form a residue signal that will be decomposed
in the subsequent iterations [8].
2.2. K-Means Clustering
We next analyzed all the TF atoms decomposed from
different beats of a subject’s PCG to group the atoms into
a finite number of clusters, that each cluster contains
atoms with similar parameters. Clustering of the atoms
was carried out by the K-means method. K-means at-
tempts to find a user-specified number of clusters (
K
),
which are represented by their centroids. One of the
common initialization methods for the K-means algo-
rithm can be performed by determining the local maxima
of the joint probability density function (PDF) of the
samples and placing a cluster centroid at each peak [9].
After detecting these maxima, their locations were used
as the initial centroids for the K-means clustering. For
each cluster, a representative TF atom was created by
merging all the atoms of that cluster.
2.3. MP-Based TF Decomposition (MPTFD)
A MPTFD was obtained by taking the WVD of the rep-
resentative TF atoms of the previous stage by
 
2
representative
1
,,
k
K
kg
k
Wta Wt




 (3)
where


representative ,W
k
gt

is the WVD of the th rep-
resentative atom, k is its coefficient, and is the
number of clusters. This cross-term-free decomposition
has very good readability and is appropriate for analysis
of nonstationary, multicomponent signals [10].
k
Ka
2.4. Feature Extraction
The four TF parameters of the MPTFD are the energy
parameter (), energy spread parameter (), fre-
quency parameter (
EP ESP
F
P) and frequency spread parameter
F
SP , as described by (4)-(7), respectively

A Time-Frequency Approach for Discrimination of Heart Murmurs 234
 
0
,
m
m
Wt
EP t





 (4)
  
12
2
0
,
m
m
Wt EPt
ESP t

















(5)
 

0
0
,
,
m
m
Wt
FP t
Wt











(6)
  

12
2
0
0
,
,
m
m
FP tWt
FSP t
Wt























(7)
where m

is the maximum frequency present in the
signal [10]. The average (, ,
mEP mESP m
F
P, m
F
SP )
and standard deviation values (s,s,EPESP s
F
P,s
F
SP )
of each parameter, described above, were used as the
features of the input vector for the classifier.
2.5. Data Collection and Preprocessing
Heart sound and ECG data of 70 patients have been col-
lected under the supervision of Dr. Sepehri’s group.
From 70 PCGs, 35 signals are from children with patho-
logical murmurs. The remaining 35 signals are from
children with normal heart valves. The PCG signals in
this da set have been labeled by a cardiologist using
echocdiography. All PCG and ECG signals have been
recorded over a time-interval of 10 seconds. For data
acquisition, a WelchAllyn Meditron stethoscope, the
ECG, and a 1.8 GHz ACER notebook with a 16 bit stereo
soundcard and sampling rate of 44.1 kHz have been used.
Preprocessing of the heart sound recordings is neces-
sary to withhold unrepresentative data and separate indi-
vidual heart beats. First, an 8th-order Butterworth low-
pass IIR filter (at 1 kHz) was used to remove the high
frequency noise from the PCG signal. Then, down sam-
pling to 2 kHz was performed prior to any processing
block. Segmentation of the raw PCG into intervals cor-
responding to different cardiac beats is done to perform
the analysis on each of the individual beats. S1 occurs
shortly before R peak in ECG, thus detecting properly
the R peaks one can pick up the beginning and end points
of every heart beat. Therefore, the automatic segmenta-
tion of a recording PCG into separate heart beats was
carried out by means of ECG’s R peaks and a method
similar to what was proposed in [1]. A sample segmented
normal PCG and an abnormal PCG with systolic murmur
(SM) are shown in Figure 2. Synchronization of PCG
and ECG is obvious.
3. Results and Discussions
For the sake of illustration, the mentioned PCG with SM
is considered here. We applied the MP algorithm to de-
compose each individual beat of this PCG. The MP algo-
rithm was allowed to proceed until the iteration reached a
preset number
M
as a stopping criterion. For the ap-
plication in hand,
M
was set to 50, because the se-
lected atoms after this iteration have negligible correla-
tion with the original signal. At this stage, the MP algo-
rithm has selected 50 Gabor atoms from the dictionary
for decomposing each of 11 beats of the analyzed PCG.
at
ar
500 100015002000 2500
-0.05
0
0.05
Samples
500 1000 1500 2000 2500
-0.05
0
0.05
Samples
S1
S2
R R
Normal
Amplitude Amplitude
5001000 1500 20002500
-0.05
0
0.05
Samples
500 100015002000 2500
-0.05
0
0.05
Samples
SM
Abnormal
Amplitude Amplitude
Figure 2. Segmented ECG & PCG of a normal subject & an abnormal subject with systolic murmur (SM).

A Time-Frequency Approach for Discrimination of Heart Murmurs235
Therefore, a total of 550 TF atoms were selected for fur-
ther clustering and analysis. Each Gabor atom is charac-
terized by a 5-D parameter vector

,,,, T upfas


3PC
.
Since clustering in a 5-D space was difficult, principle
component analysis (PCA) was applied to reduce the
dimension of the parameter vectors to three
(). The joint PDF of the new pa-
rameter vectors in the

1,2,3 T vPCPCPC

12PC PC


EP
space was
used to obtain initial points of clusters. The local peaks
of PDF with values larger than 50% of the maximum
PDF value were selected as initial centroids of clusters
which were 20 peaks. After the clustering procedure, the
550 TF atoms were categorized into twenty clusters,
named as CC . We examined statistical
properties of the parameters including their mean and
standard deviation for each cluster, which are illustrated
in Table 1. Based on the mean values of parameters, a
representative atom was created for each cluster and by
synthesizing these atoms a prototypical beat was con-
structed (Figure 3(a)). This prototypical beat provides a
robust, compact representation of the PCG signal. The
MPTFD of the representative atoms is shown in Figure
3(b). High-frequency activates have been represented
with good TF localization in this distribution. The ,
,
1, 2,,
ESP
20C
F
P, and
F
SP waveforms were obtained from
the MPTFD and their mean and standard deviation were
calculated to form feature vectors.
The classification of PCGs as normal or pathological
was achieved using a three-layer feed-forward multilayer
perceptron (MLP). The input layer consisted of 8 nodes
indicating the input feature vectors. After some prelimi-
nary simulations, it turned out that 11 nodes in the hidden
layer showed a satisfactory performance. A tan-sigmoid
transfer function was applied to each neuron of the hid-
den layer. The output layer consisted of one neuron with
a linear transfer function in which 0 represented a normal
case and 1 represented a pathological case. The neural net-
work was trained using back propagation error method
and its training was conducted until the maximum itera-
tion limit of 30 was reached. The classification accuracy
was estimated using the leave-one-out method, which
one sample is excluded from the dataset and the classifier
is trained with the remaining samples. Then the excluded
signal is used as the test data and the classification accu-
racy is determined. This is repeated for all samples of the
dataset and the performance was calculated averaging the
classification results.
For comparison purposes, another method which per-
forms beat-to-beat detection of murmur was also exe-
cuted. Unlike our proposed framework that simply ex-
amines the prototypical beat, the second technique inves-
tigates each individual beat of the PCG and classifies the
subject as having murmur if the majority of the beats are
00.1 0.2 0.3 0.4 0.5
-0.05
0
0.05
Time (s)
Amplitude
(a)
Time (s)
0.1 0.2 0.3 0.40.5 0
50
100
150
200
250
300
350
400
0
Frequency (Hz)
(b)
Figure 3. (a) Prototypical beat (b) MPTFD of the proto-
typical beat.
labeled as showing murmur. First, each beat of the PCG
was decomposed into a series of atoms by the MP algo-
rithm. Then, the TF features corresponding to that beat
were extracted from the WVD of the selected atoms.
Next, presence of murmur was diagnosed by applying the
features into the MLP classifier. Finally, identification of
subject as normal or abnormal was done based on the
labels of majority of beats.
Results are shown in Tables 2 and 3 in the form of a
confusion matrix with percentage classification accuracy.
The use of prototypical beat results higher classification
accuracy of 95.71% compared to the beat-to-beat classi-
fication accuracy of 90.01%. From the table it can be
seen that out of 35 normal signals, 34 were correctly
classified as normal, and 1 was misclassified as patho-
logical. Similarly, out of 35 pathological signals, 33 were
correctly classified as pathological and 2 were misclassi-
fied as normal. The misclassified signals were analyzed
in detail, and we observed tat they were perceptually h

A Time-Frequency Approach for Discrimination of Heart Murmurs 236
Table 1. Statistical values of parameters of first five clusters (mean ± SD).
Cluster C1 C2 C3 C4 C5
Amplitude 0.182 ± 0.1 0.124 ± 0.075 0.117 ± 0.062 0.088 ± 0.043 0.075 ± 0.032
Time position (ms) 29.45 ± 9.12 301 ± 4.55 297 ± 2.93 127.5 ± 12.41 159 ± 8.26
Scale (ms) 51.5 ± 10.73 36 ± 6.41 60 ± 4.33 14 ± 8.92 25 ± 4.27
Frequency (Hz) 21.65 ± 4.27 33.46 ± 7.77 78.74 ± 12.23 147.6 ± 6.54 139.8 ± 5.43
Phase (rad) 0.6792 ± 0.281 –1.9342 ± 0.961 –1.2938 ± 0.629 –2.0339 ± 0.876 0.777 ± 0.265
Table 2. Classification results of prototypical beat in identification of valvular disorders. Cross-validation: MLP with
leave-one-out method, %: Percentage of classification.
Method Groups Normal Pathological Total
Cross-validation Normal
Pathological
34
2
1
33
35
35
% Normal
Pathological
97.14
5.71
2.86
94.29 100
100
Table 3. Classification results of individual beats in identification of valvular disorders. Cross-validation: MLP with
leave-one-out method, %: Percentage of classification.
Method Groups Normal Pathological Total
Cross-validation Normal
Pathological
32
4
3
31
35
35
% Normal
Pathological
91.43
11.40
8.57
88.60 100 100
similar to normal and that they could be hardly classified
as pathological by an untrained listener.
4. Conclusions
In this paper, the TF features of PCG signal were ex-
tracted by using the MP algorithm, K-means clustering
method, and WVD for detection of murmurs. The MP
algorithm first decomposed signal into a set of TF atoms,
and a clustering was followed to group these atoms into
several clusters. The representative atom for each cluster
was calculated and MPTFD was obtained by taking the
WVD of these atoms. The TF features of PCG were ex-
tracted from MPTFD followed by classification using a
MLP-based classifier. The proposed method showed
good potential for the noninvasive diagnosis of murmurs.
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