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2438 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 10, OCTOBER 2010
Separation of Heart Sound Signal from Noise in Joint
Cycle Frequency–Time–Frequency Domains Based
on Fuzzy Detection
Hong Tang∗, Member, IEEE, Ting Li, Yongwan Park, and Tianshuang Qiu, Member, IEEE
Abstract—Noise is generally unavoidable during recordings of
heart sound signal. Therefore, noise reduction is one of the im-
portant preprocesses in the analysis of heart sound signal. This
was achieved in joint cycle frequency–time–frequency domains in
this study. Heart sound signal was decomposed into components
(called atoms) characterized by time delay, frequency, amplitude,
time width, and phase. It was discovered that atoms of heart sound
signal congregate in the joint domains. On the other hand, atoms
of noise were dispersed. The atoms of heart sound signal could,
therefore, be separated from the atoms of noise based on fuzzy
detection. In a practical experiment, heart sound signal was suc-
cessfully separated from lung sounds and disturbances due to chest
motion. Computer simulations for various clinical heart sound sig-
nals were also used to evaluate the performance of the proposed
noise reduction. It was shown that heart sound signal can be re-
constructed from simulated complex noise (perhaps non-Gaussian,
nonstationary, and colored). The proposed noise reduction can re-
cover variations in the both waveform and time delay of heart
sound signal during the reconstruction. Correlation coefficient and
normalized residue were used to indicate the closeness of the recon-
structed and noise-free heart sound signal. Correlation coefficient
may exceed 0.90 and normalized residue may be around 0.10 in 0-
dB noise environment, even if the phonocardiogram signal covers
only ten cardiac cycles.
Index Terms—Fuzzy detection, heart sound signal, joint cycle
frequency–time–frequency domains, noise reduction.
I. INTRODUCTION
PHONOCARDIOGRAPHY is a noninvasive technique that
is used to check the functioning of heart valves. It is, there-
fore, widely used during medical examinations carried out by
physicians. However, ambient noise and disturbances can cor-
rupt the recorded heart sound signal. The sliding movements of
the stethoscope diaphragms in contact with the patient’s skin,
Manuscript received January 25, 2010; revised April 1, 2010; accepted April
30, 2010. Date of publication June 10, 2010; date of current version September
15, 2010. This work was supported in part by the National Natural Science
Foundation of China under Grant 30570475 and Grant 60872122. Asterisk
indicates corresponding author.
∗H. Tang is with the Department of Biomedical Engineering, Faculty of Elec-
tronic Information and Electrical Engineering, Dalian University of Technology,
Dalian 116024, China (e-mail: tanghong@dlut.edu.cn).
T. Li is with the College of Electromechanical and Information En-
gineering, Dalian Nationalities University, Dalian 116600, China (e-mail:
tracyli78@yahoo.com.cn).
Y. Park is with the Department of Information and Communication, Ye-
ungnam University, Gyeongsangbuk-Do 712-749, Korea (e-mail: ywpark@
yu.ac.kr).
T. Qiu is with the Department of Biomedical Engineering, Dalian University
of Technology, Dalian 116024, China (e-mail: qiutsh@dlut.edu.cn).
Digital Object Identifier 10.1109/TBME.2010.2051225
lung sounds, the muscular activity controlling lung movements,
and surround speech sounds represent a few of the sources of
noise and disturbance affecting the accuracy of data being ac-
quired. These noises usually have high amplitude and last for
only a short period of time. Furthermore, there is considerable
overlap in the time–frequency domains of heart sound signal
and noises. As heart sound signals are transient, they are eas-
ily contaminated with the noises. Consequently, it may become
difficult for physicians to obtain the correct diagnostic informa-
tion by auscultation when noise and disturbances are important.
Noise reduction would allow a quantitative analysis of heart
sound signal and lead to a more reliable diagnosis. The distur-
bance addressed in this paper is the impulsive noise interference,
which is typically characterized by noise pulses of short time
duration.
Over the years, various techniques of noise reduction have
been proposed for different purposes. Some techniques like
adaptive noise cancellation and filtering can be applied to re-
duce noise from heart sound recordings [1], [2]. In particular, it
has been found that noise reduction performed in a time and/or
frequency domain may not be effective for non-Gaussian, non-
stationary, and colored noises. More specifically, it is considered
inappropriate because heart sound signal and noise overlap in
both time and frequency domains. On the contrary, techniques of
cyclostationary signal processing can reduce noise in the cycle
frequency domain. Beyar et al. [3] proposed to divide recordings
of heat sound signal into a sequence of repetitive cycles. Noise
was reduced simply by summations. However, heart sounds and
murmurs tend to occur with different timings from cycle to cycle
and cannot be totally preserved while noise is suppressed. In our
earlier paper [4], the timings of heart sounds and murmurs were
aligned from one cycle to next cycle by the nonlinear time scal-
ing (NTS). Noise and disturbance were subsequently reduced by
averaging. The results were promising, although segmentation
of the heart sound signal into first heart sound (S1) and second
heart sound (S2) is fundamentally needed to determine the pa-
rameters for the NTS. This preprocess can have a detrimental
effect on the efficiency of the noise reduction. Its performance
degrades, if segmentation is inaccurate, or if the assumption that
heart sounds are consistent in consecutive cycles is not valid.
To avoid these commonly encountered limitations, we propose
a new noise reduction in this paper that is performed in the joint
cycle frequency–time–frequency domains based on fuzzy de-
tection. Comparing with the earlier study [4], one more domain,
frequency domain, is exploited. This proposed noise reduction
can accommodate variations in both time delay and waveform
0018-9294/$26.00 © 2010 IEEE
TANG et al.: SEPARATION OF HEART SOUND SIGNAL FROM NOISE IN JOINT CYCLE FREQUENCY–TIME–FREQUENCY DOMAINS 2439
of heart sounds, murmurs. No segmentation is needed. On the
other hand, it can be operated in a somewhat automated manner.
The paper is organized as follows. Section II out-
lines the decomposition of heart sound signal into atoms.
Section III focuses on the quasi-cyclostationarity of the atoms. In
Section IV, we propose a fuzzy-detection method to detect atoms
of heart sound signal in the joint plane. Practical experiments
and various computer simulations are described in Section V.
In Section VI, we discuss the results, and in Section VII, ob-
servations regarding performance comparisons are presented.
Finally, Section VIII summarizes our main conclusions.
II. REPRESENTATION OF HEART SOUND SIGNAL IN
TIME–FREQUENCY DOMAINS
A. Decomposition
To our knowledge, several signal models can be found in
literature for the decomposition of heart sound signal, such as
the chirp models [5], [6], the damped sinusoidal models [7], [8],
the modified Prony models [9], and the Gaussian modulation
model [10]. Leung et al. employed the Gaussian modulation
model to decompose the second heart sound for the diagnosis
of pediatric heart diseases. This model is employed to represent
the heart sound signal of one cardiac cycle
hm(t)=
Lm
i=1
amie−(t−tmi)2/(2σ2
mi)cos(2πωmit+βmi)(1)
where hm(t)is the heart sound signal of the mth cycle. Namely,
(1) means that hm(t)is the sum of Lmatoms. Every atom is
characterized by five parameters: tmi is the time delay of the
ith atom with respect to the start of the mth cycle; ami is the
amplitude; ωmi is the frequency; σmi is the time width that
the atom needs support; βmi is the phase. Therefore, the heart
sound signal of this cycle is represented by the set of atoms
{tmi,a
mi,ω
mi,σ
mi,β
mi,1≤i≤Lm}. The number of atoms,
Lm, and the five parameters for each atom can be obtained using
short-time Fourier transform (STFT) analysis, as described in
[10].
The STFT of the heart sound signal hm(t)is
H(t, f )=hm(t)w(t−τ)e−2πωτdτ (2)
where w(t) is a Gaussian window. First, the atom with the max-
imum amplitude is identified by searching the magnitude of the
STFT. More specifically, the atom with maximum amplitude is
located by detecting the peak in the magnitude of the STFT.
Once the time delay of the atom tmi has been identified, its
amplitude ami, frequency ωmi, and phase βmi can be read di-
rectly from the STFT. σmi is obtained by the following optimal
procedure.
The waveform represented by the ith atom is
smi(t, σmi)=amie−(t−tmi)2/(2σ2
mi)cos(2πωmit+βmi).
(3)
The signal residue after the waveform of the ith atom is
subtracted from the signal h(m−1)(t)is
hmi(t, σmi)=hm(i−1)(t)−smi(t, σmi)(4)
Fig. 1. Heart sound signal of one cardiac cycle was decomposed into atoms.
(a) Recorded waveform of one cardiac cycle. (b) Atoms on the time–frequency
plane. (c) Reconstructed waveform and residue.
where hm0(t)is the original signal of the mth cycle. The nor-
malized residue energy is
ρmi(σmi)=|hmi(t, σmi)|2dt|hm0(t)|2dt. (5)
Obviously, ρmi(σmi)will be minimum, if a perfect “time
width” σmi is found. The minimum of the residue energy
ρmi(σmi)is, therefore, used as a criterion to optimize σmi.
For this purpose, we monitor ρmi(σmi)by varying σmi within
a predefined range. The decomposition stops, if ρmi(σmi)is
sufficiently small. The heart sound signal of the mth cycle can
be reconstructed from the sum of all atoms as
hm(t)≈
Lm
i=1
smi(t).(6)
B. Data Acquisition
The normal heart sound signal used in this paper was recorded
in the authors’ laboratory. The male subject (33 years of age)
was asked to lie on his back on an examination bed. The sensor
was directed toward the mitral site. ECG signals and heart sound
signal were recorded simultaneously. It is known that the domi-
nant bandwidth of a heart sound signal is approximately 500 Hz.
To avoid higher frequency noise than 500 Hz, the data was pre-
filtered by low-pass filter with cutoff frequency 500 Hz. The
sampling rate was set to 2 KHz, which is higher than the min-
imum rate required by the sampling theory. Furthermore, the
laboratory provided an environment, where even minor noise
could be controlled. These low-noise heart sound recordings
allowed us quantificationally evaluate noise reduction in simu-
lated noise.
C. Simulation
The normal heart sound signal of one single cardiac cycle was
decomposed into 16 atoms, as shown in Fig. 1. The placement
2440 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 10, OCTOBER 2010
Fig. 2. Correspondence between ECG and heart sound signal.
of each atom in the time–frequency plane is shown in Fig. 1(b).
The reconstructed waveform is shown in Fig. 1(c), where the
decomposing was stopped when the normalized residue energy
was less than 0.05. The high correlation coefficient between the
reconstructed and the original waveform (up to 0.98) lead us to
the conclusion that atoms can represent accurately heart sound
signal in the time and frequency domains.
III. QUASI-CYCLOSTATIONARITY OF THE ATOMS
Cardiac cycle is a sequence of events repeated cyclically dur-
ing every heartbeat. Heart sounds (S1–S4) are caused by vibra-
tion of heart valves and/or surrounding heart tissues following
the closing or opening of heart valves, while heart murmurs are
caused by turbulence of blood flow. The pace at which a heart
beats does not change abruptly, and therefore, the heart sound
signal is considered quasi-cyclostationary. Based on this approx-
imation, we assumed that atoms representing heart sound signal
in the time–frequency domains are also quasi-cyclostationary,
namely, if the heart sound signal was cyclostationary and the
cycle frequency corresponded to the reciprocal of cardiac cycle
duration, we expected that the atoms for one cardiac cycle will
superpose the atoms of the next cycle.
However, heart cycle duration varies from cycle to cycle. This
phenomenon, widely known as heart rate variability (HRV),
can be identified easily in the ECG [11]. The correspondence
between the ECG and heart sound signal is demonstrated in
Fig. 2. The occurrence of an R wave indicates the start of a
new cycle. In order to analyze heart sound signal at specific
cycle frequency, we perform linear time scaling on heart sound
signal of every cardiac cycle to enhance the cyclostationarity.
For example, the heart sound signal of the mth cycle hm(t)is
linearly time scaled as
hl
m(t)=hm(T0t/Tm)(7)
where T0is the cycle duration used as reference and Tmis
the mth cycle’s duration. The cycle frequency for the enhanced
signal is thus 1/T0. We decompose the enhanced signal of the
mth cycle hl
m(t)into atoms
hl
m(t)=
Ll
m
i=1
al
mie−(t−tl
mi)2/(2(σl
mi)2)cos(2πωl
mit+βl
mi).
(8)
Fig. 3. Distribution of the atoms is shown in joint plane at cycle frequency
1 Hz. This atom congregate provides sufficient evidence that atoms of enhanced
heart sound signal are quasi-cyclostationary.
The first three consecutive cardiac cycles shown in Fig. 2 are
processed as given in (7), where T0=1s. The signals hl
m(t)
with m=1, 2, and 3 are then decomposed into atoms according
to (8), as shown in Fig. 3. The atoms of one cycle almost super-
pose the atoms of another cycle. This atom congregate provides
sufficient evidence that atoms are approximately cyclostation-
ary. The reason why atoms of different cycles do not perfectly
superpose on each other may be variations in the waveform
and time delay of heart sounds, murmurs in consecutive cycles.
Noise reduction could be really robust, if these variations can
be accommodated.
We assume that atoms of heart sound signal are quasi-
cyclostationary. On the other hand, atoms for noise and dis-
turbances are random and their cycle frequency spectrum does
not overlap with that of heart sound signal.
On the basis of this assumption, it is safe to say that atoms
of heart sound signal congregate on the joint cycle frequency–
time–frequency plane. Noise and disturbances are generally ran-
dom in nature. The atoms of noise and disturbances must be
dispersed over the joint plane. The atoms of heart sound signal
and the atoms of noise can thus be easily separated. In extreme
cases where noise is cyclostationary, the atoms of heart sound
signal can still be separated from those of noise, if their cycle
frequency spectra do not overlap [4].
IV. SEPARATION OF HEART SOUND SIGNAL FROM NOISE
BASED ON FUZZY DETECTION
A. Scale Match
It is assumed that the recording of heart sound signal has M
cardiac cycles. The start of each cardiac cycle is indicated by an
R wave, while the atoms for the recording are denoted in the joint
plane as the set of atoms {tl
mi,ω
l
mi,1≤i≤Ll
m,1≤m≤
M}. The frequency components of heart sounds and murmurs
range from several to five hundreds hertz [12]; however, the
normal duration of a cardiac cycle is about 850 ms and we have
chosen to normalize the cycle frequency to 1 s for improving
comparisons between cycles and between patients. For example,
in Fig. 3, where the vertical axis ranges from 0 to 200 and
the horizontal axis ranges from 0 to 1, the frequency ωl
mi is
TANG et al.: SEPARATION OF HEART SOUND SIGNAL FROM NOISE IN JOINT CYCLE FREQUENCY–TIME–FREQUENCY DOMAINS 2441
Fig. 4. Noisy heart sound signal and atom distribution. (a) Noisy heart sound
signal. (b) Atom distribution in the joint plane at a cycle frequency of 1 Hz. The
vertical axis is the “scaled frequency”. It is obvious that atoms of heart sound
signal congregate, whereas atoms of noise are more dispersed and can easily be
separated based on density of atoms (or the membership function).
a hundred times that of tl
mi. This mismatch will enable prior
evolution on frequency axis when the detection is operated in
the plane. To avoid this scale mismatch, the frequency ωl
mi is
scaled down so that its values are within the same range as time
delay tl
mi as shown in Fig. 4, where the vertical axis is named
“scaled frequency”.
B. Fuzzy Detection
In accordance with the assumption that atoms of heart sound
signal congregate in the joint cycle frequency–time–frequency
plane, the density of an atom provides an indication of whether
this specific atom represents a heart sound signal or noise. The
density of an atom is referred to the number of atoms found
within a radius ζaround the atom. For example, the density of
the atom (tl
mi,ω
l
mi)is defined as
dmi =(number of atoms found with in ζ)
=(tl
mi −tl
nj)2+(ωl
mi −ωl
nj)2≤ζ,
1≤j≤Ll
n,1≤n≤M. (9)
For a given number of cardiac cycles, it is obvious that atoms
of higher density probably represent heart sound signal. We
define a membership function to detect the atoms that represent
heart sound signal as follows:
A(dmi)=0,d
mi <M
1,d
mi ≥M.(10)
Ideally, the density dmi is equal to the total number of car-
diac cycles M, which serves as a threshold in (10). If the density
is greater than or equal to M, then A(dmi)=1and the atom
(tl
mi,ω
l
mi)probably represents a heart sound signal. By repeat-
ing the same process across all atoms of the mth cycle, we can
identify those atoms synthesize heart sound signal of this cycle.
Fig. 5. Variations in the time delay of heart sounds S1 and S2 for two different
cycles.
C. Heart Sound Signal Reconstruction
Heart sound signal of the mth cycle hs
m(t)are approximated
by the sum
hs
m(t)=
Kl
m
k=1
al
mke−(t−tl
mk)2/(2(σl
mk)2)cos(2πωl
mkt+βl
mk)
(11)
where Kl
mis the number of atoms, which meet the condition
A(dmk)=1. The heart sound signal of this cycle are subse-
quently reconstructed through reversed linear time scaling
hr
m(t)=hs
m(Tmt/T0).(12)
Possible reconstruction errors are evaluated using the normal-
ized residue
E=M
m=1 Tm
0|hr
m(t)−hm(t)|2dt
M
m=1 Tm
0|hm(t)|2dt(13)
where Tmis the cycle duration of the mth cycle.
D. Parameter ζ
According to our assumption, the atoms of one cycle should
superpose perfectly on the atoms of another cycle, if heart sound
signal was cyclostationary and the radius ζwould be zero. How-
ever, the parameter ζis closely related to variations in the time
delay of heart sounds and murmurs. In order to determine this
parameter for the phonocardiographic signal recorded, we in-
vestigate the variations in the time delay of heart sounds S1 and
S2, as shown in Fig. 5. According to Tang et al. [4], heart sound
waveform is highly consistent between consecutive cardiac cy-
cles. Variations in the time delay of heart sounds of the mth
cycle with respect to the first cycle can, therefore, be estimated
based on the minimum mean square error criterion
rS1
m= arg min
rS1
mEs11(t)−sm1(t−ζS1
m)2,m≥2
(14)
and
rS2
m= arg min
rS2
mEs12(t)−sm2(t−ζS2
m)2,m≥2
(15)
2442 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 10, OCTOBER 2010
TAB LE I
STATISTICS OF THE PARAMETER ZETA FOR VARIOUS CLINICAL HEART
SOUND SIGNAL
where rS1
mand rS2
mdenote variations in the time delay of S1 and
S2 of the mth cycle with respect to the first cycle, respectively.
The span ζS1of rS1
mcan be calculated as
ζS1= max(rS1
m)−min(rS1
m)(16)
where max(·) and min(·) are the maximum and minimum oper-
ators, respectively. Similarly, the span ζS2of rS2
mcan be calcu-
lated as
ζS2= max(rS2
m)−min(rS2
m).(17)
The values of ζS1and ζS2for various clinical heart sound
signals are listed in Table I, for which it is obvious that ζS1
and ζS2vary for different cases. They also vary for the same
subject at different periods of time. Although there is a great in-
terest in the mechanism underlying these variations, it is beyond
the scope of this paper. The number of cases investigated (see
Table I) is limited. Still, the selected sample provides sufficient
evidence that the variation of time delay of heart sound can
vary from several to dozens of milliseconds between consecu-
tive cardiac cycles. We followed the same approach to calculate
the differences in the time delay of the third heart sound ζS3,the
fourth heart sound ζS4, as well as heart murmurs ζmurmur.For
all heart sounds and murmurs, the parameter ζshould, however,
be chosen as the maximum variation. For example, it may be
chosen equal to ζ=0.039 s (the greater one of ζS1and ζS2)
for a healthy subject (see Table I). It should be noted that the
statistics included in Table I are obtained with low-noise heart
sounds. Parameter ζmay be larger, if the heart sound signal is
contaminated with noise. Without any prior knowledge about
the noise strength, parameter ζmay be chosen experimentally.
From the statistics compiled by the authors for a wide range
of clinical cases, noise reduction to normal rhythm heart sound
signal can be achieved when parameter ζis set in the range
[0.02–0.06]. It may be larger in cases of arrhythmia due to the
high variations in the time delay of heart sounds, murmurs. In
other words, parameter ζis related to the cyclostationarity of
heart sound signal, as discussed in Section VI-A. To some ex-
tent, the proposed noise reduction can accommodate variations
in the time delays. This accommodation leads that the variations
in the waveform can also be recovered in time domain. It is one
of main advantages of the proposed noise reduction.
Fig. 6. Lung sounds, chest motion contaminating heart sound signal. (a) Con-
taminated heart sound signal. (b) Atoms distribution in the joint plane. (c) Re-
constructed heart sounds. (d) Signal residues, which is the sum of lung sounds
and slide sounds (indicated by ellipses). The latter are sounds produced by the
lungs during breathing or by the muscular activity controlling lung movements.
E. Summary
The proposed noise reduction consists of the following steps.
Step 1: ECG signal and heart sound signal are synchronously
recorded.
Step 2: The beginning of individual cardiac cycles is identified
based on the occurrence of R waves. If the corresponding ECG
is not available, other signals (for example, wrist pulse, carotid
pulse) as well as cycle detection algorithms may be employed
to divide the phonocardiographic signal into cycles.
Step 3: To ensure that every cardiac cycle has the equal cycle
duration, the linear time scaling is carried out, according to
(7). The enhanced heart sound signal of each cardiac cycle is
decomposed into atoms, according to (8).
Step 4: The fuzzy detection is applied to identify on the
joint plane the atoms, which synthesize each heart sounds and
murmurs, as described in Sections IV-A and IV-B.
Step 5: Heart sound signal is reconstructed as in Section IV-C.
V. P RACTICAL EXPERIMENT AND COMPUTER SIMULATIONS
A. Separation of Heart Sound Signal From Lung Sounds and
Chest Motion
The experiment was performed on the same subject climbing
a staircase of 100 steps, who immediately after step climbing
laid on his back on an examination bed. During the recording,
the respiration was fast and, as expected, lung sounds and the
chest motion contaminated the phonocardiographic recordings,
TANG et al.: SEPARATION OF HEART SOUND SIGNAL FROM NOISE IN JOINT CYCLE FREQUENCY–TIME–FREQUENCY DOMAINS 2443
Fig. 7. Simulated noise and disturbances. (a) Simulated noise along with ran-
domly timed disturbances. (b) Spectrum of the simulated noise and disturbance,
which overlaps the frequency spectrum of heart sounds.
as shown in Fig. 6(a). Twelve cycles of heart sound signal were
submitted to the noise-reduction algorithm. Informal listening
by the authors shows that heart sounds can often be buried by
heavy lung sounds. Atoms distribution on the joint plane at a
cycle frequency of 1 Hz is shown in Fig. 6(b), where the atoms
indicated by prisms were identified for heart sounds. The re-
constructed heart sounds are given in Fig. 6(c). It is seen that
the recovered heart sounds become clear. S1s and S2s are easily
distinguished. The separated noise and disturbance are shown
in Fig. 6(d), which may comprise lung sounds and stethoscope
sliding disturbances (indicated by ellipses) due to chest mo-
tion. These sliding disturbances have high amplitude, short time
duration, and are randomly timed. The main frequency compo-
nents of heart sounds overlap those of lung sounds, as seen in
the joint plane in Fig. 6(b). It can be concluded that the noise
and disturbances in this case are non-Gaussian, nonstationary,
and colored.
B. Simulated Noise and Disturbance
In order to evaluate the proposed noise reduction for more
clinical heart sound signal, we simulate noise and disturbances
by using the model
v(t)=H(v1(t)+v2(t)) (18)
where v1(t)is a white double-side exponential distribution, and
v2(t)are randomly timed disturbances. H(·) is a band-pass fil-
ter, whose frequency response band overlaps that of the heart
sound signal. One realization of the simulated noise is shown in
Fig. 7(a). Its spectrum is shown in Fig. 7(b).
C. Reduction of Simulated Noise From Normal Heart Sounds
A low-noise heart sound signal from the normal subject is
contaminated by the simulated non-Gaussian, nonstationary,
and colored noise. Twelve cycles of heart sound signal were
submitted to the noise-reduction algorithm. The recording plus
Fig. 8. Noise reduction for normal heart sound signal. (a) Low-noise heart
sound signal and the corresponding ECG. (b) Heart sounds contaminated with
simulated noise. Disturbances are indicated by an ellipse. (c) Atoms in the joint
plane at cycle frequency of 1 Hz. (d) Reconstructed heart sounds.
the simulated noise is given in Fig. 8(b). The SNR is 0 dB. We see
that S1s are almost completely buried by noise. The noise and
disturbances are so heavy that heart sounds cannot be identified
by the human eye. The scatter plot in the joint plane at a cycle
frequency of 1 Hz is shown in Fig. 8(c). The atoms represented
by prisms are found to form heart sounds based on fuzzy detec-
tion and the remaining atoms, represented by circles, are found
to form noise and disturbances. The reconstructed heart sounds
are shown in Fig. 8(d). It is relatively easy for the authors to
identify the heart’s rhythm from the reconstructed signal just by
listening. The correlation coefficient between the reconstructed
and the original signal is 0.92, and the normalized residue is
0.12.
D. Reduction of Simulated Noise Form Heart Sound Signal
With Aortic Valve Stenosis
The noise reduction was also applied on heart sound signal of
patients with aortic valve stenosis. The noise-free data, whose
sampling rate is 22 050 Hz, were downloaded from the website
of the School of Medicine of the University of Dundee. The sam-
pling frequency was scaled down to 2 KHz, where a low-pass
filter with cutoff frequency 1 Hz was used to prevent frequency
aliasing. The heart sound signal has long, heavy systolic mur-
murs, as shown in Fig. 9(a). The signal was contaminated by
the simulated noise, as shown in Fig. 9(b). Some disturbances,
indicated by an ellipse, overlap the murmurs. The SNR is 0 dB.
The distribution of atoms on the joint plane at a cycle frequency
of 1 Hz is shown in Fig. 9(c). The atoms, indicated by prisms,
2444 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 10, OCTOBER 2010
Fig. 9. Noise reduction for heart sound signal with aortic valve stenosis.
(a) Low-noise recording. (b) Heart sounds contaminated with simulated noise.
Some disturbances indicated by an ellipse overlap heart murmurs in time do-
main. (c) Atoms in the joint plane at cycle frequency of 1 Hz. (d) Reconstructed
heart sound signal.
are identified to form heart sounds by fuzzy detection. The re-
constructed heart sound signal, shown in Fig. 9(d), seems to
be closer to the noise-free heart sound signal. The correlation
coefficient between the reconstructed and original signal is 0.90
and the normalized residue 0.18.
E. Reduction of Simulated Noise From Heart Sound Signal With
the Fourth Heart Sound (S4)
The fourth example involves the reduction of noise from heart
sound signal with the fourth heart sounds (S4), as shown in
Fig. 10(a). The noise-free data, whose sampling frequency was
22050 Hz, was downloaded from the website of the Medicine
Department of the University of Dundee. We scaled the sampling
frequency down to 2 KHz, where the technology of preventing
frequency aliasing was also used. S4 generally has low ampli-
tude and is easily buried by noise. In this example, we show the
robustness of the proposed noise reduction in recovering S4 in
heavy noise and disturbance environments. The heart sound sig-
nal contaminated by the simulated noise is shown in Fig. 10(b).
The SNR is 0 dB. The S4 sounds can hardly be perceived by
the human eye. The disturbances, indicated by ellipses, are ran-
domly timed and cause the disordering of rhythms. The authors
could hardly observe the occurrence of S4 s. The distribution of
the atoms in the joint plane at a cycle frequency of 1 Hz is shown
in Fig. 10(c). The fuzzy detection identifies the atoms of heart
sound signal, which are represented by prisms. The remaining
atoms, represented by circles, are identified from noise and dis-
turbances. The reconstructed heart sound signal are shown in
Fig. 10. Noise reduction for heart sound signal with the fourth heart sound.
(a) Low-noise recording. (b) Heart sound signal contaminated with simulated
noise. Disturbances are indicated by an ellipse. (c) Atoms in the joint plane at
cycle frequency of 1 Hz. (d) Reconstructed heart sounds.
Fig. 10(d). It is seen that the reconstructed waveform shows a
high level of approximation to the original waveform. The cor-
relation coefficient between the reconstructed and the original
waveforms is up to 0.98, and the normalized signal residue is as
low as 0.05.
VI. DISCUSSION
A. Cyclostationarity Strength
The atoms of heart sound signal can be easily identified
by fuzzy detection because heart sound signal are quasi-
cyclostationary. The atoms of heart sound signal congregate
in the joint plane at a specific cycle frequency. The performance
of noise reduction is thus directly related to the cyclostationar-
ity strength of heart sound signal. We may safely conclude that
as the cyclostationary of heart sound signal increases, the level
of noise reduction increases. Ideally, the atoms of heart sound
signal superpose, if the recording is perfectly cyclostationary.
However, it is impossible for heart sound signal to be perfect
cyclostationary because of variations in the waveform and time
delay of heart sounds, murmurs between different cardiac cy-
cles. One question that arises is how to quantitatively evaluate
the cyclostationarity strength for given heart sound signals.
We introduce cyclic statistics to assess the cyclostationarity
strength of heart sound signals. ρα
x(f)is the cyclic spectral
coherence function, which is defined as
ρα
x(f)= Sα
x(f)
[S0
x(f+α/2)S0
x(f−α/2)]1/2(19)
TANG et al.: SEPARATION OF HEART SOUND SIGNAL FROM NOISE IN JOINT CYCLE FREQUENCY–TIME–FREQUENCY DOMAINS 2445
TAB LE I I
CYCLOSTATIONARITY STRENGTH
where Sα
x(f)is the cyclic spectrum of signal x(t) at the cycle
frequency α.Sα
x(f)is written as
Sα
x(f)=+∞
−∞
Rα
x(τ)e−j2πfτ dτ (20)
and
Rα
x(τ)=
t
x(t)x(t+τ)e−j2παtdt. (21)
Rα
x(τ)is the cyclic correlation function. Rα
x(τ)degrades to a
traditional correlation when the cycle frequency αis zero.
In (19), ρα
x(f)represents a second-order cyclic statistics that
shows the cyclostationarity strength of a signal at a given cycle
frequency α. The larger the amplitude of ρα
x(f)is, the higher
the degree of cyclostationarity of the signal is. However, a heart
sound signal is not completely cyclostationary. It is partly sta-
tionary. ρ0
x(f)indicates the stationarity strength. In order to
evaluate the relative strength, we calculate the rate
γx(α)= ρα
x(f)df
ρ0
x(f)df +ρα
x(f)df .(22)
It is clear that γx(α)is 0.5, if the cyclostationarity strength is
equal to the stationarity strength. γx(α)is always less than or
equal to 1. In order to study how the cyclostationarity strength
affects noise reduction, we calculate γx(α)for the normal heart
sound signal shown in Fig. 8, heart sound signal with aortic
stenosis shown in Fig. 9, and the heart sound signal with S4
shown in Fig. 10 at a cycle frequency α=1 Hz. The rates are
listed in Table II. It is found that γAS(1) has the lowest value,
γFHS(1) has the highest value, and γNHS(1) has an intermediate
value. This means that the heart sound signal shown in Fig. 9
has the lowest cyclostationarity, the heart sound signal shown
in Fig. 10 has the highest cyclostationarity, and the heart sound
signal shown in Fig. 8 has medium cyclostationarity. These
results imply that the noise reduction shown in Fig. 10 is the
best and the noise reduction shown in Fig. 9 is the worst. These
results are confirmed by comparing them with the results of
our simulations. The correlation coefficients for the heart sound
signals shown in Figs. 8 and 9 are 0.92 and 0.90, respectively,
and the normalized residues are 0.12 and 0.18, respectively.
However, the correlation coefficient and normalized residue for
Fig. 10 are 0.98 and 0.05, respectively.
It is well known that HRV is unavoidable for a live sub-
ject, namely, there are no heart sound signals that are perfectly
cyclostationary. We employ linear time scaling to enhance cy-
clostationarity, as shown in (7). However, this is not sufficient
to align the timings of the heart sounds and murmurs. To further
enhance cyclostationarity, some special techniques may be em-
ployed, such as NTS proposed in our earlier paper [4]. Another
TABLE III
INFLUENCE OF THE NUMBER OF CYCLES
factor that can affect cyclostationarity is the variations in the
waveform. In the past, there have been few studies that have
used waveform improvement techniques to enhance cyclosta-
tionarity.
B. Influence of the Number of Cycles
As shown in the simulations, the quasi-cyclostationarity of
heart sound signal can be indicated by the density of atoms
in the joint plane at a specific cycle frequency. The quasi-
cyclostationarity may be sufficient as the number of cycles in-
creases. The density of atoms is thus a suitable indicator for
the detection of heart sound signal. To evaluate the performance
of the noise reduction with respect to the number of cycles,
we perform independent noise reduction simulations for nor-
mal heart sound signal in 0-dB environments when the number
of cycles is 5, 10, 20, and 30. The statistics of performance
indicators are listed in Table III. We see that the correlation co-
efficient between the reconstructed and the noise-free signal is
0.90 and the normalized signal residue is 0.15 when only five
cardiac cycles are covered. As the number of cycle increases,
the performance improves. However, the performance does not
improve linearly with respect to the number of cycles. It does not
show any improvement as the number of cycles increases from
20 to 30. We drew the following conclusion from this absence of
improvement: cyclostationarity cannot be always improved by
increasing the number of cycles. Therefore, there is a limit to the
degree to which the performance can be improved by increasing
the number of cycles. This proves that noise reduction mainly
depends on the cyclostationarity strength. The statistics show
that an acceptable performance can be achieved, if the number
of cycles is selected to be 10.
VII. PERFORMANCE COMPARISONS
A. Short Description of Our Earlier Study
In our earlier study [4], we made the assumption that heart
sound waveforms are consistent between consecutive cardiac
cycles. NTS was proposed to minimize variations in the timing
of heart sounds, murmurs and ultimately allow the exploita-
tion of the cyclostationarity features of the signal. In the ideal
case that NTS was successful, the enhanced heart sound signal
could be considered to be cyclostationary. Noise was reduced
by obtaining the average of consecutive cardiac cycles, namely,
it operated in joint cycle frequency–time domains. We called
this technique NR-NTS. It is theoretically insensitive to: 1) sta-
tionary noise; 2) zero-mean noise; and 3) cyclostationary noise,
whose cycle frequency does not coincide with that of heart sound
signal. However, first, heart sounds need to be segmented into
first and second heart sounds in order to determine the parame-
ters for NTS. If segmentation is inaccurate or if the assumption
2446 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 10, OCTOBER 2010
TAB LE I V
PERFORMANCE COMPARISONS
that heart sounds are consistent in consecutive cycles is not
valid, this preprocessing phase can have a detrimental effect on
the efficiency of the NR-NTS.
B. Comparison
The noise reduction proposed in this paper is referred to as
NR-FD, since it is based on fuzzy detection. It is performed
in the joint cycle frequency–time–frequency domains, namely,
one more domain, frequency domain, is exploited. To compare
the performance of the two algorithms, we applied them on
the same normal heart sound signal in simulated noise environ-
ments. Correlation coefficients between the reconstructed and
the noise-free are listed in Table IV.
Based on the assumption that heart sound waveforms are con-
sistent between consecutive cardiac cycles [4], the efficiency of
NR-NTS is improved by increasing the number of cycles. How-
ever, this assumption holds for ten cardiac cycles or so, and
while noise is reduced, variations in the heart sound waveform
become more prominent. As listed in Table IV, the correla-
tion coefficient decreased where the number of cardiac cycles
increased from 10 to 30 regardless of whether the signal was
contaminated with 0 dB or −5 dB noise.
Unlike NR-NTS, NR-FD can accept, to some degree, the
variations in the waveform and time delay of the heart sounds
because of the use of fuzzy detection. Both these variations
can be recovered during the reconstruction of the heart sound
signal, and no segmentation is needed as preprocess for NT-FD,
leading us to the conclusion that NR-FD is more robust than
NR-NTS. The performance of NR-FD does not degrade when
heart sound signal covers more than ten cardiac cycles. As a
consequence, the correlation coefficients obtained with NR-FD
are significantly better than those obtained with NR-NTS in 0
dB noise (see Table IV). These features make NR-FD suitable
for the automated analysis of heart sounds. We note, however,
that the correlation coefficients obtained with NR-FD are not
significantly higher than those obtained with NR-NTS in −5dB
noise. The reason behind this performance may be that atoms
of heart sound signal are diluted on the joint plane due to the
presence of excessive noise.
VIII. CONCLUSION
In this study, noise reduction for heart sound signal has been
achieved in the joint cycle frequency–time–frequency domains.
The beginning of cardiac cycles is identified based on the oc-
currence of R waves, and subsequently, each heart sound signal
of a cardiac cycle is linearly time scaled and decomposed into
atoms by means of a Gaussian modulation model. The atoms of
heart sound signal congregate on the joint plane. In contrast, the
atoms of noise and disturbances are dispersed in the joint plane.
The atoms of heart sound signal can then be easily identified
based on fuzzy detection. Variations in both the waveform and
time delay of the heart sound signal can be recovered during the
reconstruction. In practical experiment, heart sound signal was
successfully separated from lung sounds and stethoscope sliding
disturbance produced by chest muscular activities during breath-
ing. Computer simulations are used to test the performance of
the proposed noise reduction for various heart sound signals
contaminated with simulated non-Gaussian, nonstationary, and
colored noise. The statistics show that its performance may be
maintained even for short heart sound signal covering only five
cardiac cycles. Furthermore, the algorithm can be operated in a
rather unsupervised manner.
ACKNOWLEDGMENT
The authors would like to thank the data collectors. The au-
thors would also like to thank the anonymous reviewers for their
valuable comments. The heart sound data used in this paper were
downloaded from the website of the Medicine Department, Uni-
versity of Dundee, Texas Heart Institute at St. Luke’s Episcopal
Hospital.
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TANG et al.: SEPARATION OF HEART SOUND SIGNAL FROM NOISE IN JOINT CYCLE FREQUENCY–TIME–FREQUENCY DOMAINS 2447
Hong Tang (M’10) received the B.S. degree
in mechanical manufacture and automation from
Zhongyuan University of Technology, Zhengzhou,
Henan, China, in 2000, the M.S. degree in biomed-
ical engineering from Jilin University, Changchun,
Jilin, China, in 2003, and the Ph.D. degree in sig-
nal processing from the Dalian University of Tech-
nology (DUT), Dalian, Liaoning, China, in 2006,
respectively.
From 2006 to 2007, he was a Research Fellow
in the Regional Innovation Center, Yeungnam Uni-
versity, Korea. He is currently an Assistant Professor at DUT. His research
interests include non-Gaussian signal processing, biomedical signal processing,
and wireless location.
Ting Li received the B.S. degree in electronic en-
gineering, and the M.S. degree in signal process-
ing, both from the Dalian University of Technol-
ogy (DUT), Dalian, China, in 2002 and 2005,
respectively.
She is currently an Assistant Professor at Dalian
Nationalities University, Dalian. Her research in-
terests include non-Gaussian signal processing and
biomedical signal processing.
Yongwan Park received the B.E. and M.E. degrees
in electrical engineering from Kyungpook University,
Daegu, Korea, in 1982 and 1984, respectively, and the
M.S. and Ph.D. degrees in electrical engineering from
the State University of New York, Buffalo, in 1989
and 1992, respectively.
From 1992 to 1993, he was a Research Fellow at
the California Institute of Technology. From 1994 to
1996, he was a Chief Researcher at SK Telecom, Ko-
rea, where he was involved in developing IMT-2000
system. Since September 1996, he has been a Pro-
fessor of information and communication engineering at Yeungnam University,
Gyeongsan, Korea. His current research interests include beyond 3G/4G sys-
tem, orthogonal frequency-division multiplexing system, peak-to-average ratio
reduction, and biomedical signal processing, etc.
Tianshuang Qiu (M’97) received the B.S. degree
from Tianjin University, Tianjin, China, in 1983, the
M.S. degree from Dalian University of Technology,
Dalian, China, in 1993, and the Ph.D. degree from
Southeastern University, Nanjing, China, in 1996, all
in electrical engineering.
He was a Research Scientist at Dalian Institute
of Chemical Physics, Chinese Academy of Sciences,
Dalian during 1983 through 1996. He was with the
faculty of electrical engineering, Dalian Railway In-
stitute during 1996. He was a Postdoctoral Researcher
in the Department of Electrical Engineering, Northern Illinois University,
DeKalb. He is currently a Professor in the Department of Electronic Engineering,
Dalian University of Technology. His research interests include non-Gaussian
and nonstationary signal processing, radio-frequency signal processing, and
biomedical signal processing.
