Feature Analysis of Heart Sound Based on the Improved Hilbert-Huang Transform
Lihan Liu, Haibin Wang, Yan Wang, Ting Tao
Xiaochen Wu
School of Electrical and Information Engineering,
Xihua University
Chengdu, China
E-mail: [email protected]
Cardiothoracic Surgery
Chengdu Military General Hospital of PLA
Chengdu, China
E-mail: [email protected]
stationary and nonlinear signal analysis in time-frequency
domain. It broke the limitations of Fourier Transform (FT),
and also equipped with a self-adaptive compared with
wavelet transform. However, it can be provided a good
resolution in time domain and frequency domain [5]. The
successful application of heart sound characteristic analysis
establishes the basis for the following classification and
identification of heart sound.
Abstract—In order to analyze the feature of heart sound
accurately and effectively, this paper presents a feature
analysis approach of heart sound based on the improved
Hilbert-Huang Transform after a large number of analysis of
heart sounds in time frequency domain . The validity of the
proposed method has been verified through Empirical Mode
Decomposition (EMD) for a typical vibratory. Calculating and
obtaining the characteristic parameter of heart sound by
Hilbert spectrum analysis of several cases of normal and
abnormal heart sounds. Experimental results show that the
presented algorithm is able to identify different heart sounds in
time frequency domain, and it also establishes the basis for the
classification and recognition of heart sound.
II.
Keywords-Heart sound; Hilbert-Huang Transform; EMD;
Hilbert spectrum analysis
I.
COMMON TIME-FREQUENCY ANALYSIS METHOD
Common methods of time-frequency analysis include
FFT, STFT, Winger-Ville, Choi-Williams, Cone-kernel and
Wavelet transform etc. As early as 1998, Yanwen Wang and
Haibin Wang who have addressed common quadratic timefrequency analysis of acoustic signal processing, but also
made a good compare and analysis. This paper have made
briefly compared to the following typical time-frequency
analysis before presenting a feature analysis of heart sound
based on the improved Hilbert-Huang Transform.
The traditional methods of Fourier Transform can
characterize the signal commendably in frequency domain,
but it completely lost the information of the signal at any
time domain. STFT is simple and easy to implement, but its
main flaw is that the "window effect", the distributive law in
time-frequency was restricted by the fixed window. So it is
used to analysis various signals which roughly have the
same characteristic scale, but not the Multi-scale and
mutation signals.
Winger-Ville distribution has high distributive law in
time-frequency domain. It has been applied widely in
various signal processing fields by its excellent performance.
There will be arise "cross-term interference" when the
anglicizing signal is the multi-component, and signal
introduced fuzzy in the time-frequency spectrum because it
is bilinear transform.
Wavelet Transform uses a variable window to analysis
the signal, and it's one of the best time-frequency analysis
methods which solved the contradiction of resolution ratio
between time and frequency. However, the disadvantages in
wavelet analysis are also obviously: the quantitative timefrequency analysis is difficult and have no self-adaptive and
so on.
Therefore, this paper proposed a feature analysis
approach of heart sound based on the improved HHT when
analyze the characteristics of heart sounds, the next section
will be expounded specifically.
INTRODUCTION
Cardiovascular disease as a major disease which has
been a serious threat to people’s health and life for a long
time, and its incidence increased year by year with the
improvement of living standards. According to the report of
World Health Organization in 2008[1]: each year, there
would be 17 million people died of the disease in the world
(one third of the patients who died because of heart disease).
Therefore, how to find the symptom of heart disease early
and understanding of its disease status timely is extremely
significant for the prevention and timely treatment of heart
disease.
Heart sound is a typical non-stationary, nonlinear signal,
and it's difficult to be processed by traditional signal
processing methods. In this case, Norden E. Huang and
others in NASA advanced a new signal Time-frequency
analysis—Hilbert-Huang Transform (HHT). And this
method has been widely used in the speech feature
extraction [2], seismic signal analysis [3], mechanical failure
diagnosis [4] and other fields.
This paper is based on the research above and with the
cooperation of our project team and department of
mechanical engineering of Yamaguchi University in Japan.
We have completed the development of intelligent heart
stethoscope and analysis of heart sound characteristic
waveform in time frequency domain and classification of
heart murmurs and other related research [7-8]ˈand presented
a feature analysis approach of Heart Sound based on the
improved Hilbert-Huang Transform. This method followed
the FFT, wavelet transform and so on which aimed at non-
378
III.
BASIC THEORY OF HHT
and s1 (t ) is original signal, c1 (t ) is the first IMF component.
Ville presented Hilbert Transform (HT) named of the
famous mathematician David Hilbert summarized the work
of which Carson, Fry and Gabor did together in the year
1948. s (t ) represents real signal, and its Hilbert transform
is H [ s (t )] . HT is essentially a linear time-invariant system
output of the impulse response 1/ S t , it can only change the
phase of the signal but not change its energy and power
through HT. The definition of HT is as following:
Hilbert Transform: H [ s (t )]
1
S³
f
f
Inverse Transform: H 1[ sˆ(t )] 1
s (W )
dW
t W
sˆ(W )
dW
f t W
S³
f
b) c1 (t ) is taken as the next original signal s2 (t ) , We
can gain s2 (t ) m2 (t ) c2 (t ) by find the center line of the
envelope m2 (t ) and keep on decomposition, then c2 (t ) is
taken as the second IMF component.
c) Repeat the above process, we can gain c1 (t ) ,
c2 (t ) ,…, ck (t ) ,and we define r ck (t ) is the last residue
which representative of the average trend of the signal, this
procedure should be repeated of k times until the last
residue r is small enough or becomes a monotonic
function .then the signals can be expressed as:
(1)
k
(2)
s (t )
¦ c (t ) r
(3)
i
i 1
HT is only suitable for the study of simple component
signal. The instantaneous frequency in HT will not make
sense when the signal is multi-component signal. So Huang
proposed the HHT later [9].
HHT include Empirical Mode Decomposition (EMD)
and Hilbert spectrum analysis. Decomposing complex
multi-component signals into a set of single component
intrinsic mode function (IMF) by EMD, and then extracting
the instantaneous variables of each IMF component by HT
in order to analyze the time-varying characteristics of it.
B.
Hilbert Spectrum Analysis
H [ci (t )] could be gained by HT to each of the IMF
component ci (t ) , analytic function X i (t ) ci (t ) jH [ci (t )] .
Then we can calculate for instantaneous variables each
component of the signal as follows:
Instantaneous amplitude: ai (t )
A. Empirical Mode Decomposition
When we process the signal of empirical mode
decomposition, the following assumptions must be made:
x Any complex signal is composed by a set of
different components of IMF, each IMF component
has the same number of extreme points and zero
points, whether it is linear, nonlinear or nonstationary, there is only one extreme point between
the adjacent two zero points, the upper and lower
envelope is local symmetry about time axis, and any
two zero points are independent.
x We can obtain IMF by differential, decomposition
and integral again if the data points have flawed
points but lack of extreme points.
x The characteristic time scale of Signal is defined by
the time interval between extreme points.
We can apply EMD to decompose any signal s (t )
through the following steps based on the assumption.
a) For any signal s (t ) : Firstly, identify all the extreme
points of s (t ) . Then find out all the local maximum and
minimum points and synthesize it into envelope by select
the appropriate interpolation function, so that all data are
included between the upper and lower envelope. At last,
obtaining the mean curve use the local maximum and local
minimum envelope we have defined. We define the mean
value is m(t ) , then we can gain c(t ) by calculating the
difference between s (t ) and m(t ) ,that is s1 (t ) m1 (t ) c1 (t ) ,
| ci (t ) |2 | H [ci (t )] |2
(4)
H [ci (t )]
ci (t )
(5)
) i (t )
arctan
Instantaneous frequency: f i (t )
Zi (t )
2S
Instantaneous phase:
1 d
[) i (t )]
2S dt
(6)
Then the original signal can be taken as:
k
s (t )
Re ¦ ai (t )e j)i (t )
i 1
k
Re ¦ ai (t )e
j 2S
³ fi (t ) dt
(7)
i 1
Equation (7) is called Hilbert spectrum which reflected
time frequency characteristics of the signal, that is:
k
H ( f i , t)
Re ¦ ai (t )e
j 2S
³f
i
( t ) dt
(8)
i 1
And equation (8) can reflect the frequency-energy
distribution of the signal.
C.
Problems Existed in HHT and Solution Methods
In this paper, we analyzed several difficulty
problems Existed in HHT and gave the solution
methods.
1) Interpolation Algorithm
The extracted envelope which have contradictories
between flexible and smoothness and so on.
379
from the original signal by EMD, and it was decomposed
thoroughly which
was shown in figure 2.
1
Some scholars have made use of sectional power
function interpolation algorithm and the parabolic
parameter spline interpolation algorithm to extract the
envelope of the signals [6] , however, this paper selected
the cubic spline interpolation algorithm to extract the
heart sound envelope after compared the interpolation
method of Lagrange and Newton and so on.
2) Endpoint Effect
The main reason of the endpoint effect was caused
by which the data absence of a flying wing of the end
constraint node, the endpoint effect would be
engendering when we apply EMD or the Hilbert
transform to process the signal.
In this paper, we apply the method of direct
extension to extend two ends of the data before EMD,
and it restrained the end effect very well.
3) End Conditions
Decomposition of termination conditions are too strict
will lead to excessive decomposition, while the conditions
are too loose will cause the IMF component decomposition
is not complete. This paper referenced the weight
termination condition which Dr.Youming Zhong of
Chongqing University brought up. End variable: sd1 sd2 tol,
sd1, sd2 and tol all between zero and one, sd1<sd2.
m(t )
Let sx(t ) |
| , sx(t ) is the specific value of
emax (t ) emin (t )
which the absolute value of the mean envelope and
amplitude envelope. m(t ) , emax (t ) and emin (t ) are mean
envelope, up-envelope and lower-envelope of the signal.
There are three conditions as follow:
a) The value of any point in sx(t ) is less than sd2.
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
100
200
300
400
500
600
700
800
900
1000
signal
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0
-1
0
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c2
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r
0
-0.01
ḋᴀᑣো n
Figure 2.
Empirical Mode Decomposition of vibration signal
B. Heart Sound
1) Envelope Extraction of Heart Sound
Figure 3 is the amplitude envelope of two cardiac cycle
of normal heart sound by HT, and the normal heart sound
come from 3MLittmann ® Stetho-scopes database. We can
gain the heart sound characteristics as follow: heart rate, the
time when first heart sound (s1) and second heart sound (s2)
occurs and its proportion in the cardiac cycle and so on.
b) The ratios which sx(t ) overrun of sd1 are not
greater than tol.
c) The difference between which Extreme points and
zero-points are not greater than one.
The decomposition must be terminate when it meet any
one of the above conditions. The first condition guaranteed
that there wouldn't be present the local asymmetry off base.
The second condition is to ensure the symmetry, so the
individual singular point or the overshoot-point caused
excessive screen which couldn't damage the amplitude
fluctuation. The third condition is the simple termination
criterion.
IV.
0
Figure 1. Instantaneous envelope of vibration signal
1.5
A
1
0.5
0
0
0.2
0.4
0.6
0.8
1
t
1.2
1.4
1.6
1.8
2
Figure 3. Heart sound amplitude envelope base on HT
2) Empirical Mode Decomposition
A normal heart sound signal was decomposed by the
improved EMD. The sampling time is two seconds, the
sampling frequency is 2205Hz, signal is the original heart
sound signal before decomposition, c1̚c10 are ten IMF
components, r is decomposition margin. We can see the
process of EMD clearly in figure 5.
The IMF components of heart sounds were separated by
EMD which arranged by frequency from high to low. It
revealed the frequency components of heart sound perfectly
and conduce to the further analysis of heart sound.
FEATURE ANALYSIS OF SIGNALS
A. Vibration Signal
Let x(t ) 0.4sin(2S f1t 1) 0.4sin(2S f 2 t 1) , x(t ) is a
vibration signal, N is sampling points, fs is sampling
frequency, f1 and f2 are the component-frequency. N=1000,
fs=400Hz, f1=10Hz, f2=6Hz. We can gain the results shown
in Fig 1 and Fig 2 by the improved HHT to x(t ) .The signal
envelope extracted have good flexibility and smoothness as
it shown in figure 1, the two components were separated
380
signal
1
0
-1
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0
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c8
0.05
0
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r
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c9
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c10
c7
c6
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c2
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t/s
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Figure 4.
second heart sound (s2), A12 is the intensity ratio of s1 and
s2, Ƹf1 DQGƸf2 are the frequency ranges of s1 and s2. And
it clearly shown that the difference between the standard
heart sounds and the various types of abnormal heart sounds
by the comparison and analysis from table 7, it's helpful to
the classification and recognition of heart sound.
IV. CONCLUSIONS
Heart sound is a complex signal, and the traditional
signal processing methods (such as FFT, Winger-Ville and
wavelet transforms etc) have lots of drawback due to this
reason the processing of heart sound are limited.
In this paper, Author presented a feature analysis
approach of heart sound based on the improved HilbertHuang Transform, and applied the improved HHT by
Hilbert spectrum analysis of various cases of heart sounds.
The results show that: this method can adaptively extract
local mean curve of non-stationary data and decompose the
complex heart sounds into a limited number of IMF which
have physical significance. It reflected the spectral
characteristics of heart sounds clearly and established the
fundament for the classification and recognition of heart
sound. And it has certain values for clinical application.
Empirical Mode Decomposition of heart sound
3) Hilbert Spectrum Analysis of Heart Sounds
Heart sound is complicated which is difficult to analyze
the whole time-frequency characteristics. Hilbert marginal
spectrum of heart sounds which characterized the energy
distribution of the first and the second heart sound as it
shown in Figure 7, and it plotted the frequency range of the
first heart sound and the second heart sound clearly.
ACKNOWLEDGMENT
0.03
Thanks to the support of Sichuan Education Department
Natural Science Key Project (09209025) and Graduate
Innovation Fund Project of Xihua University (Ycjj200935).
And thanks to the corresponding author of Xiaochen Wu.
0.025
E
0.02
0.015
REFERENCES
0.01
[1]
0.005
0
0
100
200
300
400
f/ Hz
500
600
700
800
[2]
Figure 5. Marginal spectrum of heart sound
[3]
TABLE 1ˊ FEATURE COMPARISON OF DIFFERENT HEART SOUNDS
feature
type
standard HS
ASD
VSD
AS
AI
MS
MR
Hr
(T/S)
T12(s)
A12
Ƹf1 (Hz)
Ƹf2 (Hz)
75
63
102
105
83
62
61
3
2.4
—
5.3
7.65
1.8
1.2
1.03
1.01
—
1.71
0.75
1.03
1.30
50̚65
10̚45
35̚70
20̚60
15̚45
55̚73
35̚60
60̚75
80̚130
50̚180
50̚70
30̚65
80̚160
75̚200
[4]
[5]
[6]
[7]
This article only selected seven cases of heart sounds for
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time intervals between the first heart sound (s1) and the
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