Applications of The Discrete
Wavelet Transform in Beat
Rate Detection
Advisor:Jian-Jiun Ding
Speaker:Jian-Hwu Wang
Date:11/25/2010
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1
Outline
• Introduction to Wavelet Transform
• Applications of the Discrete Wavelet Transform in
Beat Rate Detection
– DWT Based Beat Rate Detection in ECG
Analysis.
– Improved ECG Signal Analysis Using Wavelet
and Feature.
• Conclusion
• Reference
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Introduction to wavelet transform
• Fourier transform is the well-known tool for
signal processing.

X ( f )   x(t )e j 2ft dt

• One limitation is that a Fourier transform can’t deal
effectively with non-stationary signal.
• Short time Fourier transform

X (t , f )   w(t   )x( )e j 2f d

where w(t ) is mask function
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Introduction to wavelet transform
• Gabor Transform
– The mask function is satisfied with Gaussian
distribution.
• Uncertainly principle
 t f 
1
4
t x(t ) dt


, 
 x(t ) dt
2
2
where 
2
t
2
f X ( f ) df


 X ( f ) df
2
2
2
f
2
• We expected to occur a high resolution in time domain, and then
adjust  t2 or  2f .
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Introduction to wavelet transform
• The principle of wavelet transform is based on the
concept of STFT and Uncertainly principle.
– A mother wavelet  (t ) .
1
t
 ( ) and translating  (t  b) .
– Scaling
a
a
• Sub-wavelets
 a ,b (t ) 
• Fourier transform
1
t b
(
)
a
a
 (t )  F[ (t )]
a,b (t )  F[ a,b (t )]
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Introduction to wavelet transform
• Continuous wavelet transform(CWT)
wa ,b
1
  a ,b , x(t ) 
a



x(t ) a ,b (
t b
)dt
a
• ICWT
1
x(t ) 
C


dadb
  wa,b a,b (t ) a 2
where C  

0
 ( w)
w
dw and
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


 ( w) dw  
6 /22
Introduction to wavelet transform
• Discrete wavelet transform(DWT)
wm,n  x(t ), m,n  a0m / 2  f (t ) (a0m (t )  nb0 )dt
– Sub-wavelets
 m,n (t )  a0m/ 2 (a0m (t )  nb0 )
• IDWT
m, n  Z
x(t )   wm,n m,n (t )
m
n
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DWT applications for
beat rate detection
• DWT Based Beat Rate Detection in ECG
Analysis
– The purpose of this paper is to detect heart beat
rate by the concept of discrete wavelet
transform, which is suitable for the non
stationary ECG signals as it has adeuate scale
values and shifting in time.
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DWT Based Beat Rate
Detection in ECG Analysis
• ECG(Electrocardiogram) signal
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DWT Based Beat Rate
Detection in ECG Analysis
• Preprocessing
– Denoise
• Baseline wandering
• Moving average method and subtraction procedure.
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DWT Based Beat Rate
Detection in ECG Analysis
• Preprocessing
– Denoising : The wavelet transform is used prefiltering step for subsequent R spike detection
by thresholding of the coefficients.
• Decomposition.
• Thresholding detail coefficients.
• Reconstruction.
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DWT Based Beat Rate
Detection in ECG Analysis
• Feature extraction using DWT
– Detect R-waves.
– Thresholding.
• Positive threshold.
• Negative threshold.
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DWT applications for
beat rate detection
• Improved ECG Signal Analysis Using
Wavelet and Feature.
– This paper introduced wavelet to extract
features and then distinguish several heart beat
condition, such as normal beats, atrial
premature beats, and premature ventricular
contractions.
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Improved ECG Signal Analysis Using
Wavelet and Feature.
• Some kinds of ECG signal:
Atrial premature beat
Normal beat
Premature ventricular
contractions
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Improved ECG Signal Analysis Using
Wavelet and Feature.
• ECG signal analysis flow
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Improved ECG Signal Analysis Using
Wavelet and Feature.
• Feature Extraction
– Matlab : wpdec function, the wavelet ‘bior5.5’.
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Improved ECG Signal Analysis Using
Wavelet and Feature.
• Feature Extraction
– Energy
1 N
2
E( j)n 
(
x

m
)

i
N  1 i 1
– Normal Energy
E( j )norm_ n 
E( j)n
E( j )12  E( j ) 22    E( j ) 2n
– Entorpy
N
Ent( j )log_ n   log(xi2 )
i 1
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Improved ECG Signal Analysis Using
Wavelet and Feature.
• Feature Extraction
– Clustering
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Improved ECG Signal Analysis Using
Wavelet and Feature.
• Method 1
wavelet: bior5.5, decomposition level: 1 and 3 with Method 1(●: normal
beats, □: atrial premature beats, ○ : premature ventricular contractions)
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Improved ECG Signal Analysis Using
Wavelet and Feature.
• Method 2
wavelet: bior5.5, decomposition level: 1 and 3 with Method 2(●: normal
beats, □: atrial premature beats, ○ : premature ventricular contractions)
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Conclusion
• Wavelet analysis is widely used in many
application. Because it provides both time and
frequency information, can overcome the
limitation of Fourier transform.
• We can learn about the wavelet transform which
is able to detect beat rate of signals and to classify
the difference of signals.
• We also use the wavelet transform on the
other beat rate detection.
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Reference
• Chui, C.K. (1992). An Introduction to Wavelets. Academic
Press, San Diego, CA.
• S.S. Joshi, C.V. Ghule, "DWT Based Beat Rate Detection in
ECG Analysis," Proc. of IEEE International Conference and
Workshop on Emerging Trends in Technology(ICWET 2010),
pp. 765-769, 2010.
• A. Matsuyama, M. Jonkman, F. de Boer, ”Improved ECG
Signal Analysis Using Wavelet and Feature Extraction”,
Methods Inf. Med.,vol. 46, pp.227-230, 2007
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Q&A
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