18-04-2011, 11:05 AM
• CLASSIFICATION OF ECG SIGNAL USING
WAVELET ANALYSIS
PRESENTED BY
RANJIT KUMAR
ROBINS
SANDEEP KUMAR PANDEY
SANJAY KUMAR
[attachment=12280]
INTRODUCTION
What is signal ?
A signal is defined as a physical quantity that varies with time space or any other independent variable or variables.
Classification of signals:-
It is of two types:-
(1) Stationary signal
(2) Non-stationary signal
(1) Stationary signal :-
It is a signal whose frequency component does not change over time.
e.g.:- white noise.
CLASSIFICATION OF STATIONARY SIGNAL
• Stationary signal classification is done with the help of power spectrum estimation.
• Here signal energy is infinite but power is finite.
• We estimate the power.
• Power is taken as the figure of merit for classification
(2)Non-stationary signal:-
It is a signal whose frequency components changes over time.
e.g.:- speech signal , ECG etc..
• It is a represented in 3-D
• Thus, we need another axis to determine the Non-stationary signals.
• This three dimension plot is called time-frequency distribution in which signal is plotted agents time as well as frequency
SOME NONSTATIONARY SIGNALS
ECG SIGNAL(Electrocardiography)
The electrocardiogram or ECG (sometimes called EKG) is today used worldwide as a relatively simple way of diagnosing heart conditions.
It is an electrical activity of the heart over time captured and externally recorded by skin electrodes.
• In Greek
• electro- electrical activity
• cardio- heart
• graphy – graph.
It is a non-stationary signal because the frequency varies with time.
HOW ECG WAVE COME FROM HEART BEAT
Classification of ECG
The different techniques used for ECG classification purpose are given as follows.
• Classification of ECG waveforms for Diagnosis of Diseases
• Classification of ECG patterns using fuzzy rules derived from ID3-induced decision trees
• Signal-adaptive kernel function design technique
• Statistical analysis technique
• Neural network technique
USES OF ECG CLASSIFICATION
ECG Classification is mostly used in:-
• Cardiac diagnosis
• Detecting rhythmic problems
SHORT-TIME FOURIER TRANSFORM(STFT)
• In this method we do not consider the whole signal.
• A small part of signal is taken and multiplied with a selected window function, and determine the Fourier transform.
• The short-time Fourier transform of a signal is given by the equation.
F(w, b) = ∫h(t-b)e^-jwt s(t)dt
where,
h is a reference window
• Some important applications of
non-stationary signal :-
• System identification
• Moving target detection
• Oil exploration
• Pattern recognition
• Speech recognition
• Image processing
Work Done
we have taken three similar test signals.
We plotted them using matlab.
we found their wavelets using wavelet tools.
we plotted wavelets in 3D graph.
In 1st method we found their SVD individually.
we plot their signatures and superimpose them on same plot to find the difference.
In 2nd method we found PCA and plot them them to find difference.
we generated ECG signal and found their SVD and plotted it .
WAVELET
• A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.
• It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor.
• Wavelets can be combined, using a "shift, multiply and sum" technique called convolution, with portions of an unknown signal to extract information from the unknown signal.
WAVELET
• In comparison to sine wave
It is a waveform of limited duration that has average value of zero.
It tends to be irregular and asymmetric.
Signal with sharp changes might be better analyzed with wavelet.
SIGNATURE FOR A SIGNAL
• It is set of attributes of a classification approach for the associated signal.
• It should
- be independent of signal length , location &
magnitude .
- have few parameters.
-have fast classification routines.
POWER SIGNATURE
SC(a,b)=|C(a,b)|2
SC(a,b)=time scale power density fn
COMPARISION OF TEST SIGNALS
We have taken three test signals ,which are almost similar.
x1=ej.5π.tsinc(t/3)
x2= ej.55π.tsinc(t/3)
x3= ej.555π.tsinc(t/3)
SINGULAR VALUE DECOMPOSITION(SVD)
• In linear algebra, the singular value decomposition (SVD) is an important factorization of a rectangular real or complex matrix, with many applications in signal processing and statistics.
APPLICATIONS OF SVD
(1) The pseudo inverse ,
(2)least squares fitting of data ,
(3) matrix approximation and determining the rank,
(4) range and null space of a matrix.
PRINCIPAL COMPONENT ANALYSIS
• Principal component analysis (PCA) involves a mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components
• PCA involves the calculation of the eigenvalue or singular value decomposition of a data matrix, usually after mean centering the data for each attribute.
• The results of a PCA are usually discussed in terms of component scores and loadings.
WAVELET ANALYSIS
PRESENTED BY
RANJIT KUMAR
ROBINS
SANDEEP KUMAR PANDEY
SANJAY KUMAR
[attachment=12280]
INTRODUCTION
What is signal ?
A signal is defined as a physical quantity that varies with time space or any other independent variable or variables.
Classification of signals:-
It is of two types:-
(1) Stationary signal
(2) Non-stationary signal
(1) Stationary signal :-
It is a signal whose frequency component does not change over time.
e.g.:- white noise.
CLASSIFICATION OF STATIONARY SIGNAL
• Stationary signal classification is done with the help of power spectrum estimation.
• Here signal energy is infinite but power is finite.
• We estimate the power.
• Power is taken as the figure of merit for classification
(2)Non-stationary signal:-
It is a signal whose frequency components changes over time.
e.g.:- speech signal , ECG etc..
• It is a represented in 3-D
• Thus, we need another axis to determine the Non-stationary signals.
• This three dimension plot is called time-frequency distribution in which signal is plotted agents time as well as frequency
SOME NONSTATIONARY SIGNALS
ECG SIGNAL(Electrocardiography)
The electrocardiogram or ECG (sometimes called EKG) is today used worldwide as a relatively simple way of diagnosing heart conditions.
It is an electrical activity of the heart over time captured and externally recorded by skin electrodes.
• In Greek
• electro- electrical activity
• cardio- heart
• graphy – graph.
It is a non-stationary signal because the frequency varies with time.
HOW ECG WAVE COME FROM HEART BEAT
Classification of ECG
The different techniques used for ECG classification purpose are given as follows.
• Classification of ECG waveforms for Diagnosis of Diseases
• Classification of ECG patterns using fuzzy rules derived from ID3-induced decision trees
• Signal-adaptive kernel function design technique
• Statistical analysis technique
• Neural network technique
USES OF ECG CLASSIFICATION
ECG Classification is mostly used in:-
• Cardiac diagnosis
• Detecting rhythmic problems
SHORT-TIME FOURIER TRANSFORM(STFT)
• In this method we do not consider the whole signal.
• A small part of signal is taken and multiplied with a selected window function, and determine the Fourier transform.
• The short-time Fourier transform of a signal is given by the equation.
F(w, b) = ∫h(t-b)e^-jwt s(t)dt
where,
h is a reference window
• Some important applications of
non-stationary signal :-
• System identification
• Moving target detection
• Oil exploration
• Pattern recognition
• Speech recognition
• Image processing
Work Done
we have taken three similar test signals.
We plotted them using matlab.
we found their wavelets using wavelet tools.
we plotted wavelets in 3D graph.
In 1st method we found their SVD individually.
we plot their signatures and superimpose them on same plot to find the difference.
In 2nd method we found PCA and plot them them to find difference.
we generated ECG signal and found their SVD and plotted it .
WAVELET
• A wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero.
• It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor.
• Wavelets can be combined, using a "shift, multiply and sum" technique called convolution, with portions of an unknown signal to extract information from the unknown signal.
WAVELET
• In comparison to sine wave
It is a waveform of limited duration that has average value of zero.
It tends to be irregular and asymmetric.
Signal with sharp changes might be better analyzed with wavelet.
SIGNATURE FOR A SIGNAL
• It is set of attributes of a classification approach for the associated signal.
• It should
- be independent of signal length , location &
magnitude .
- have few parameters.
-have fast classification routines.
POWER SIGNATURE
SC(a,b)=|C(a,b)|2
SC(a,b)=time scale power density fn
COMPARISION OF TEST SIGNALS
We have taken three test signals ,which are almost similar.
x1=ej.5π.tsinc(t/3)
x2= ej.55π.tsinc(t/3)
x3= ej.555π.tsinc(t/3)
SINGULAR VALUE DECOMPOSITION(SVD)
• In linear algebra, the singular value decomposition (SVD) is an important factorization of a rectangular real or complex matrix, with many applications in signal processing and statistics.
APPLICATIONS OF SVD
(1) The pseudo inverse ,
(2)least squares fitting of data ,
(3) matrix approximation and determining the rank,
(4) range and null space of a matrix.
PRINCIPAL COMPONENT ANALYSIS
• Principal component analysis (PCA) involves a mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components
• PCA involves the calculation of the eigenvalue or singular value decomposition of a data matrix, usually after mean centering the data for each attribute.
• The results of a PCA are usually discussed in terms of component scores and loadings.