teo modelling for non-linear signals
TRANSCRIPT
![Page 1: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/1.jpg)
TEO modeling for non-linear signals
TRIPURNA CHARY.D(10281A0402)
GOUTHAM.P(10281A04A9)
JAGADISH REDDY.N(11285A0404)
SURENDER.M(10281A04B4)
YESHWANTH.K(10281A0414)
![Page 2: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/2.jpg)
Topics
1.Problem Formulation2.Electro Cardio Gram
i. How the heart works?ii. Electrical Conduction System iii. Arrhythmias
3. TEO (Teager Energy Operator)i. Signal energyii. Teager’s Energy Operator
a. Continuous TEOb. Discrete TEO
- Generalizationiii. T-test & Scatter plot
a. Test results on different MIT-BIH data baseb. Features observed
4.Conclusion
![Page 3: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/3.jpg)
Aim & Introduction
Objective of this project is to analyze noise free ECG signal and to discriminate the arrhythmia data from normal sinus rhythm data.
![Page 4: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/4.jpg)
Existing method
Fourier transform :
Fourier transform of the signalS[n]=DFT{S}
then, |S[n]|^2 represents the how much energy the signal contains at frequency band n.
![Page 5: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/5.jpg)
INTRODUCTION
The Teager Energy Operator (TEO) is a non-linear operator
TEO provides an advantage over conventional Fourier analysis methods in capturing the characteristics of nonlinear systems
Basic Idea
![Page 6: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/6.jpg)
ECGStructure of Heart
![Page 7: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/7.jpg)
Functioning of heart
![Page 8: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/8.jpg)
Electrical conduction System
SA node
AV node Bundle of his Left & Right bundle branches Purkinje fibers
![Page 9: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/9.jpg)
Electrical Conduction System Waveforms
One complete cardiac cycle =P, Q, R, S, (QRS complex), and T wave
P wave Atrial depolarization (contraction) QRS Complex Ventricular depolarization, atrial
repolarizationT wave Ventricular repolarization (resting
phase)
![Page 10: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/10.jpg)
Arrhythmias
Premature Ventricular Contraction(PVC)
![Page 11: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/11.jpg)
Arrhythmias
Left Bundle Branch Block(LBBB)
![Page 12: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/12.jpg)
Arrhythmias
Right Bundle Branch Block(RBBB)
![Page 13: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/13.jpg)
TEO (Teager Energy Operator)
i. Signal energyEnergy of the signal over some time 2T
Fourier transform of the signalS[n]=DFT{S}
then, |S[n]|^2 represents the how much energy the signal contains at frequency band n.
![Page 14: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/14.jpg)
Kaiser used the following differential equation as a starting point for the operator:
The solution of the above periodic oscillation is given by
The total energy of the object is in newtonian physics given as
![Page 15: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/15.jpg)
Continuous TEO
In continuous time, we define the Teager Energy Operator to be
![Page 16: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/16.jpg)
Discrete TEO
Generalization:
Basic definition for the discrete Teager Energy Operator:
For a digital signal x[n]
We get
&
![Page 17: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/17.jpg)
Proposed System
ECG dataAcquisition
transducer
MIT-BHT database
TeagerOperator
T-test
Scatter plot
BLOCK DIAGRAM
Energy in TD & FD
arrhythmia detection
![Page 18: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/18.jpg)
T-test & Scatter plot
T-testNormal Data
Arrhythmia data Te in time domain
Te in frequency domainFFTn n
kk
![Page 19: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/19.jpg)
T-test & Scatter plot
T-testTe in time domain
Te in frequency domain
Arrhythmia data
FFT
LBBB
n n
kk
![Page 20: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/20.jpg)
T-test & Scatter plot
T-testTe in time domain
Te in frequency domainFFT
Arrhythmia data
PVC
n n
kk
![Page 21: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/21.jpg)
T-test & Scatter plot
Te in time domain
Te in frequency domainFFT
Arrhythmia data
RBBB
n n
kk
![Page 22: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/22.jpg)
T-test & Scatter plot
Scatter Plot
Total of 67960 beats55465 Normal12495 arrhythmia
3685 paced3270 LBBB2280 RBBB3260 PVC
![Page 23: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/23.jpg)
Features observed
Accuracy
Sensitivity
Specificity
95%
80%
100%
![Page 24: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/24.jpg)
![Page 25: TEO modelling for non-Linear signals](https://reader033.vdocuments.net/reader033/viewer/2022042716/55a7594b1a28ab67458b464c/html5/thumbnails/25.jpg)
THANK
Q ?