ece 501 introduction to bme
DESCRIPTION
ECE 501 Introduction to BME. Dr. Hang. ECE 501. Part V Biomedical Signal Processing Introduction to Wavelet Transform. Dr. Hang. ECE 501. Introduction. Fourier Analysis. Dr. Hang. ECE 501. Introduction. Fourier Analysis. A serious drawback: time information is lost - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/1.jpg)
ECE 501 Introduction to BME
ECE 501 Dr. Hang
![Page 2: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/2.jpg)
Part V Biomedical Signal Processing Introduction to Wavelet Transform
ECE 501 Dr. Hang
![Page 3: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/3.jpg)
ECE 501 Dr. Hang
Fourier Analysis
Introduction
![Page 4: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/4.jpg)
ECE 501 Dr. Hang
Fourier Analysis
Introduction
• A serious drawback: time information is lost
• Cannot handle transitory characteristics
0 200 400 600 800 1000 1200-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
![Page 5: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/5.jpg)
ECE 501 Dr. Hang
Short-Time Fourier Analysis
Introduction
• A compromise between the time- and frequency-based views of a signal: analyze a small section of the signal at a time
• A drawback: The window is the same for all frequencies
![Page 6: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/6.jpg)
ECE 501 Dr. Hang
Wavelet Analysis
Introduction
• A windowing technique with variable-sized regions: long time interval for low-frequency information, shorter regions for high-frequency information
• Time-scale region
![Page 7: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/7.jpg)
ECE 501 Dr. Hang
What is Wavelet Analysis
Introduction
• A wavelet is a waveform of effectively limited duration that has an average value of zero
• Wavelet analysis is the breaking up of a signal into shifted and scaled versions of the original (mother) wavelet.
![Page 8: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/8.jpg)
ECE 501 Dr. Hang
Fourier Analysis The sum over all time of the signal multiplied by a complex exponential
Continuous Wavelet Transform
![Page 9: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/9.jpg)
ECE 501 Dr. Hang
CWT The sum over all time of the signal multiplied by scaled , shifted version of the wavelet function
Continuous Wavelet Transform
![Page 10: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/10.jpg)
ECE 501 Dr. Hang
Scaling• Scaling a wavelet: stretching or compressing it• a: scaling factor
Continuous Wavelet Transform
![Page 11: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/11.jpg)
ECE 501 Dr. Hang
Scaling• Low scale High frequency • High scale Low frequency
Continuous Wavelet Transform
![Page 12: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/12.jpg)
ECE 501 Dr. Hang
Shifting
Continuous Wavelet Transform
![Page 13: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/13.jpg)
ECE 501 Dr. Hang
Five Steps to a CWT
1. Take a wavelet and compare it to a section at the start of the original signal
2. Calculate the wavelet coefficient C
Continuous Wavelet Transform
![Page 14: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/14.jpg)
ECE 501 Dr. Hang
Five Steps to a CWT
3. Shift the wavelet to the right and repeat steps 1 and 2 until the whole signal is covered.
Continuous Wavelet Transform
![Page 15: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/15.jpg)
ECE 501 Dr. Hang
Five Steps to a CWT
4. Scale the wavelet and repeat steps 1 through 3
Continuous Wavelet Transform
![Page 16: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/16.jpg)
ECE 501 Dr. Hang
Five Steps to a CWT
5. Repeat steps 1 through 4 for all scales
Continuous Wavelet Transform
![Page 17: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/17.jpg)
ECE 501 Dr. Hang
Plot CWT coefficients
Continuous Wavelet Transform
![Page 18: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/18.jpg)
ECE 501 Dr. Hang
Plot CWT coefficients
Continuous Wavelet Transform
![Page 19: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/19.jpg)
ECE 501 Dr. Hang
• Dyadic scales and positions:
• Mallat algorithm: fast algorithm via filtering
• Accurate analysis: compression, denoising
Discrete Wavelet Transform
![Page 20: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/20.jpg)
ECE 501 Dr. Hang
One-Stage filtering: Approximations and Details
Discrete Wavelet Transform
Not Efficient!
![Page 21: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/21.jpg)
ECE 501 Dr. Hang
One-Stage filtering: Approximations and Details
Discrete Wavelet Transform
Efficient!
![Page 22: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/22.jpg)
ECE 501 Dr. Hang
One-Stage filtering: Approximations and Details
Discrete Wavelet Transform
![Page 23: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/23.jpg)
ECE 501 Dr. Hang
One-Stage filtering: Approximations and Details
Discrete Wavelet Transform
![Page 24: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/24.jpg)
ECE 501 Dr. Hang
Multiple-Level Decomposition
Discrete Wavelet Transform
![Page 25: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/25.jpg)
ECE 501 Dr. Hang
Multiple-Level Decomposition
Discrete Wavelet Transform
![Page 26: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/26.jpg)
ECE 501 Dr. Hang
Wavelet Reconstruction
Discrete Wavelet Transform
Up Sampling
![Page 27: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/27.jpg)
ECE 501 Dr. Hang
Wavelet Reconstruction
Discrete Wavelet Transform
![Page 28: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/28.jpg)
ECE 501 Dr. Hang
Wavelet Reconstruction
Discrete Wavelet Transform
![Page 29: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/29.jpg)
ECE 501 Dr. Hang
Wavelet Families
Daubechies family
![Page 30: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/30.jpg)
ECE 501 Dr. Hang
Wavelet Families
Symlets
![Page 31: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/31.jpg)
ECE 501 Dr. Hang
Denoising
1. Decompose
2. Threshold detail coefficients
3. Reconstruct
![Page 32: ECE 501 Introduction to BME](https://reader034.vdocument.in/reader034/viewer/2022051517/568159df550346895dc72c4a/html5/thumbnails/32.jpg)
ECE 501 Dr. Hang
Denoising
Two thresholding method: (1) Soft (2) Hard