ECE 501 Introduction to BME

1. ECE 501 Introduction to BME Dr. Hang ECE501

2. Part V Biomedical Signal ProcessingIntroduction toWavelet Transform Dr. Hang ECE 501

3. Introduction • Fourier Analysis Dr. Hang ECE 501

4. Introduction • Fourier Analysis • A serious drawback: time information is lost • Cannot handle transitory characteristics Dr. Hang ECE 501

5. Introduction • Short-Time Fourier Analysis • 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 Dr. Hang ECE 501

6. Introduction • Wavelet Analysis • A windowing technique with variable-sized regions: long time interval for low-frequency information, shorter regions for high-frequency information • Time-scale region Dr. Hang ECE 501

7. Introduction • What is Wavelet Analysis • 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. Dr. Hang ECE 501

8. Continuous Wavelet Transform • Fourier Analysis • The sum over all time of the signal multiplied by a complex exponential Dr. Hang ECE 501

9. Continuous Wavelet Transform CWT The sum over all time of the signal multiplied by scaled , shifted version of the wavelet function Dr. Hang ECE 501

10. Continuous Wavelet Transform • Scaling • Scaling a wavelet: stretching or compressing it • a: scaling factor Dr. Hang ECE 501

11. Continuous Wavelet Transform • Scaling • Low scale High frequency • High scale Low frequency Dr. Hang ECE 501

12. Continuous Wavelet Transform • Shifting Dr. Hang ECE 501

13. Continuous Wavelet Transform • Five Steps to a CWT • Take a wavelet and compare it to a section at the start of the original signal • Calculate the wavelet coefficient C Dr. Hang ECE 501

14. Continuous Wavelet Transform • Five Steps to a CWT • Shift the wavelet to the right and repeat steps 1 and 2 until the whole signal is covered. Dr. Hang ECE 501

15. Continuous Wavelet Transform • Five Steps to a CWT • Scale the wavelet and repeat steps 1 through 3 Dr. Hang ECE 501

16. Continuous Wavelet Transform • Five Steps to a CWT • Repeat steps 1 through 4 for all scales Dr. Hang ECE 501

17. Continuous Wavelet Transform • Plot CWT coefficients Dr. Hang ECE 501

18. Continuous Wavelet Transform • Plot CWT coefficients Dr. Hang ECE 501

19. Discrete Wavelet Transform • Dyadic scales and positions: • Mallat algorithm: fast algorithm via filtering • Accurate analysis: compression, denoising Dr. Hang ECE 501

20. Discrete Wavelet Transform • One-Stage filtering: Approximations and Details Not Efficient! Dr. Hang ECE 501

21. Discrete Wavelet Transform • One-Stage filtering: Approximations and Details Efficient! Dr. Hang ECE 501

22. Discrete Wavelet Transform • One-Stage filtering: Approximations and Details Dr. Hang ECE 501

23. Discrete Wavelet Transform • One-Stage filtering: Approximations and Details Dr. Hang ECE 501

24. Discrete Wavelet Transform • Multiple-Level Decomposition Dr. Hang ECE 501

25. Discrete Wavelet Transform • Multiple-Level Decomposition Dr. Hang ECE 501

26. Discrete Wavelet Transform • Wavelet Reconstruction Up Sampling Dr. Hang ECE 501

27. Discrete Wavelet Transform • Wavelet Reconstruction Dr. Hang ECE 501

28. Discrete Wavelet Transform • Wavelet Reconstruction Dr. Hang ECE 501

29. Wavelet Families Daubechies family Dr. Hang ECE 501

30. Wavelet Families Symlets Dr. Hang ECE 501

31. Denoising • Decompose • Threshold detail coefficients • Reconstruct Dr. Hang ECE 501

32. Denoising Two thresholding method: (1) Soft (2) Hard Dr. Hang ECE 501