1. An Introduction to S-Transform for Time-Frequency Analysis S.K. Steve Chang SKC-2009

2. Question: Do we live in… Time-Domain or Frequency-Domain? SKC-2009

3. Time Domain vs Frequency Domain Time information is lost. 200040006000 Frequency (Hz) Spectrum 0.1 0.9 Time (Seconds) Waveform SKC-2009

4. Spectrogram (time-Frequency) Time (Seconds) 0.10.30.50.70.9 Frequency (HZ) 2000 4000 6000 8000 SKC-2009

5. Fourier Transform & Short Time Fourier Transform Window SKC-2009

6. STFT Fourier Transform SKC-2009

7. STFT: Fixed Window, Fixed Resolution Window Length Frequency Resolution Time Resolution SKC-2009

8. Example (400 msec sample) SKC-2009

9. (T=25 ms) Poor Frequency Resolution SKC-2009

10. (T=125 ms) Fixed Resolution SKC-2009

11. (T=375 ms) Fixed Resolution SKC-2009

12. (T=1000 ms) Poor High Frequency Time Resolution SKC-2009

13. S-Transform & Short Time Fourier Transform SKC-2009

14. Gaussian Window for S-Transform Function of Frequency SKC-2009

15. Gaussian Window for S-Transform High Frequency Low Frequency Time Shifted SKC-2009

16. and from SKC-2009

17. Two Chirps and Two Bursts S-T STFT Wigner SKC-2009

18. S-Transform and Wavelet Transform Mother Wavelet: SKC-2009

19. S-Transform is not Wavelet Transform Mother Wavelet does not have zero mean: Morlet’s Wavelet Phase Correction SKC-2009

20. Generalized S-Transform Resolution p TimeFrequency Standard Deviation SKC-2009

21. Generalized S-Transform: Bi-Gaussian SKC-2009

22. Generalized S-Transform: Bi-Gaussian Sharper Front Edge For Arrival Time Sacrifice Frequency Resolution SKC-2009

23. Generalized S-Transform: Bi-Gaussian Sharper Arrival Time SKC-2009

24. Generalized S-Transform: Your Own SKC-2009

25. Generalized S-Transform: Your Own Constraint: SKC-2009

26. Examples - Applications Engine Knock Pressure STFT S-Transform with New Window S-Transform SKC-2009

27. Power Disturbance Detection Power Disturbance Contour Stationary Phase Power Disturbance SKC-2009

28. Earthquake Detection Noisy Signal Time-Frequency Filter Inverse S-Transform Earthquake Signal SKC-2009

29. Earthquake Seismology Original Data Filter 1 Filter 2 S-Filters SKC-2009

30. Seismic Data STFTS- Transform Seismic Trace SKC-2009

31. Medical: Forearm Blood Flow Rest Activities Occlusion SKC-2009

32. Geomagnetic Storm Induced Current SKC-2009

33. Gear Vibration Signal Decoposition Helicopter Rotor under Fatigue Test Transient Components SKC-2009

34. Image Analysis Original ImageDominant Frequency SKC-2009

35. S-Transform We live in Time-Frequency World. Similar to Short-Time Fourier Transform Similar to Continuous Wavelet Transform Generalized S-Transform: Many Different Window Choices Time-Frequency Analysis: Many Applications SKC-2009