1. Effects of Sampling Rate Question on the Nyquist Frequency

2. Sampling rate requirements In the past, we only stated that the sampling rate, or the Nyquist Frequency, should be higher than the Fourier analysis. Only recently, Rilling and Flandrin (2009) studied this problem quantitative: –Rilling, G and P. Flandrin, 2009: Sampling effects on the Empirical Mode Decomposition. Adv. Adaptive Data Analys. 1, 43-59.

3. Rilling-Flandrin Criterion

4. Observations The criterion is not important, but we have to realize that sampling effect is indeed an critical issue when we acquire data. Using the Rilling-Flandrin criterion, the error for Fourier Nyquist frequency, k=1, is approaching to 50%. For k=2, the error could drop to less than 15%, a criterion we suggested empirically. This is not a criterion for the frequency values. And it seems hopeless at this time to discuss the effects on frequency accuracy, except empirically.

5. Examples of Sampling Effects And Remedial Steps.

6. Model Data Simple sinusoidal function

7. A Simple sinusoidal function

8. Under-sampled rate 100/19

9. Spline-Improved Data 100/19

10. Under-sampled rate 100/23

11. Spline-Improved Data 100/23

12. Under-sampled rate 100/35

13. Spline-Improved Data 100/35

14. Under-sampled rate 100/47

15. Spline-Improved Data 100/47

16. IMF Spline-Improved Data 100/47

17. IMF Data 100/47

18. IMF Spline-improved Data 100/35

19. IMF Data 100/35

20. IMF Spline-improved Data 100/23

21. IMF spline-improved Data 100/19

22. IMF Data 100/19

23. Data-IMF1: 100/19

24. Data-IMF1: 100/23

25. Data-IMF1: 100/35

26. Data-IMF1: 100/47

27. Random Signal Spline improvements

28. Random Data

29. Under-sampled Random Data

30. Under-sampled Random Data Details

31. Under-sampled Random Data : IMF1

33. Under-sampled Random Data : IMF2

34. Under-sampled Random Data : IMF3

36. Summary Based on the theoretical and empirical studies, sampling rate should be 4 times the Nyquist frequency. Splined up-sampling could improve the EMD results and also the instantaneous frequency computations. We should examine the sampling rate, Fs, and make sure the Nyquist frequency at ¼ of Fs is acceptable.