Random noise attenuation by a selective hybrid approach using f-x empirical mode decomposition |

Provided that , , , and denote the original non-stationary signal, the separated IMFs, the residual and the number of IMFs, respectively, EMD can be expressed as:

For a non-stationary signal , using equation 1, we get a finite set of sub-signals ,( ).

A special property of EMD is that the IMFs represent different oscillations embedded in the data, where the mean frequency for each sub-signal decreases with IMF order increasing.

Figures 1 and 2 give a example of EMD for a non-stationary signal. Figure 1 shows a non-stationary signal and its corresponding instantaneous frequency, which is similar to that used by Herrera et al. (2013). From the instantaneous frequency we can see that the signal can be divided into four temporal regions. From 0 s - 4 s, the signal is composed of two frequency components corresponding to 5 Hz and 15 Hz. From 4 s - 6 s, the signal is composed of three frequency components corresponding to 5 Hz, 15 Hz, and 34 Hz, respectively. From 6 s- 7.8 s, the signal is composed of two frequency components corresponding to 10 Hz and 34 Hz. The last part from 7.8 s to 10 s is a monotonic signal, whose frequency is 10 Hz. Figure 2 shows the separated signal component using EMD. The separated components are consistent with the instantaneous frequency map as shown in Figure 1. Each individual frequency components have been separated out, with negligible edge effects and residual.

s-sf
Non-stationary signal and its instantaneous frequency. Up: Non-stationary signal. Down: Corresponding instantaneous frequency.
Figure 1. |
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Imf
EMD separated signal. From up to down: first IMF, second IMF, third IMF, and the residual.
Figure 2. |
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Random noise attenuation by a selective hybrid approach using f-x empirical mode decomposition |

2015-11-23