EMD-seislet transform |

in order to best characterize the non-stationary signal. denotes the prediction filter at time . In the physical domain, the linear prediction and updating operators can be expressed as:

where and are operators that predict an element from its left and right neighbors by modulating each element according to their local frequency .

Figure 1 shows a comparison between the wavelet transform and the 1D stationary and non-stationary seislet transforms in compressing a 1D signal with smooth frequency components. The frequency ranges from 250 to 186 Hz. Both the wavelet transform and stationary seislet transform fail to compress the signal well while the non-stationary seislet transform obtains a perfectly sparse representation.

non-comp2
Demonstration of 1D non-stationary seislet transform for non-stationary signal. Upper: non-stationary chirp signal, frequency ranges from 250 to 186 Hz. Upper middle: compressed using 1D wavelet transform. Down middle: compressed using 1D stationary seislet transform with the frequency of 250 Hz. Down: compressed using 1D non-stationary seislet transform.
Figure 1. |
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EMD-seislet transform |

2019-02-12