This project computes the Ensemble Empirical Decomposition (EEMD), and their significance test based on t-student distribution in two ways:
- (1) Given the time series' signal to noise ratio, it creates n amounts of surrogate time series and then, evaluates the EEMD and the significance test.
- (2) Given a signal with observational uncertainty previoulsy simulated, it evaluates the EEMD and the significance test (Suitable for paleoclimatic data).
This project uses some builtin matlab functions. So, it is advisable to run this project with matlab versions after R2017a.
- (i) Create the surrogate time series or simulates the observational uncertainty. See the file BTC.mlx in folder example/.
- (ii) call the class EMD_timeseries as:
EEMD = EMD_timeseries(time,serie,opt);
where time is the time axis, an array of floats, integers or datetime object, serie is the time series data that can be a single array or a matrix with dimensions (mxn), with the rows with the same size of the time axis and opt is the interpolating method for the envelope, opt can be 'pchip' for raw data and 'spline' for smoothed data
- (iii) A figure for the significance test can be obtained by calling the function:
plot_sign(EEMD, title, opt);
where EEMD is the Ensemble EMD object, title is the figure title string and opt is an option to plot the 95% confidence bound ellipsoid of the surrogates IMFs, opt can be '-1sigma' to show the ellipsoid and otherwise to not show.
Empirical Mode Decomposition (EMD), decomposes a signal into a finite set of Intrinsic Mode Functions (IMFs) and residual series, with each IMF representing a scale of data variability, where the sum of the IMFs and the residual component represent the full data.
First of all, the time series upper and lower envelope is computed and thus, averaged and then subtracted from the signal, generating a residual time series, this residual time series, becomes an IMF. So, the process above is repeated up to number of time series zero crossing or tolerance (between the full series and residual series - relative tolerance) is no more verified.
The figure bellow shows how EEMD decomposes the signal into a set of IMFs.
The statistical significance test for the IMFs, will verify the capacity of the IMFs in representing signal band. If the band is too wide, one can say that the signal is "contaminated" with white noise, or that the IMF is unable to represent the signal in a given band. In physics and engineering studies, it is extremely important that the EMD is able to correctly decompose the signal.
The figure bellow shows the EEMD significance test. The blue and red curves represent the 95% and 99% significance range, values outside this range are statiscally significant at the level of 95% and 99% respectivelly.
