Fast Intrinsic Mode Decomposition of Time Series Data with Sawtooth Transform
For researchers analyzing non-stationary time series, this method offers a computationally cheaper alternative to EMD, though it is incremental and limited to the specific domain of signal decomposition.
The paper introduces a faster and more predictable method for intrinsic mode decomposition of time series data, replacing the iterative sifting in EMD with a single-pass sawtooth transform. The method constructs envelopes directly in the sawtooth space, yielding a unique IMF component without repetitive sifting.
An efficient method is introduced in this paper to find the intrinsic mode function (IMF) components of time series data. This method is faster and more predictable than the Empirical Mode Decomposition (EMD) method devised by the author of Hilbert Huang Transform (HHT). The approach is to transforms the original data function into a piecewise linear sawtooth function (or triangle wave function), then directly constructs the upper envelope by connecting the maxima and construct lower envelope by connecting minima with straight line segments in the sawtooth space, the IMF is calculated as the difference between the sawtooth function and the mean of the upper and lower envelopes. The results found in the sawtooth space are reversely transformed into the original data space as the required IMF and envelopes mean. This decomposition method process the data in one pass to obtain a unique IMF component without the time consuming repetitive sifting process of EMD method. An alternative decomposition method with sawtooth function expansion is also presented.