Spline manipulations for empirical mode decomposition (EMD) on bounded intervals and beyond. (English) Zbl 1532.94014
The core of empirical mode decomposition (EMD) of a time series \(f(t)\) on some finite time-domain \([a,b]\) is the iterative sifting process for computing the intrinsic mode functions and the trend of \(f(t)\). To compute each IMF, \(f_k (t)\) for \(k = 1,\dots,n\), there are \(L_k\) iterative steps of the sifting process, and in each step, two cubic spline functions are to be computed, with one to represent the upper envelope and the other to represent the lower envelope, determined by the local maxima and local minima, respectively on the open interval \((a,b)\). In this paper, four cubic spline representations are proposed by the authors.
Reviewer: Antonio López-Carmona (Granada)
MSC:
| 94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |
| 41A15 | Spline approximation |
| 65T40 | Numerical methods for trigonometric approximation and interpolation |
Keywords:
EMD on truncated time-domains with minimal boundary artifacts; quasi-interpolation spline basis functions; Hilbert transform on bounded intervals without singularities; real-time quasi-interpolation for other applicationsReferences:
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