A Remark on Adaptive Decomposition for Nonlinear Time-Frequency Analysis (Communications in Mathematical Research, 2021)
In recent study the bank of real square integrable functions that havenonlinear phases and admit a well-behaved Hilbert transform has been constructedfor adaptive representation of nonlinear signals. We first show in this paper that theavailable basic functions are adequate for establishing an ideal adaptive decomposition algorithm. However, we also point out that the best approximation algorithm,which is a common strategy in decomposing a function into a sum of functions in aprescribed class of basis functions, should not be considered as a candidate for theideal algorithm.
Keywords: Hilbert transform; empirical mode decomposition; adaptive decomposition algorithm; best approximation.