@inproceedings{000cf1bc46bf454a815d8a6e486777ba,

title = "Oscillatory + transient signal decomposition using overcomplete rational-dilation wavelet transforms",

abstract = "This paper describes an approach for decomposing a signal into the sum of an oscillatory component and a transient component. The method uses a newly developed rational-dilation wavelet transform (WT), a selfinverting constant-Q transform with an adjustable Q-factor (quality-factor). We propose that the oscillatory component be modeled as signal that can be sparsely represented using a high Q-factor WT; likewise, we propose that the transient component be modeled as a piecewise smooth signal that can be sparsely represented using a low Q-factor WT. Because the low and high Q-factor wavelet transforms are highly distinct (having low coherence), morphological component analysis (MCA) successfully yields the desired decomposition of a signal into an oscillatory and non-oscillatory component. The method, being non-linear, is not constrained by the limits of conventional LTI filtering.",

keywords = "Constant Q, Morphological component analysis, Q-factor, Sparsity, Wavelets",

author = "Selesnick, {Ivan W.} and {\"I}lker Bayram",

year = "2009",

doi = "10.1117/12.826237",

language = "English (US)",

isbn = "9780819477361",

series = "Proceedings of SPIE - The International Society for Optical Engineering",

booktitle = "Wavelets XIII",

note = "Wavelets XIII ; Conference date: 02-08-2009 Through 04-08-2009",

}