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 self-inverting 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.

Date Published: 4 September 2009
PDF: 14 pages
Proc. SPIE 7446, Wavelets XIII, 74460V (4 September 2009); doi: 10.1117/12.826237

Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)