Robustness Analysis of Synchrosqueezed Transforms
نویسنده
چکیده
Synchrosqueezed transforms are non-linear processes for a sharpened time-frequency representation of wave-like components. They are efficient tools for identifying and analyzing wave-like components from their superposition. This paper is concerned with the statistical properties of compactly supported synchrosqueezed transforms for wave-like components embedded in a generalized Gaussian random process in multidimensional spaces. Guided by the theoretical analysis of these properties, new numerical implementations are proposed to reduce the noise fluctuations of these transforms on noisy data. A MATLAB package SynLab together with several heavily noisy examples is provided to support these theoretical claims.
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1Department of Mathematics, Stanford University, Stanford, CA 94305 USA 2Departments of Mathematics, Chemistry, and Physics, Duke University, Durham, NC 27708 USA 3North Carolina Museum of Art, Raleigh, NC 27607 USA 4Department of Mathematics, Duke University, Durham, NC 27708 USA 5Department of Mathematics and Institute for Computational and Mathematical Engineering, Stanford University, Stanf...
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