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Gabor frames and higher dimensional boundaries in signal analysis on manifolds (2309.04094v1)

Published 8 Sep 2023 in eess.SP, cs.RO, math.DG, and math.FA

Abstract: We provide a construction of Gabor frames that encode local linearizations of a signal detected on a curved smooth manifold of arbitrary dimension, with Gabor filters that can detect the presence of higher-dimensional boundaries in the manifold signal. We describe an application in configuration spaces in robotics with sharp constrains. The construction is a higher-dimensional generalization of the geometric setting developed for the study of signal analysis in the visual cortex.

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