Processing Asynchronous Time-Simplex Signals
F. Ji (Nanyang Technological University)
X. Jian (Nanyang Technological University)
W.P. Tay (Nanyang Technological University)
M. Yang (TU Delft - Electrical Engineering, Mathematics and Computer Science, TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
Topological signal processing (TSP) over simplicial complexes typically assumes observations associated with the simplicial complexes are real scalars. In this paper, we develop a TSP framework for the case where observations on a simplicial complex belong to function spaces that are commonly used to represent time-varying signals. Our approach generalizes the Hodge decomposition and allows for signal processing tasks to be performed on these more complex observations, which can better model signals in practice. We propose a unified and flexible framework for TSP over simplicial complexes that expands its applicability to a wider range of signal processing applications. Numerical results demonstrate the effectiveness of this approach and provide a foundation for future research in this area.