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Takens' Embedding Theorem asserts that when the states of a hidden dynamical system are confined to a low-dimensional attractor, complete information about the states can be preserved in the observed time-series output through the delay coordinate map. However, the conditions for the theorem to hold ignore the effects of noise and time-series analysis in practice requires a careful empirical determination...
Signals of interests can often be thought to come from a low dimensional signal model. The exploitation of this fact has led to many recent interesting advances in signal processing, one notable example being in the field of compressive sensing (CS). The literature on CS has established that many matrices satisfy the Restricted Isometry Property (RIP), which guarantees a stable (i.e., distance-preserving)...
Takens' embedding theorem remarkably established that concatenating previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state space. However, Takens' theorem is fragile in the sense that even small imperfections can induce arbitrarily large errors in this attractor representation. We extend...
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