Abstract
A numerical algorithm is presented for the purpose of reducing noise from a discretely sampled input signal where the underlying signal of interest has a broadband spectrum. It is designed to be useful even if the clean signal is contaminated with 100% or more noise (signal to noise ratio less than or equal to zero). The method is based on time delay embedding using coordinates generated by local low-pass filtering, which we call a low-pass embedding. The singular value decomposition is then used locally in embedding space to distinguish between the dynamics and the noise. The algorithm is evaluated for chaotic signals generated by the Lorenz and Rössler systems, to which Gaussian white noise has been added.
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