Generalization of Hilbert transform for symbolic analysis of noisy signals

A recent publication has reported a Hilbert-transform-based partitioning method, called analytic signal space partitioning (ASSP), which essentially replaces wavelet space partitioning (WSP) for symbolic analysis of time series data in dynamical systems. When used in conjunction with D-Markov machines, also reported in the recent literature, ASSP provides a fast method of pattern recognition. However, wavelet transform facilitates denoising, which allows D-Markov machines to have a small depth D even if the time series data have a low signal-to-noise ratio. Since Hilbert transform does not specifically address the issue of noise reduction, usage of D-Markov machines with a small D could potentially lead to information loss for noisy signals. On the other hand, a large D tends to make execution of pattern recognition computationally less efficient due to an increased number of machine states. This paper explores generalization of Hilbert transform that addresses symbolic analysis of noise-corrupted dynamical systems. In this context, theoretical results are derived based on the concepts of information theory. These results are validated on time series data, generated from a laboratory apparatus of nonlinear electronic systems.