Symbolic analysis of time series signals using generalized Hilbert transform

A recent publication has shown a Hilbert-transform-based partitioning method, called analytic signal space partitioning (ASSP). When used in conjunction with D-Markov machines, also reported in recent literature, ASSP provides a fast tool for pattern recognition. However, Hilbert transform does not specifically address the issue of noise reduction and the usage of D-Markov machines with a small depth 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.