Im~ortance and modes of energy storage 1.1The importance of energy storage 1.2 Influence of type and extent of mismatch on storage 1.3 Size and duration of storage 1.4 Applications 1.4.1 Stationary applications 1.4.2 Transport applications 1.5 Quality of energy and modes of energy storage 1.6 Thermal energy storage 1.6.1 Sensible heat storage 1.6.2 Storage in phase change 27 materials (PCM) 1.7 Mechanical energy stcrage 31 1.7.1 Storage as potential energy 31 1.7.2 Storage as kinetic energy 1.7.3 Energy storage in a compressed gas 1.8 Electrical and magnetic energystorage55 1.9.1 Storage in electrical capacitors 1.8.2 Storage in electrom8gnets 1.8.3 Storage in magnets with superconducting coils 1.8.4 Storage in a battery 1.9 Chemical energy storage 1.9.1 Synthetic fuels 61 1.9.2 Thermochemical storage 1.9.3 Electrochemical storage 1.9.4 Photochemical storage vii
This paper reports results of the estimation of dynamical invariants, namely Lyapunov exponents, dimension, and metric entropy for speech signals. Two optimality criteria from dynamical systems literature, namely singular value decomposition method and the redundancy method, are used to reconstruct state space trajectories of speech and make observations. The positive values of the largest Lyapunov exponent of speech signals in the form of phoneme articulations show the average exponential divergence of nearby trajectories in the reconstructed state space. The dimension of a time series is a measure of its complexity and gives bounds on the number of state space variables needed to model it. It is found that most speech signals in the form of phoneme articulations are low dimensional. For comparison, a statistical model of a speech time series is also used to estimate the correlation dimension. The second-order dynamical entropy (which is a lower bound of metric entropy) of speech time series is found to be positive. This independently corroborates the interpretation of the largest Lyapunov exponent results and gives an estimate of the predictability time.
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