Nonlinear energy operator (NEO) gives the estimate of energy content of a linear oscillator. This has been used to quantify the AM-FM modulating signals present in a sinusoid. In this paper, we give a new interpretation of NEO and extend its use in stochastic signals. We show that NEO accentuates the high-frequency content. This instantaneous nature of NEO and its very low computational burden make it an ideal tool for spike detection. The efficacy of the proposed method has been tested with simulated signals as well as with real electroencephalograms (EEG's).

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In this paper, we consider the problem of delay-dependent stability of a class of Lur’e systems of neutral type with time-varying delays and sector-bounded nonlinearity using Lyapunov–Krasovskii (LK) functional approach. By using a candidate LK functional in the stability analysis, a less conservative absolute stability criterion is derived in terms of linear matrix inequalities (LMIs). In addition to the LK functional, conservatism in the proposed stability analysis is further reduced by imposing tighter bounding on the time-derivative of the functional without neglecting any useful terms using minimal number of slack matrix variables. The proposed analysis, subsequently, yields a stability criterion in convex LMI framework, and is solved nonconservatively at boundary conditions using standard LMI solvers. The effectiveness of the proposed criterion is demonstrated through a standard numerical example and Chua’s circuit.

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