Nonlinear Energy Operator Research Articles

A new interpretation of nonlinear energy operator and its efficacy in spike detection.

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).

Limits on discrete modulated signals

We develop theorems of a general nature that apply to the analysis of AM-FM signals of the form a(m)exp [j/spl phi/(m)] or a(m) cos [/spl phi/(m)] and to their behavior both in linear systems and in simple nonlinear systems comprised of products of linear elements. Such product-systems include interesting nonlinear demodulation operators, such as the Teager-Kaiser (1990) operator. Expressions for the approximate system responses to AM-FM signals are derived by making an analogy to the eigenfunction interpretation of sinusoids in linear systems; for the case of sinusoidal signals, the approximations are exact. These expressions are collectively called quasieigenfunction approximations (QEAs). For nonsinusoidal AM-FM signals, the approximations have errors that are tightly bounded by functionals that express the smoothness of the AM and FM information signals and the durations of the involved system impulse responses. The bounds are independent of the bandwidths of the AM and FM functions. Two general applications are considered. First, the approximations are found to be useful for analyzing discrete-time nonlinear energy operators, including the Teager-Kaiser operator. Next, the approximation theorems lead to the selection of an optimal class of bandpass filters for use in a discrete multiband AM-FM demodulation system. The filter class selected is optimal in the sense of achieving the lower bound of a novel discrete uncertainty principle.

Energy demodulation of two-component AM-FM signal mixtures

An algorithm for the separation and energy-based demodulation of two-component mixtures of AM-FM signals is presented. The proposed algorithm is based on the generating differential or difference equation of the mixture signal and nonlinear differential energy operators.

AM-FM energy detection and separation in noise using multiband energy operators

This paper develops a multiband or wavelet approach for capturing the AM-FM components of modulated signals immersed in noise. The technique utilizes the recently-popularized nonlinear energy operator Psi (s)=(s)/sup 2/-ss to isolate the AM-FM energy, and an energy separation algorithm (ESA) to extract the instantaneous amplitudes and frequencies. It is demonstrated that the performance of the energy operator/ESA approach is vastly improved if the signal is first filtered through a bank of bandpass filters, and at each instant analyzed (via Psi and the ESA) using the dominant local channel response. Moreover, it is found that uniform (worst-case) performance across the frequency spectrum is attained by using a constant-Q, or multiscale wavelet-like filter bank. The elementary stochastic properties of Psi and of the ESA are developed first. The performance of Psi and the ESA when applied to bandpass filtered versions of an AM-FM signal-plus-noise combination is then analyzed. The predicted performance is greatly improved by filtering, if the local signal frequencies occur in-band. These observations motivate the multiband energy operator and ESA approach, ensuring the in-band analysis of local AM-PM energy. In particular, the multi-bands must have the constant-Q or wavelet scaling property to ensure uniform performance across bands. The theoretical predictions and the simulation results indicate that improved practical strategies are feasible for tracking and identifying AM-FM components in signals possessing pattern coherencies manifested as local concentrations of frequencies. >