Measuring amplitude and frequency modulations in noise using multiband energy operators

The statistical properties of the nonlinear energy operator Ψ( s)=(ds/dt)²-sd² /dt² and a related energy separation algorithm (ESA) are developed. The ESA uses Ψ to demodulate noisy AM-FM signals. The performance of Ψ and the ESA when applied to bandpass noisy AM-FM signals is examined. The predicted performance is found to be greatly improved if the local signal frequencies occur within the filter passband. Using this observation, a multiband energy operator and ESA approach are devised. The results suggest that greatly improved practical strategies are feasible for tracking and identifying local pattern coherencies manifested as local concentrations of signal frequencies