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

Abstract

Abstract-This paper develops a multiband or wavelet approach for capturing the AM-FM components of modulated signals immersed in noise. The technique utilizes the recentlypopularized nonlinear energy operator Y (s) = (S)' -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 I 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 and of the ESA are developed first. The performance of P and the ESA when applied to bandpass filtered versions of an AM-FM signat-plusnoise combination is then analyzed. The predicted performance is greatly improved by filtering, if the local signal frequencies occur in-hand. These observations motivate the multiband energy operator and ESA approach, ensuring the in-band analysis of local AM-FM 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.

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