Instantaneous Energy Operators: Applications to Speech Processing and Communications 1. Speech Processing Applications 2. Higher-order Energy Operators

The nonlinear energy operator (x) _ x] 2 ? x x and its discrete-time counterpart have found numerous applications including development of the energy separation algorithm (ESA) for demodulat-ing AM-FM signals, tracking speech modulations, and detecting various events in nonstationary signals. In this paper we rst present some improvements on the energy operator and ESA when applied to demodulating speech resonances and using the extracted information signals for speech processing applications. Then we introduce some new nonlinear operators (diierential in continuous time and quadratic in discrete time) that can provide higher-order energy measurements with applications to co-channel demodulation and separation of AM{FM signal mixtures. Finally, we present a cross-coupled ESA for co-channel demodulation. The nonlinear continuous-time energy operator (x)(t) _ x(t)] 2 ? x(t) x(t) and its discrete-time counterpart (x))n] x 2 n] ? xn ? 1]xn + 1] were developed by Teager in his work on nonlinear speech modeling 1] and were both introduced systematically by Kaiser 2, 3]. Since its introduction, the energy operator has found numerous applications to demodulating AM and/or FM signals, tracking speech modulations, detecting various events in nonstationary signals and multiband analysis 5, 6, 7, 8, 9]. For example, given an AM{FM signal x(t) = a(t) cos(R t 0 !()dd), by applying to both the signal and its derivative and separating their energies into amplitude and frequency components, Maragos, Kaiser and Quatieri 6, 8] have developed the following energy separation algorithm (ESA) !(t) p (_ x)=(x) ; ja(t)j (x)= p (_ x) which can estimate the time-varying instantaneous frequency !(t) and amplitude envelope ja(t)j at any time instant, with negligible estimation error provided the amplitude and frequency signal do not vary too fast or too much with respect to the carrier. In this paper we report (i) some improvements on the energy operator and ESA when applied to demodulat-ing speech resonances and using the extracted information signals for a vocoder and speech recognition; and (ii) some new nonlinear operators (diierential in continuous time and quadratic in discrete time) that can provide higher-order energy measurements with applications to co-channel demodulation and separation of AM{FM signal mixtures. Finally, we present a cross-coupled ESA for co-channel demodulation. In 5, 8] an AM-FM modulation model is introduced, that represents a speech resonance (formant) as an AM{FM signal. Each resonance is demodulated into instantaneous amplitude and frequency signals using the ESA. This mod-eling/analysis approach has been recently applied to …