Automatic speech recognition (ASR) systems can benefit from including into their acoustic processing part new features that account for various nonlinear and time-varying phenomena during speech production. In this paper, we develop robust continuoustime expansions used to demodulate the instantaneous amplitudes and frequencies of the speech resonances and extract novel acoustic features from speech signals. Further, we concatenate the new non-linear speech features with the standard linear ones (melfrequency cepstrum) to develop an augmented set of acoustic features and demonstrate its efficacy by showing improvements in HMM-based phoneme recognition over speech databases. The continuous-time models retain the excellent time resolution of the ESAs, based on discrete energy operators, but perform better in the presence of noise.