Nonlinear Nonlocal Cochlear Models, Multitones, Noises and Masking Thresholds

Abstract : An important part of voice signal processing is to perform a nonlinear operation along frequency on the short time spectrogram, while the nonlinear adaptation along time is better understood. We developed, computed and analyzed a class of nonlinear nonlocal cochlear models to approximate this nonlinear aspect. The model is mechanical in nature, and outputs the acoustic responses on the basilar membrane. In case of two or three tones, our results are in qualitative agreement with existing data. We prove that the model is well-posed in Sobolev spaces for all time, and admits exact multi-frequency solutions (quasi-periodic in time) if the nonlinearity is cubic and weak enough. We upscale the model output towards modeling psychoacoustic responses to help direct applications in signal processing based on first principles. For input of tone plus a banded noise, we calibrate the model with absolute masking thresholds (on noise only), then rely on model nonlinearity to capture tonal masking of noise and modified thresholds resulting from their interactions.