Une ou deux composantes ? La réponse de la diffusion en ondelettes
This work addresses the challenge of modeling auditory perception for applications in audio processing and neuroscience, though it appears incremental as it builds on existing wavelet scattering frameworks.
The paper tackled the problem of representing multicomponent stationary signals in a biologically plausible machine listening model using wavelet scattering networks, showing that renormalizing second-order nodes provides a criterion for psychoacoustic interference and that a network depth of M = log2 N suffices to characterize Fourier series terms with invariance properties.
With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by their first-order parents gives a simple numerical criterion to establish whether two neighboring components will interfere psychoacoustically. Secondly, we generalize the `one or two components' framework to three sine waves or more, and show that a network of depth $M = \log_2 N$ suffices to characterize the relative amplitudes of the first $N$ terms in a Fourier series, while enjoying properties of invariance to frequency transposition and component-wise phase shifts.