2020/03/02 by Vincent Lostanlen, Lostanlen, Vincent, Alice Cohen-Hadria +3 · 1 citation
Computer Science · #Audio and Speech Processing (eess.AS) #Digital Media Forensic Detection #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Music and Audio Processing #Sound (cs.SD) #Speech and Audio Processing #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2003.01037
openalex publication_date 2020/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 assess whether two neighboring components will interfere psychoacoustically. Secondly, we run a manifold learning algorithm (Isomap) on scattering coefficients to visualize the similarity space underlying parametric additive synthesis. Thirdly, we generalize the "one or two components" framework to three sine waves or more, and prove that the effective scattering depth of a Fourier series grows in logarithmic proportion to its bandwidth.