One or Two Components? The Scattering Transform Answers
arXiv:2003.01037
Abstract
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.
5 pages, 4 figures, in English. Proceedings of the European Signal Processing Conference (EUSIPCO 2020)
References in corpus (6)
- Understanding Deep Convolutional Networks
- Deep Scattering Spectrum
- Joint Time-Frequency Scattering
- Deep convolutional networks on the pitch spiral for musical instrument recognition
- Wavelet Scattering on the Pitch Spiral
- Linear Time Complexity Deep Fourier Scattering Network and Extension to Nonlinear Invariants