  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.
