Wavelet Scattering on the Pitch Spiral

We present a new representation of harmonic sounds that linearizes the dynamics of pitch and spectral envelope, while remaining stable to deformations in the time-frequency plane. It is an instance of the scattering transform, a generic operator which cascades wavelet convolutions and modulus nonlinearities. It is derived from the pitch spiral, in that convolutions are successively performed in time, log-frequency, and octave index. We give a closed-form approximation of spiral scattering coefficients for a nonstationary generalization of the harmonic source-filter model.

• Type: Journal
• Year: 2016
• Where: CORR
• Authors: Vincent Lostanlen, Stéphane Mallat
• Keywords: CORR 2016, Education