Wavelet Scattering on the Pitch Spiral
This work addresses the challenge of analyzing harmonic sounds in audio processing, but it appears incremental as it builds on existing scattering transform methods.
The authors tackled the problem of representing harmonic sounds by introducing a new representation that linearizes pitch and spectral envelope dynamics while maintaining stability to time-frequency deformations, using a scattering transform derived from 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.