# Wavelet Scattering on the Pitch Spiral

arXiv: https://arxiv.org/abs/1601.00287 · HTML: https://mlsanity.com/paper/1601.00287/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jan 2016.

## Built on by (most cited first, 2 of 2)

- [Radar-based Materials Classification Using Deep Wavelet Scattering Transform: A Comparison of Centimeter vs. Millimeter Wave Units](https://mlsanity.com/paper/2202.05169/) (2022)
- [SCRAPL: Scattering Transform with Random Paths for Machine Learning](https://mlsanity.com/paper/2602.11145/) (2026)

## Abstract (arXiv)

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.