Understanding the Scattering Transform Using Univariate Signals

In this paper, we review the scattering transform in the univariate setting. After reviewing its properties including translation invariance, stability under small diffeomorphism, and ability to carry high-frequency information, we investigate how these properties can be used in understanding the effect of the scattering transform when various types of signal deformation are considered. We find that, together with the Fourier transform modulus, the scattering transform can be used in classifying some of these deformations.