Related papers: Wavelet Scattering on the Pitch Spiral
We introduce a scattering representation for the analysis and classification of sounds. It is locally translation-invariant, stable to deformations in time and frequency, and has the ability to capture harmonic structures. The scattering…
The scattering transform is a non-linear signal representation method based on cascaded wavelet transform magnitudes. In this paper we introduce phase scattering, a novel approach where we use phase derivatives in a scattering procedure. We…
A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…
We introduce the joint time-frequency scattering transform, a time shift invariant descriptor of time-frequency structure for audio classification. It is obtained by applying a two-dimensional wavelet transform in time and log-frequency to…
In time series classification and regression, signals are typically mapped into some intermediate representation used for constructing models. Since the underlying task is often insensitive to time shifts, these representations are required…
A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus…
Time-frequency scattering is a mathematical transformation of sound waves. Its core purpose is to mimick the way the human auditory system extracts information from its environment. In the context of improving the artificial intelligence of…
We introduce an audio texture synthesis algorithm based on scattering moments. A scattering transform is computed by iteratively decomposing a signal with complex wavelet filter banks and computing their amplitude envelop. Scattering…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
Stability is a key aspect of data analysis. In many applications, the natural notion of stability is geometric, as illustrated for example in computer vision. Scattering transforms construct deep convolutional representations which are…
Harmonic generation in the scattered fields produced by a dielectric sphere coated with a time-varying conductive shell is studied using a Mie theory approach hybridized with conversion matrix methods. Analytic results are derived for plane…
Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a…
Conventional approaches for scattering manipulations rely on the technique of field expansions into spherical harmonics (electromagnetic multipoles), which nevertheless is non-generic (expansion coefficients depend on the position of the…
We investigate the scattering of scalar harmonic source fields by a periodic pillar, that is, a spatial structure that is periodic in one dimension and of finite extent in the other two. Uniqueness of scattering solutions can be abstracted…
Resonances of open non-Hermitian systems are associated with the poles of the system scattering matrix. Perturbations of the system cause these poles to shift in the complex frequency plane. In this work, we introduce a novel method for…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…
Consider the time-harmonic acoustic scattering from a bounded penetrable obstacle imbedded in an isotropic homogeneous medium. The obstacle is supposed to possess a circular conic point or an edge point on the boundary in three dimensions…
Scattering wave systems that are periodically modulated in time offer many new degrees of freedom to control waves both in spatial and frequency domains. Such systems, albeit linear, do not conserve frequency and require the adaptation of…