Related papers: A Synthesizer Based on Frequency-Phase Analysis an…
Coupled nonlinear systems under certain conditions exhibit phase synchronization, which may change for different frequency bands or with presence of additive system noise. In both cases, Fourier filtering is traditionally used to preprocess…
In this work, we propose a new mathematical vocoder algorithm(modified spectral inversion) that generates a waveform from acoustic features without phase estimation. The main benefit of using our proposed method is that it excludes the…
Synchrosqueezed transforms are non-linear processes for a sharpened time-frequency representation of wave-like components. They are efficient tools for identifying and analyzing wave-like components from their superposition. This paper is…
We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral…
The object of this work is to design an adequate regularization for the problem of recovering missing Fourier coefficients, particularly in some non standard situations were low frequency coefficients are lost. In the framework of non-local…
A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn's method and L\"owdin method such that…
The central object in wave turbulence theory is the wave kinetic equation (WKE), which is an evolution equation for wave action density and acts as the wave analog of the Boltzmann kinetic equations for particle interactions. Despite recent…
Motivated by the product of periodic distributions, we give a new description of the wave front and the Sobolev-type wave front of a distribution $f\in\mathscr{D}'(\mathbb{R}^d)$ in terms of Fourier series coefficients.
We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating…
The connection between derivative operators and wavelets is well known. Here we generalize the concept by constructing multiresolution approximations and wavelet basis functions that act like Fourier multiplier operators. This construction…
This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source in linear elasticity. The approach also applies to the compressional (resp. shear) part of the…
The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper…
Frequency Map Analysis is a numerical method based on refined Fourier techniques which provides a clear representation of the global dynamics of many multi-dimensional systems, and which is particularly adapted for systems of 3-degrees of…
Timing noise in pulsars is often modelled with a Fourier-basis Gaussian process that follows a power law with periodic boundary conditions on the observation time, $T_\mathrm{span}$. However the actual noise processes can extend well below…
This paper concerns diffraction-tomographic reconstruction of an object characterized by its scattering potential. We establish a rigorous generalization of the Fourier diffraction theorem in arbitrary dimension, giving a precise relation…
This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…
Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function.…