Related papers: A Kotel'nikov Representation for Wavelets
Natural images are characterized by the multiscaling properties of their contrast gradient, in addition to their power spectrum. In this work we show that those properties uniquely define an {\em intrinsic wavelet} and present a suitable…
Using a prime element of a local field K of positive characteristic p, the concepts of multiresolution analysis (MRA) and wavelet can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this…
Quantum signal processing is a powerful framework in quantum algorithms, playing a central role in Hamiltonian simulation and related applications. The sequence of polynomials implemented at each step of this protocol provides a polynomial…
In this paper, we study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate a 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and…
An efficient scalable data representation is an important task especially in the medical area, e.g. for volumes from Computed Tomography (CT) or Magnetic Resonance Tomography (MRT), when a downscaled version of the original signal is…
In the present paper we investigate the transmission and reflection band behavior for a plane electromagnetic wave falling obliquely on an ideal layered structure. The dependence of this behavior on the problem parameters and wave incident…
This paper provides new insights into the problem of selecting filter center frequencies for the auditory filterbanks. We propose to use a constant frequency distance and a consistent frequency coverage as the two metrics that motivate the…
Signals and datasets that arise in physical and engineering applications, as well as social, genetics, biomolecular, and many other domains, are becoming increasingly larger and more complex. In contrast to traditional time and image…
We give a complete description of spectrum of the wavelet Galerkin operator $$R_{m_0,m_0}f(z)=\frac{1}{N}\sum_{w^N=z}|m_0|^2(w)f(w),\quad(z\in\m athbb{T})$$ associated to a a low-pass filter $m_0$ and a scale $N$, in the Banach spaces…
This paper deals with the estimation of multiantenna channels in the line-of-sight conditions that are prevalent in the near field. By expressing the curved wavefront as a polynomial via a power series expansion of a sphere, the estimation…
This work introduces a wavelet neural network to learn a filter-bank specialized to fit non-stationary signals and improve interpretability and performance for digital signal processing. The network uses a wavelet transform as the first…
There has been a growing interest in wideband spectrum sensing due to its applications in cognitive radios and electronic surveillance. To overcome the sampling rate bottleneck for wideband spectrum sensing, in this paper, we study the…
Electromagnetic properties depend on the composition of materials, i.e. either angstrom scales of molecules or, for metamaterials, subwavelength periodic structures. Each material behaves differently in accordance with the frequency of an…
It is demonstrated that the wavelets can be used to considerably speed up simulations of the wave packet propagation in multiscale systems. Extremely high efficiency is obtained in the representation of both bound and continuum states. The…
As an alternative to the traditional sampling theory, compressed sensing allows acquiring much smaller amount of data, still estimating the spectra of frequency-sparse signals accurately. However, compressed sensing usually requires random…
Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…
The Easy Path Wavelet Transform is an adaptive transform for bivariate functions (in particular natural images) which has been proposed in [1]. It provides a sparse representation by finding a path in the domain of the function leveraging…
A new type of low-pass filter based on a leaky coaxial waveguide is presented. The filter has minimal insertion loss in the pass band, while at the same time high attenuation in the stop band is achieved. Thanks to its arrangement, the…
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…
In this paper we combine partial-wave (`modal') methods with a wavelet analysis of the CMB bispectrum. Our implementation exploits the advantages of both approaches to produce robust, reliable and efficient estimators which can constrain…