Related papers: A Short Survey on Arithmetic Transforms and the Ar…
The metaplectic transform (MT), also known as the linear canonical transform, is a unitary integral mapping which is widely used in signal processing and can be viewed as a generalization of the Fourier transform. For a given function…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
This algorithm is designed to perform numerical transforms to convert data from the temporal domain into the spectral domain. This algorithm obtains the spectral magnitude and phase by studying the Coefficient of Determination of a series…
Image reconstruction is likely the most predominant auxiliary task for image classification, but we would like to think twice about this convention. In this paper, we investigated "approximating the Fourier Transform of the input image" as…
In this paper, we propose a new regression-based algorithm to compute Graph Fourier Transform (GFT). Our algorithm allows different regularizations to be included when computing the GFT analysis components, so that the resulting components…
There is proposed a method for improving the convergence of Fourier series by function systems, orthogonal at the segment, the application of which allows for smooth functions to receive uniformly convergent series. There is also proposed…
In this paper, we propose an incremental algorithm for computing cylindrical algebraic decompositions. The algorithm consists of two parts: computing a complex cylindrical tree and refining this complex tree into a cylindrical tree in real…
The Airy transform is an ideally suited tool to treat problem in classical and quantum optics. Even though the relevant mathematical aspects have been thoroughly investigated, the possibility it offers are wide and some aspects, as the link…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
Several papers have been published recently, particularly in the field of topological insulators, that use a Fourier-transform technique in a way that can be misleading or otherwise inaccurate, and the processing is not always described in…
Unitary Fourier transform lies at the core of the multitudinous computational and metrological algorithms. Here we show experimentally how the unitary Fourier transform-based phase estimation protocol, used namely in quantum metrology, can…
Circular-harmonic spectra are a compact representation of local image features in two dimensions. It is well known that the computational complexity of such transforms is greatly reduced when polar separability is exploited in steerable…
In his approach to Jones theorem on the interpolation of Hardy spaces on the torus, Pisier introduced an original method allowing the computation of complex interpolation spaces by means of real interpolation techniques. This approach has…
We report the realization of a new iterative Fourier-transform algorithm for creating holograms that can diffract light into an arbitrary two-dimensional intensity profile. We show that the predicted intensity distributions are smooth with…
The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors for the…
In classic graph signal processing, given a real-valued graph signal, its graph Fourier transform is typically defined as the series of inner products between the signal and each eigenvector of the graph Laplacian. Unfortunately, this…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
The metaplectic transform (MT), a generalization of the Fourier transform sometimes called the linear canonical transform, is a tool used ubiquitously in modern optics, for example, when calculating the transformations of light beams in…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…