Chrestenson generalized Walsh transform factorizations for parallel processing imbedded implementations on field programmable gate arrays are presented. This general base transform, sometimes referred to as the Discrete Chrestenson transform, has received special attention in recent years. In fact, the Discrete Fourier transform and Walsh-Hadamard transform are but special cases of the Chresten...

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L (R), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions which are smooth away from singularities along k-planes in R. We also develop tools to help decide whether in fact k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tig...

LetGn,k(K) be the Grassmannian manifold of k-dimensional K-subspaces in K where K = R,C,H is the field of real, complex or quaternionic numbers. For 1 ≤ k ≤ k ≤ n − 1 we define the Radon transform (Rf)(η), η ∈ Gn,k′(K), for functions f(ξ) on Gn,k(K) as an integration over all ξ ⊂ η. When k+ k ≤ n we give an inversion formula in terms of the G̊arding-Gindikin fractional integration and the Cayley...

Let G be a locally compact hypergroup and let K sub-hypergroup of G. (G, K) is Gelfand pair if Mc(G//K), the algebra measures with support on double coset G//K, commutative for convolution. In this paper, assuming that pair, we define study Fourier transform then establish Plancherel theorem K).

Abstract We prove an inequality that unifies previous works of the authors on properties Radon transform convex bodies including extension Busemann–Petty problem and a slicing for arbitrary functions. Let $K$ $L$ be star in ${\mathbb R}^n,$ let $0&amp;lt;k&amp;lt;n$ integer, $f,g$ non-negative continuous functions $L$, respectively, so $\|g\|_\infty =g(0)=1.$ Then $$\begin{align*} &amp; \frac{\...

the stolt (f-k) migration algorithm is a direct (i.e. non-recursive) fourier-domain technique based on a change of variables (or equivalently, a mapping) that converts the input spectrum to the output spectrum. the algorithm is simple and efficient but limited to constant velocity. a v(z)(f-k) migration method, capable of very high accuracy for vertical variations of velocity, can be formulated...

The strength of any conventional cipher system relies on the underlying cryptographic Boolean functions employed in the system. The design of such systems requires that the employed Boolean functions meet specific security criteria. Two of such criteria are the correlation immunity and resiliency of a given Boolean function. To determine whether such criteria are met, a designer needs the help ...

We consider the sparse Fourier transform problem: given a complex vector x of length n, and a parameter k, estimate the k largest (in magnitude) coefficients of the Fourier transform of x. The problem is of key interest in several areas, including signal processing, audio/image/video compression, and learning theory. We propose a new algorithm for this problem. The algorithm leverages technique...

It is shown that for any expansive, integer valued 2×2 matrix, there exists a (multi-)wavelet whose Fourier transform is compactly supported and smooth. A key step is showing that for almost every equivalence class of integrally similar matrices there is a representative A which is strictly expansive in the sense that there is a compact set K which tiles the plane by integer translations and su...

An analogue of the correspondence between GL(k)-conjugacy classes of matricial polynomials and line bundles is given for K-conjugacy classes, where K ⊂ GL(k) is one of the following: maximal parabolic, maximal torus, GL(k − 1) embedded diagonally. The generalised Legendre transform construction of hyperkähler metrics is studied further, showing that many known hyperkähler metrics (including the...