Harmonic analysis is at the heart of much of signal and image processing. This is mainly the harmonic analysis of abelian groups, and ultimately, after sampling, and quantizing, finite abelian groups. Nevertheless, this general group theoretic viewpoint has proved fruitful, yielding a natural group-based multiresolution framework as well as some new and potentially useful nonabelian examples. T...

Computing the Fourier transform is a basic building block used in numerous applications. For data intensive applications, even the O(N logN) running time of the Fast Fourier Transform (FFT) algorithm may be too slow, and sub-linear running time is necessary. Clearly, outputting the entire Fourier transform in sub-linear time is infeasible, nevertheless, in many applications it suffices to find ...

This paper is concerned with the approach to teaching an introductory course on Fourier theory for engineers. Commonly called Signals and Systems (or some variation), this course generally introduces four transforms: the Fourier Transform, the Fourier Series, the Discrete-Time Fourier Transform (DTFT), and the Discrete Fourier Transform (DFT). Our concern is that the method and order of topic p...

It is proven that, for any soft potential φ(r) characterized by a finite Fourier transform e φ(k), the virial and energy thermodynamic routes are equivalent if the Fourier transform of the total correlation function divided by the density ρ, eh(k)/ρ, is an arbitrary function of ρβ e φ(k), where β is the inverse temperature. This class of approximations includes the mean spherical approximation ...

Different numerical approaches for the stray-field calculation in the context of micromagnetic simulations are investigated. We compare finite difference based fast Fourier transform methods, tensor-grid methods and the finite-element method with shell transformation in terms of computational complexity, storage requirements and accuracy tested on several benchmark problems. These methods can b...

the problem of several finite moving cracks in a functionally graded material is solved by dislocation technique under the condition of anti-plane deformation. by using the fourier transform the stress fields are obtained for a functionallygraded strip containing a screw dislocation. the stress components reveal the familiar cauchy singularity at thelocation of dislocation. the solution is empl...

in the present study, a spectral finite element method is developed for free and forced transverse vibration of levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. in the first step, the governing out-of-plane differential equations are tr...

A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for the finite Fourier transform are given.

The mathematical study of the diatonic and chromatic universes in the tradition of David Lewin (9) and John Clough (6) is a point of departure for several recent investigations. Surprisingly, Lewin’s original idea to apply finite Fourier transform to musical structures has not been further investigated for four decades. It turns out that several music-theoretically interesting properties of cer...