In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing

Ahmw-This Pw!r mak = available a concise review of data win- compromise consists of applying windows to the sampled daws pad the ^ affect On the Of in the data set, or equivalently, smoothing the spectral samples. '7 of aoise9 m the ptesence of sdroag bar- The two operations to which we subject the data are momc mterference. We dm call attention to a number of common- = in be rp~crh of windows den used with the fd F ~- sampling and windowing. These operations can be performed transform. This paper includes a comprehensive catdog of data win- in either order. Sampling is well understood, windowing is less related to sampled windows for DFT's. HERE IS MUCH signal processing devoted to detection and estimation. Detection is the task of determiningif a specific signal set is present in an observation, while estimation is the task of obtaining the values of the parameters

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a “true” two-dimensional transform that can capture the intrinsic geometrical structure

by aliasing; this explains the name of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just values of the transform. The mathematical centerpiece of the Fourier-series method is the Poisson summation formula, which identifies the discretization error

exponentials based on Fourier transforms on finite groups. As an example, we consider spherically symmetric PDEs, where the discretization preserves the 120 symmetries of the icosahedral group. This motivates the study of spectral element discretizations based on triangular subdivisions. In the second part

This survey presents a unified and essentially self-contained approach to the asymptotic analysis of a large class of sums that arise in combinatorial mathematics, discrete probabilistic models, and the average-case analysis of algorithms. It relies on the Mellin transform, a close relative

Classic convergence analysis for geometric multigrid The constant coefficient case The classic convergence analysis for multigrid methods assumes: • d-dimensional PDE with constant coefficients (−1)q d∑ i=1 d 2q dx2qi u(x) = g(x), x ∈ Ω = (0, 1)d, q ≥ 1. • Periodic boundary conditions on ∂Ω

Abstract—Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between

Abstract. In this paper, we present some new results on the selective discrete Fourier spectra attack, introduced first as the recent Rønjom-Helleseth attack and the modifications due to Gong et al. The focal point of this paper is to fill some gaps in the theory of analysis in terms of discrete

Abstract-A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can