A watermarking method for copyright protection of color images against print-andscan operations is proposed. A watermark is embedded in an input image as coefficientvalue peaks that are circularly and symmetrically distributed in a middle band of the discrete Fourier transform (DFT) domain of the input image. By detecting the robust peaks in the DFT domain of a reproduced image obtained by scan...

As is often the case when Fourier series techniques are used, we consider spaces of complex valued functions. Let Lp(S1) denote the Banach space of Lebesgue p-integrable functions and its norm by ‖ · ‖p. In the case of L2(S1), the norm is derived from the hermitian product ∫ 2π 0 f(θ)g(θ)dθ. Let Rθ and fφ denote the extension R of r according to (3.2) and fβ after the reparameterization. Our ta...

[2] Amiot’s book amply demonstrates that the DFT is relevant to a wide variety of musical questions—about rhythm, about pitch-class sets and interval content, and about tonality and nontonality—so many theorists will find something in the book relevant to questions in their own research. Within each of these topics, Amiot’s discourse varies between questions of primarily mathematical interest a...

Article history: Available online 17 October 2013

Basically, what we can try to do is to take the Fourier transform of 1R (the indicator function for the set R), and then use Fourier inversion to show that for each shift t+L of the lattice L, this shift intersects the set R. Actually, it will not quite be enough to take the Fourier transform of just 1R, but instead we will need to work with a smoothed version of 1R in order to make the Fourier...

In addition to their inestimable importance in mathematics and its applications, Fourier series also serve as the entry point into the wonderful world of Fourier analysis and its wide-ranging extensions and generalizations. An entire industry is devoted to further developing the theory and enlarging the scope of applications of Fourier–inspired methods. New directions in Fourier analysis contin...

The search for a canonical set of eigenvectors of the discrete Fourier transform has been ongoing for more than three decades. The goal is to find an orthogonal basis of eigenvectors which would approximate Hermite functions – the eigenfunctions of the continuous Fourier transform. This eigenbasis should also have some degree of analytical tractability and should allow for efficient numerical c...

In this paper, we present variants of the Dual-Tree Complex Wavelet Transform (DT-CWT) in order to automatically classify endoscopic images with respect to the Marsh classi cation. The feature vectors either consist of the means and standard deviations of the subbands from a DT-CWT variant or of the Weibull parameter of these subbands. To reduce the e ects of di erent distances and perspectives...

The discrete evolutionary transform is applied to signals in a blind–way without any signal parameters. For this reason, discrete evolutionary transform is not optimal and needs an improvement by using some information about the signal. In this paper, we propose an improvement for the discrete evolutionary transform. We redefine the generalized timebandwidth product optimal short–time Fourier t...

AMS Subject Classi cation: 20-04, 05C25, 20C30 Rockmore was supported in part by a National Science Foundation Mathematical Sciences Postdoctoral Fellowship. We study the complexity of performing Fourier analysis for the group SL2(Fq), where Fq is the finite field of q elements. Direct computation of a complete set of Fourier transforms for a complex-valued function f on SL2(Fq) requires q6 ope...