In this paper Mersenne number transforms are converted into cyclic convolutions, in which form they are amendable to simple hardware interpretation. Such realisation structures are proposed that can make the computation of Mersenne number transforms very fast indeed. This new approach can be extended to the implementation of other number theoretic transforms, in particular to Fermat number tran...

Integral transforms play an important rôle in Analytic number theory, the part of Number theory where problems of a number-theoretic nature are solved by the use of various methods from Analysis. The most common integral transforms that are used are: Mellin transforms (Robert Hjalmar Mellin, 18541933), Laplace transforms (Pierre-Simon, marquis de Laplace, 1749-1827) and Fourier transforms (Jose...

Fast trigonometric transforms and periodic orthogonal wavelet transforms are essential tools for numerous practical applications. It is very important that fast algorithms work stable in a floating point arithmetic. This survey paper presents recent results on the worst case analysis of roundoff errors occurring in floating point computation of fast Fourier transforms, fast cosine transforms, a...

This paper describes design of transforms for extended block sizes for video coding. The proposed transforms are orthogonal integer transforms, based on a simple recursive factorization structure, and allow very compact and efficient implementations. We discuss techniques used for finding integer and scale factors in these transforms, and describe our final design. We evaluate efficiency of our...

We study Darboux and Christooel transforms of isothermic surfaces in Euclidean space. These transformations play a signiicant role in relation to integrable system theory. Surfaces of constant mean curvature turn out to be special among all isothermic surfaces: their parallel constant mean curvature surfaces are Christooel and Darboux transforms at the same time. We prove | as a generalization ...

Let Mn,m be the space of real n × m matrices which can be identified with the Euclidean space R. We introduce continuous wavelet transforms on Mn,m with a multivalued scaling parameter represented by a positive definite symmetric matrix. These transforms agree with the polar decomposition on Mn,m and coincide with classical ones in the rank-one case m = 1. We prove an analog of Calderón’s repro...

This paper presents a brief overview of the multiresolution transform designs used in a few image and video compression systems, namely H.264, PTC (progressive transform coder), and JPEG2000. The first two use hierarchical transforms, and the third uses wavelet transforms. We review the basis constructions for the hierarchical transforms, and compare some of their characteristics with those of ...

Invertible wavelet transforms that map integers to integers are important for lossless representations. In this paper, we present an approach to build integer to integer wavelet transforms based upon the idea of factoring wavelet transforms into lifting steps. This allows the construction of an integer version of every wavelet transform. We demonstrate the use of these transforms in lossless im...

electrocardiogram (ecg) is one of the most common biological signals which plays a significant role in diagnosis of heart diseases. one of the most important parts of ecg signal processing is interpretation of qrs complex and obtaining its characteristics. r wave is one of the most important sections of this complex which has an essential role in diagnosis of heart rhythm irregularities and als...