Multiresolution analysis and synthesis for discretetime signals is described in this paper. Concepts of scale and resolution are first reviewed in discrete time. The resulting framework allows one to treat the discrete wavelet transform, octave-band perfect reconstruction filter banks, and pyramid transforms from a unified standpoint. This approach is very close to previous work on multiresolut...

and Applied Analysis 3 Wj and W̃j of Vj and Ṽj , respectively, satisfying Vj 1 Vj ̇Wj , Wj ⊥ Ṽj and Ṽj 1 Ṽj ̇W̃j , W̃j ⊥ Vj . The corresponding biorthogonal wavelets are given by ψj ∑ n∈Z −1 ã j 1−nφj 1 2 · −n , ψ̃j ∑ n∈Z −1 a j 1−nφ̃j 1 2 · −n . 1.4 A generalization of the biorthogonal wavelets of Cohen-Daubechies-Feuveau 1 was introduced that was based on exponential B-splines 12 . By generalizing...

Modern programming languages have effects and mix multiple calling conventions, and their core calculi should too. We characterize calling conventions by their “substitution discipline” that says what variables stand for, and design calculi for mixing disciplines in a single program. Building on variations of the reducibility candidates method, including biorthogonality and symmetric candidates...

We point out a connection between Gabor analysis and noncommutative analysis. Especially, the strong Morita equivalence of noncommutative tori appears as underlying setting for Gabor analysis, since the construction of equivalence bimodules for noncommutative tori has a natural formulation in the notions of Gabor analysis. As an application we show that Feichtinger’s algebra is such an equivale...

The nonsymmetric Lanczos algorithm, which belongs to the class of Krylov subspace methods, is increasingly being used for model reduction of large scale systems of the form f(s) = c (sI−A)−1b, to exploit the sparse structure and reduce the computational burden. However, a good approximation is, usually, achieved only with relatively high order reduced models. Moreover, the computational cost of...

The eigenvectors of a symmetric matrix can be chosen to form a biorthogonal set with respect to the identity and to the matrix itself. Similarly, the eigenvectors of a symmetric de nite linear pencil can be chosen to be biorthogonal with respect to the pair.This paper presents the three sets of matrix weights, with respect to which the eigenvectors of the symmetric de nite quadratic pencil are ...

The present television system was designed nearly 50 years ago. Since then, there have been significant developments in technology, which are highly relevant to the television industry. For example, advances in the very large scale integration (VLSI) technology and signal processing theories make it feasible to incorporate frame-store memory and sophisticated signal processing capabilities in a...

The demand for high-quality audio in transmission systems such as Digital Audio Broadcast (DAB) and High-Definition TeleVision (HDTV), as well as commercial products such as the MiniDisc (MD) and the Digital Compact Cassette (DCC), has generated considerable interest in audio compression schemes. The common objective is to achieve high quality at a rate significantly smaller than the 16 bits/sa...

The formal calculus System F models the essence of polymorphism and abstract data types, features that exist in many programming languages. calculus’ core property is parametricity: a theorem expressing language’s abstractions validating important principles like information hiding modularity. When combined with recursive mutable state, continuations or exceptions, formulation parametricity nee...

After brieey reviewing the interrelation between Riesz-bases, biorthogonality and a certain stability notion for multiscale basis transformations we establish a basic stability criterion for a general Hilbert space setting. An important tool in this context is a strengthened Cauchy inequality. It is based on direct and inverse estimates for a certain scale of spaces induced by the underlying mu...