In our previous work, we showed empirically that independent wavelet models were parsimonious, computationally efficient, and accurate in modeling heterogeneous network traffic measured by both auto-covariance functions and buffer loss rate. In this work, we focus on auto-covariance functions, to establish a theory of independent wavelet models as unified models for heterogeneous network traffi...

In this work, a class of multivariate multiwavelet packages with multi-scale are introduced, which are generalizations of multivariant wavelet packages. A method for designing a sort of biorthogonal multiwavelet packages in higher dimensions is presented and their biorthogonality property is characterized by virtue of time-frequency analysis method, matrix theory, and operator theory. Three bio...

The relationship between multiresolution analysis and filtering schemes is a well-known facet of wavelet theory. However, in the case of rational dilation factors, the wavelet literature is somewhat lacking in its treatment of this relationship. This work seeks to establish a means for the construction of stable filtering schemes with rational dilations through the theory of shift-invariant spa...

The present work documents the design and implementation of a wavelet-based excitation algorithm for low sample-rate audio files. This algorithm is an analysis/resynthesis method which converts a low sample-rate audio file to a higher sample-rate audio file, while inserting high frequency content in the wavelet domain. This paper presents relevant wavelet theory, along with the theory of the ex...

The concepts of basis and frame are studied in the classical literature of functional analysis, Fourier analysis, and wavelet theory in a wide range. In this paper, we consider an operator-theoretic approach to discrete frame theory on a separable Hilbert space. For this purpose, we define a special type of frames and bases, called wavelet-type frames and wavelet-type bases, obtained by acting ...

Wavelet analysis is a powerful tool withmodern applications as diverse as: image processing, signal processing, data compression, data mining, speech recognition, computer graphics, etc. The aim of this paper is to introduce the concept of atomic decomposition of fuzzy normed linear spaces, which play a key role in the development of fuzzy wavelet theory. Atomic decompositions appeared in appli...

It is shown that Euclidean field theory with polynomial interaction , can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered.

It is shown that Euclidean field theory with polynomial interaction , can be regularized using the wavelet representation of the fields. The connections between wavelet based regularization and stochastic quantization are considered.

The Euclidean quantum field theory for the fields φ∆x(x), which depend on both the position x and the resolution ∆x, constructed in SIGMA 2 (2006), 046, on the base of the continuous wavelet transform, is considered. The Feynman diagrams in such a theory become finite under the assumption there should be no scales in internal lines smaller than the minimal of scales of external lines. This regu...

We consider a class of convergence questions for infinite products that arise in wavelet theory when the wavelet filters are more singular than is traditionally built into the assumptions. We establish pointwise convergence properties for the absolute square of the scaling functions. Our proofs are based on probabilistic tools.