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## ‣ A WAVELET-BASED SPEAKER VERIFICATION ALGORITHM

Fonte: WORLD SCIENTIFIC PUBL CO PTE LTD
Publicador: WORLD SCIENTIFIC PUBL CO PTE LTD

Tipo: Artigo de Revista Científica

Português

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#Speaker verification#discrete wavelet transform#FIR filters#TRANSFORM#Computer Science, Software Engineering#Mathematics, Interdisciplinary Applications

This paper presents a study on wavelets and their characteristics for the specific purpose of serving as a feature extraction tool for speaker verification (SV), considering a Radial Basis Function (RBF) classifier, which is a particular type of Artificial Neural Network (ANN). Examining characteristics such as support-size, frequency and phase responses, amongst others, we show how Discrete Wavelet Transforms (DWTs), particularly the ones which derive from Finite Impulse Response (FIR) filters, can be used to extract important features from a speech signal which are useful for SV. Lastly, an SV algorithm based on the concepts presented is described.; Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP); FAPESP Sao Paulo Research Foundation[2005/00015-1]

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## ‣ Contribuições para pós processamento da transformada wavelet na codificação roi e spiht com aplicação na transmissão de imagens; Contributions for post processing of wavelet transform with SPIHT ROI coding and application in the transmission of images

Fonte: Biblioteca Digital da Unicamp
Publicador: Biblioteca Digital da Unicamp

Tipo: Tese de Doutorado
Formato: application/pdf

Publicado em 31/01/2012
Português

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#Compressão de imagens#Wavelet (Matematica)#Processamento de imagens#Image compression#Wavelets (Mathematics)#Image processing

A área que trata de compressão de imagem com perdas é, atualmente, de grande importância. Isso se deve ao fato de que as técnicas de compressão permitem representar de uma forma eficiente uma imagem reduzindo assim, o espaço necessário para armazenamento ou um posterior envio da imagem através de um canal de comunicações. Em particular, o algoritmo SPIHT (Set Partitioning of Hierarchical Trees) muito usado em compressão de imagens é de implementação simples e pode ser aproveitado em aplicações onde se requer uma baixa complexidade. Este trabalho propõe um esquema de compressão de imagens utilizando uma forma personalizada de armazenamento da transformada DWT (Discrete Wavelet Transform), codificação flexível da ROI (Region Of Interest) e a compressão de imagens usando o algoritmo SPIHT. A aplicação consiste na transmissão dos dados correspondentes usando-se codificação turbo. A forma personalizada de armazenamento da DWT visa um melhor aproveitamento da memória por meio do uso de algoritmo SPIHT. A codificação ROI genérica é aplicada em um nível alto da decomposição DWT. Nesse ponto, o algoritmo SPIHT serve para ressaltar e transmitir com prioridade as regiões de interesse. Os dados a serem transmitidos...

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## ‣ Identificação de sinais radar pulsados por meio de transformada de Wavelet contínua e redes neurais artificiais; Identification of pulsed radar signals by means of Wavelet continuous transform and artificial neural networks

Fonte: Universidade de Brasília
Publicador: Universidade de Brasília

Tipo: Dissertação

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Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2006.; O Deinterleaving de seqüências de pulsos de sinais radar é uma tarefa essencial para a identificação de radares em guerra eletrônica. Algumas formas de se realizar o deinterleaving baseiam-se em técnicas temporais, que utilizam histogramações e recursividade, e em técnicas baseadas em transformadas ortogonais, que utilizam as assinaturas espectrais para detecção das seqüências. Qualquer uma das abordagens onera grande esforço computacional. Entretanto, as técnicas que utilizam transformadas ortogonais são mais robustas devido às propriedades de minimização da correlação entre as diversas fontes de sinais. As assinaturas espectrais no espaço transformado apresentam um comportamento típico mais evidente. Este trabalho propõe uma técnica composta de três etapas distintas. Primeiramente, tem-se um pré-processamento pelo qual toda a faixa de valores de interesse é segmentada em sub-faixas por meio de subamostragens e filtragem digital. Em seguida, utiliza-se a análise tempo-freqüência por meio da transformada de wavelet contínua de forma a separar os padrões espectrais de interesse. Na última etapa...

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## ‣ Mixed Needlets

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/06/2010
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#Mathematics - Classical Analysis and ODEs#Astrophysics - Cosmology and Nongalactic Astrophysics#Mathematics - Statistics Theory#42C40, 60G60, 33C55, 62M15, 83F05, 58J05

The construction of needlet-type wavelets on sections of the spin line
bundles over the sphere has been recently addressed in Geller and Marinucci
(2008), and Geller et al. (2008,2009). Here we focus on an alternative proposal
for needlets on this spin line bundle, in which needlet coefficients arise from
the usual, rather than the spin, spherical harmonics, as in the previous
constructions. We label this system mixed needlets and investigate in full
their properties, including localization, the exact tight frame
characterization, reconstruction formula, decomposition of functional spaces,
and asymptotic uncorrelation in the stochastic case. We outline astrophysical
applications.; Comment: 26 pages

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## ‣ Microlocal Analysis of the Geometric Separation Problem

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 18/04/2010
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#Mathematics - Functional Analysis#Computer Science - Information Theory#Mathematics - Numerical Analysis

Image data are often composed of two or more geometrically distinct
constituents; in galaxy catalogs, for instance, one sees a mixture of pointlike
structures (galaxy superclusters) and curvelike structures (filaments). It
would be ideal to process a single image and extract two geometrically `pure'
images, each one containing features from only one of the two geometric
constituents. This seems to be a seriously underdetermined problem, but recent
empirical work achieved highly persuasive separations. We present a theoretical
analysis showing that accurate geometric separation of point and curve
singularities can be achieved by minimizing the $\ell_1$ norm of the
representing coefficients in two geometrically complementary frames: wavelets
and curvelets. Driving our analysis is a specific property of the ideal (but
unachievable) representation where each content type is expanded in the frame
best adapted to it. This ideal representation has the property that important
coefficients are clustered geometrically in phase space, and that at fine
scales, there is very little coherence between a cluster of elements in one
frame expansion and individual elements in the complementary frame. We formally
introduce notions of cluster coherence and clustered sparsity and use this
machinery to show that the underdetermined systems of linear equations can be
stably solved by $\ell_1$ minimization; microlocal phase space helps organize
the calculations that cluster coherence requires.; Comment: 59 pages...

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## ‣ Closed subspaces which are attractors for representations of the Cuntz algebras

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Operator Algebras#Mathematics - Functional Analysis#Primary 46L60, 47L30, 42A16, 43A65#Secondary 33C45, 42C10, 94A12,
46L45, 42A65, 41A15

We analyze the structure of co-invariant subspaces for representations of the
Cuntz algebras O_N for N = 2,3,..., N < infinity, with special attention to the
representations which are associated to orthonormal and tight-frame wavelets in
L^2(R) corresponding to scale number N.; Comment: 32 pages, LaTeX2e "birkart" document class; accepted for publication
in the Proceedings of the 2002 IWOTA conference at Virginia Tech in
Blacksburg, VA. v4 revision: changes and corrections to Theorem 4.4 and
Corollary 7.1. Also Theorem 4.4 is relabeled "Proposition 4.4", and
clarifying remarks are added

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## ‣ Resolution of the wavefront set using general continuous wavelet transforms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/12/2014
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We consider the problem of characterizing the wavefront set of a tempered
distribution $u\in\mathcal{S}'(\mathbb{R}^{d})$ in terms of its continuous
wavelet transform, where the latter is defined with respect to a suitably
chosen dilation group $H\subset{\rm GL}(\mathbb{R}^{d})$. In this paper we
develop a comprehensive and unified approach that allows to establish
characterizations of the wavefront set in terms of rapid coefficient decay, for
a large variety of dilation groups.
For this purpose, we introduce two technical conditions on the dual action of
the group $H$, called microlocal admissibilty and (weak) cone approximation
property. Essentially, microlocal admissibilty sets up a systematical
relationship between the scales in a wavelet dilated by $h\in H$ on one side,
and the matrix norm of $h$ on the other side. The (weak) cone approximation
property describes the ability of the wavelet system to adapt its
frequency-side localization to arbitrary frequency cones. Together, microlocal
admissibility and the weak cone approximation property allow the
characterization of points in the wavefront set using multiple wavelets.
Replacing the weak cone approximation by its stronger counterpart gives access
to single wavelet characterizations.
We illustrate the scope of our results by discussing -- in any dimension
$d\ge2$ -- the similitude...

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## ‣ Modular frames for Hilbert C*-modules and symmetric approximation of frames

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/10/2000
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We give a comprehensive introduction to a general modular frame construction
in Hilbert C*-modules and to related modular operators on them. The Hilbert
space situation appears as a special case. The reported investigations rely on
the idea of geometric dilation to standard Hilbert C*-modulesover unital
C*-algebras that admit an orthonormal Riesz basis. Interrelations and
applications to classical linear frame theory are indicated. As an application
we describe the nature of families of operators {S_i} such that SUM_i
S*_iS_i=id_H, where H is a Hilbert space. Resorting to frames in Hilbert spaces
we discuss some measures for pairs of frames to be close to one another. Most
of the measures are expressed in terms of norm-distances of different kinds of
frame operators. In particular, the existence and uniqueness of the closest
(normalized) tight frame to a given frame is investigated. For Riesz bases with
certain restrictions the set of closetst tight frames often contains a multiple
of its symmetric orthogonalization (i.e. L\"owdin orthogonalization).; Comment: SPIE's Annual Meeting, Session 4119: Wavelets in Signal and Image
Processing; San Diego, CA, U.S.A., July 30 - August 4, 2000. to appear in:
Proceedings of SPIE v. 4119(2000)...

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## ‣ A module frame concept for Hilbert C*-modules

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 22/11/2000
Português

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The goal of the present paper is a short introduction to a general module
frame theory in C*-algebras and Hilbert C*-modules. The reported investigations
rely on the idea of geometric dilation to standard Hilbert C*-modules over
unital C*-algebras that possess orthonormal bases, and of reconstruction of the
frames by projections and other bounded module operators with suitable ranges.
We obtain frame representation and decomposition theorems, as well as
similarity and equivalence results. The relative position of two and more
frames in terms of being complementary or disjoint is investigated in detail.
In the last section some recent results by P. G. Casazza are generalized to our
setting. The Hilbert space situation appears as a special case. For detailled
proofs we refer to another paper also contained in the ArXiv.; Comment: Latex2e, amsproc.cls required, 21 pages, presented at: Functional and
Harmonic Analysis of Wavelets (Joint Math. Meeting, San Antonio, TX, Jan.
1999)

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## ‣ Wavelets in mathematical physics: q-oscillators

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

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We construct representations of a q-oscillator algebra by operators on Fock
space on positive matrices. They emerge from a multiresolution scaling
construction used in wavelet analysis. The representations of the Cuntz Algebra
arising from this multiresolution analysis are contained as a special case in
the Fock Space construction.; Comment: (03/11/03):18 pages; LaTeX2e, "article" document class with
"letterpaper" option An outline was added under the abstract (p.1),
paragraphs added to Introduction (p.2), mat'l added to Proofs in Theorems 1
and 6 (pgs.5&17), material added to text for the conclusion (p.17), one add'l
reference added [12]. (04/22/03):"number 1" replace with "term C" (p.9),
single sentences reformed into a one paragraph (p.13), QED symbol moved up
one paragraph and last paragraph labeled as "Concluding Remarks."

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## ‣ Wavelet frames, Bergman spaces and Fourier transforms of Laguerre functions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 11/04/2007
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The Fourier transforms of Laguerre functions play the same canonical role in
wavelet analysis as do the Hermite functions in Gabor analysis. We will use
them as analyzing wavelets in a similar way the Hermite functions were recently
by K. Groechenig and Y. Lyubarskii in "Gabor frames with Hermite functions, C.
R. Acad. Sci. Paris, Ser. I 344 157-162 (2007)". Building on the work of K.
Seip, "Beurling type density theorems in the unit disc, Invent. Math., 113,
21-39 (1993)", concerning sampling sequences on weighted Bergman spaces, we
find a sufficient density condition for constructing frames by translations and
dilations of the Fourier transform of the nth Laguerre function. As in
Groechenig-Lyubarskii theorem, the density increases with n, and in the special
case of the hyperbolic lattice in the upper half plane it is given by b\log
a<\frac{4\pi}{2n+\alpha}, where alpha is the parameter of the Laguerre
function.; Comment: 15 pages

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## ‣ Extending wavelet filters. Infinite dimensions, the non-rational case, and indefinite-inner product spaces

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/06/2011
Português

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In this paper we are discussing various aspects of wavelet filters. While
there are earlier studies of these filters as matrix valued functions in
wavelets, in signal processing, and in systems, we here expand the framework.
Motivated by applications, and by bringing to bear tools from reproducing
kernel theory, we point out the role of non-positive definite Hermitian inner
products (negative squares), for example Krein spaces, in the study of
stability questions. We focus on the non-rational case, and establish new
connections with the theory of generalized Schur functions and their associated
reproducing kernel Pontryagin spaces, and the Cuntz relations.

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## ‣ Deconvolution of Poissonian Images Using Variable Splitting and Augmented Lagrangian Optimization

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/04/2009
Português

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Although much research has been devoted to the problem of restoring
Poissonian images, namely in the fields of medical and astronomical imaging,
applying the state of the art regularizers (such as those based on wavelets or
total variation) to this class of images is still an open research front. This
paper proposes a new image deconvolution approach for images with Poisson
statistical models, with the following building blocks: (a) a standard
regularization/MAP criterion, combining the Poisson log-likelihood with a
regularizer (log-prior) is adopted; (b) the resulting optimization problem
(which is difficult, since it involves a non-quadratic and non-separable term
plus a non-smooth term) is transformed into an equivalent constrained problem,
via a variable splitting procedure; (c) this constrained problem is addressed
using an augmented Lagrangian framework. The effectiveness of the resulting
algorithm is illustrated in comparison with current state-of-the-art methods.; Comment: Submitted to the 2009 IEEE Workshop on Statistical Signal Processing

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## ‣ Tokens: An Algebraic Construction Common in Combinatorics, Analysis, and Physics

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/01/2002
Português

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#Mathematics - Functional Analysis#Mathematical Physics#Mathematics - Combinatorics#43A20, 05A40, 81S40

We give a brief account of a construction called tokens here, which is
significant in algebra, analysis, combinatorics, and physics. Tokens allow to
express a semigroup on one set via a semigroup convolution on another set.
Therefore tokens are similar to intertwining operators but are more flexible.
Keywords: semigroups, hypergroups, tokens, poset, multiplicative functions,
polynomial sequence of binomial type, integral kernel, wavelets, refinement
equation, special functions, quantum propagator, path integral, quantum
computing.; Comment: LaTeX, 10 pages, 3 PS figures

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## ‣ Wavelet representations and Fock space on positive matrices

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/04/2002
Português

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#Mathematics - Classical Analysis and ODEs#Mathematics - Operator Algebras#[2000] 42C40, 42A16, 43A65, 42A65

We show that every biorthogonal wavelet determines a representation by
operators on Hilbert space satisfying simple identities, which captures the
established relationship between orthogonal wavelets and Cuntz-algebra
representations in that special case. Each of these representations is shown to
have tractable finite-dimensional co-invariant doubly-cyclic subspaces.
Further, motivated by these representations, we introduce a general Fock-space
Hilbert space construction which yields creation operators containing the
Cuntz--Toeplitz isometries as a special case.; Comment: 32 pages, LaTeX ("amsart" document class), one EPS graphic file used
for shading, accepted March 2002 for J. Funct. Anal

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## ‣ On the Analytic Wavelet Transform

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Statistics Theory#Mathematics - Functional Analysis#Statistics - Methodology#42C40, 62G08

An exact and general expression for the analytic wavelet transform of a
real-valued signal is constructed, resolving the time-dependent effects of
non-negligible amplitude and frequency modulation. The analytic signal is first
locally represented as a modulated oscillation, demodulated by its own
instantaneous frequency, and then Taylor-expanded at each point in time. The
terms in this expansion, called the instantaneous modulation functions, are
time-varying functions which quantify, at increasingly higher orders, the local
departures of the signal from a uniform sinusoidal oscillation. Closed-form
expressions for these functions are found in terms of Bell polynomials and
derivatives of the signal's instantaneous frequency and bandwidth. The analytic
wavelet transform is shown to depend upon the interaction between the signal's
instantaneous modulation functions and frequency-domain derivatives of the
wavelet, inducing a hierarchy of departures of the transform away from a
perfect representation of the signal. The form of these deviation terms
suggests a set of conditions for matching the wavelet properties to suit the
variability of the signal, in which case our expressions simplify considerably.
One may then quantify the time-varying bias associated with signal estimation
via wavelet ridge analysis...

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## ‣ H\"older regularity of arithmetic Fourier series arising from modular forms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Number Theory#Mathematics - Classical Analysis and ODEs#Primary 42A16, Secondary 11F03, 11J70, 26A15, 65T60

Given a modular form which is not a cusp form
$M_k(z)=\sum_{n=0}^{\infty}r_ne^{2\pi inz}$ of weight $k \geq 4$, we define the
series $M_{k,s}(x)=\sum_{n=1}^{\infty}\frac{r_n}{n^s}\sin(2\pi nx),$ which
converges for all $x\in\mathbb{R}$ when $s>k$. In this paper, we compute the
H\"{o}lder regularity exponent of $M_{k,s}$ at irrational points. In our
analysis we apply wavelets methods proposed by Jaffard in 1996 in the study of
the Riemann series. We find that the H\"{o}lder regularity exponent at a point
$x$ is related to the fine diophantine properties of $x$, in a very precise
way.; Comment: 19 pages, added references, improved results

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## ‣ Continuous Wavelets and Frames on Stratified Lie Groups I

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Let G be a stratified Lie group and L be the sub-Laplacian on G. Let 0 \neq
f\in S(R^+).
We show that Lf(L)\delta, the distribution kernel of the operator Lf(L), is
an admissible function on G. We also show that, if \xi f(\xi) satisfies
Daubechies' criterion, then L f(L)\delta generates a frame for any sufficiently
fine lattice subgroup of G.; Comment: 30 pages

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## ‣ Convergence rates for density estimators of weakly dependent time series

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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Assuming that $(X_t)_{t\in\Z}$ is a vector valued time series with a common
marginal distribution admitting a density $f$, our aim is to provide a wide
range of consistent estimators of $f$. We consider different methods of
estimation of the density as kernel, projection or wavelets ones. Various cases
of weakly dependent series are investigated including the Doukhan & Louhichi
(1999)'s $\eta$-weak dependence condition, and the $\tilde \phi$-dependence of
Dedecker & Prieur (2005). We thus obtain results for Markov chains, dynamical
systems, bilinear models, non causal Moving Average... From a moment inequality
of Doukhan & Louhichi (1999), we provide convergence rates of the term of error
for the estimation with the $\L^q$ loss or almost surely, uniformly on compact
subsets.

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## ‣ Discrete-Time continuous-dilation construction of linear scale-invariant systems and multi-dimensional self-similar signals

Fonte: Rochester Instituto de Tecnologia
Publicador: Rochester Instituto de Tecnologia

Tipo: Dissertação

Português

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#Descrete time#LSI Linear Scale-Invariant systems#QA402 .Z493 1998#Discrete-time systems#Signal processing--Mathematics#Linear time invariant systems#Wavelets (Mathematics)

This dissertation presents novel models for purely discrete-time self-similar processes and
scale- invariant systems. The results developed are based on the definition of a discrete-time
scaling (dilation) operation through a mapping between discrete and continuous frequencies.
It is shown that it is possible to have continuous scaling factors through this operation even
though the signal itself is discrete-time. Both deterministic and stochastic discrete-time
self-similar signals are studied. Conditions of existence for self-similar signals are provided.
Construction of discrete-time linear scale-invariant (LSI) systems and white noise driven
models of self-similar stochastic processes are discussed. It is shown that unlike continuous-time
self-similar signals, a wide class of non-trivial discrete-time self-similar signals can
be constructed through these models. The results obtained in the one-dimensional case
are extended to multi-dimensional case. Constructions of discrete-space self-similar ran
dom fields are shown to be potentially useful for the generation, modeling and analysis
of multi-dimensional self-similar signals such as textures. Constructions of discrete-time
and discrete-space self-similar signals presented in the dissertation provide potential tools
for applications such as image segmentation and classification...

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