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- Universidade Federal do Rio Grande do Norte; BR; UFRN; Programa de Pós-Graduação em Matemática Aplicada e Estatística; Probabilidade e Estatística; Modelagem Matemática
- Universidade Federal de Uberlândia
- IEEE-Inst Electrical Electronics Engineers Inc
- Universidade Rice
- Universidade Cornell
- Instituto de Tecnologia da Califórnia
- Centro de Investigación en computación, IPN
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## ‣ Estudo da transformada rápida wavelet e sua conexão com banco de filtros

Fonte: Universidade Federal do Rio Grande do Norte; BR; UFRN; Programa de Pós-Graduação em Matemática Aplicada e Estatística; Probabilidade e Estatística; Modelagem Matemática
Publicador: Universidade Federal do Rio Grande do Norte; BR; UFRN; Programa de Pós-Graduação em Matemática Aplicada e Estatística; Probabilidade e Estatística; Modelagem Matemática

Tipo: Dissertação
Formato: application/pdf

Português

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#Análise de multiresolução#Banco de filtros#Wavelets#Transformada rápida wavelet#Multiresoluction analysis#Filters banks#Wavelets and fast transform eavelet#CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

In this work we presented an exhibition of the mathematical theory of orthogonal compact support wavelets in the context of multiresoluction analysis. These are particularly attractive wavelets because they lead to a stable and very efficient algorithm, that is Fast Transform Wavelet (FWT). One of our objectives is to develop efficient algorithms for calculating the coefficients wavelet (FWT) through the pyramid algorithm of Mallat and to discuss his connection
with filters Banks. We also studied the concept of multiresoluction analysis, that is the context in that wavelets
can be understood and built naturally, taking an important step in the change from the Mathematical universe (Continuous Domain) for the Universe of the representation (Discret Domain); Neste trabalho apresentamos uma exposição da teoria matemática das wavelets ortogonais de suporte compacto no contexto de análise de multiresolução. Estas wavelets são particularmente atraentes porque conduzem a um algoritmo estável e muito eficiente, isto é, a Transformada Rápida Wavelet (FWT). Um dos nossos objetivos é desenvolver algoritmos eficientes para o calculo dos coeficientes wavelet (FWT) através do algoritmo pirâmidal de Mallat e discutir sua
conexão com Banco de Filtros. Estudamos também o conceito de análise de multiresolução...

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## ‣ Decomposição de sinais eletromiográficos utilizando filtros casados; EMG signal decomposition using matched filters

Fonte: Universidade Federal de Uberlândia
Publicador: Universidade Federal de Uberlândia

Tipo: Tese de Doutorado

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#Engenharia Elétrica#Eletromiografia#Decomposição de sinais EMG#Filtros casados#Processamento de sinais biomédicos#Electromyography#EMG signal decomposition#Matched filters#Biomedical singnal processing

A detecção e classificação dos potenciais de ação de unidade motora (PAUMs) de sinais EMG é uma ferramenta importante no estudo do sistema neuromuscular. A partir de informações dessa classificação é possível diagnosticar distúrbios motores. Entretanto, apesar de existirem diversas propostas na literatura para executar tais ações, a grande maioria depende de algoritmos complexos e instrumentação específica. Dependendo do sistema, o custo computacional ou o mecanismo de captação envolvendo, matrizes de eletrodos, pode limitar sua utilização em aplicações clínicas, biofeedback ou em sistemas embarcados para controle de próteses. Outra questão importante consiste na detecção e classificação de disparos em sinais com baixa relação sinal ruído (SNR). Um método capaz de operar em sinais com baixa SNR é interessante em aplicações onde não se pode controlar completamente a coleta do sinal. Como exemplo, podemos citar aplicações da eletromiografia em interfaces homem máquina (IHM), onde o posicionamento dos eletrodos pode ser realizado por um usuário com pouco treinamento e o ambiente pode conter alto nível de interferência eletromagnética, diminuindo a SNR do sinal captado. Como solução para tais problemas...

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## ‣ Design of two-band critically sampled rational rate filter banks with multiple regularity orders and associated discrete wavelet transforms

Fonte: IEEE-Inst Electrical Electronics Engineers Inc
Publicador: IEEE-Inst Electrical Electronics Engineers Inc

Tipo: Artigo de Revista Científica

Publicado em //2012
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An approach for designing two-band rational rate critically sampled nonorthogonal filter banks with perfect reconstruction and multiple regularity orders is proposed. This approach relies on an updated result on the relationship between the filters in the filter bank to achieve all the desired properties. Filter responses are optimized to approximate ideal brick wall responses, subject to linear and nonlinear constraints derived from regularity and perfect reconstruction conditions, respectively. The obtained designs are approximately shift invariant as a result of strong frequency selectivity and multiple regularity orders. Two methods for solving the nonconvex optimization design problem are presented and the results from the proposed approach are compared against existing designs in the literature.; Si Tran Nguyen Nguyen and Brian W.-H. Ng

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## ‣ Design of oversampled multichannel filter banks

Fonte: Universidade Rice
Publicador: Universidade Rice

Português

Relevância na Pesquisa

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This thesis introduces a general approach for the design of oversampled multichannel filter banks including one-dimensional and nonseparable multidimensional filter banks, as well as filter banks with linear phase and complex-valued coefficients. The approach is carried within the framework of rectangular polyphase matrices, developed to design perfect reconstruction filter banks with uniform sampling in the subbands and finite impulse response filters.
This thesis introduces an approach for the design of two-dimensional oversampled filter banks that allows directional frequency selectivity with low redundancy. Directional two-dimensional filter banks find application in texture classification, denoising, segmentation, and enhancement. In several of these applications, the frequency directionality relies on oversampled filter banks with redundancy factors that range from two to four. This thesis uses non uniform frequency division of the unit frequency cell to design multichannel oversampled filter banks that have frequency directionality and redundancy factor less than two.
Additionally, this thesis expands the tools available for the design of wavelet systems by providing a formulation of the problem of filter bank design that covers polyphase matrices of one-dimensional perfect reconstruction filter banks...

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## ‣ Maximizing the Signal-to-Alias Ratio in Non-Uniform Filter Banks for Acoustic Echo Cancellation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/02/2014
Português

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A new method for designing non-uniform filter-banks for acoustic echo
cancellation is proposed. In the method, the analysis prototype filter design
is framed as a convex optimization problem that maximizes the signal-to-alias
ratio (SAR) in the analysis banks. Since each sub-band has a different
bandwidth, the contribution to the overall SAR from each analysis bank is taken
into account during optimization. To increase the degrees of freedom during
optimization, no constraints are imposed on the phase or group delay of the
filters; at the same time, low delay is achieved by ensuring that the resulting
filters are minimum phase. Experimental results show that the filter bank
designed using the proposed method results in a sub-band adaptive filter with a
much better echo return loss enhancement (ERLE) when compared with existing
design methods.; Comment: IEEE Transactions on Circuits and Systems I: Regular Paper, vol. 59,
no. 10, Oct. 2012

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## ‣ A Design of Paraunitary Polyphase Matrices of Rational Filter Banks Based on (P,Q) Shift-Invariant Systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 27/04/2010
Português

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In this paper we present a method to design paraunitary polyphase matrices of
critically sampled rational filter banks. The method is based on (P,Q)
shift-invariant systems, and so any kind of rational splitting of the frequency
spectrum can be achieved using this method. Ideal (P,Q) shift-invariant system
with smallest P and Q that map of a band of input spectrum to the output
spectrum are obtained. A new set of filters is obtained that characterize a
(P,Q) shift-invariant system. Ideal frequency spectrum of these filters are
obtained using ideal $(P,Q)$ shift-invariant systems. Actual paraunitary
polyphase matrices are then obtained by minimizing the stopband energies of
these filters against the parameters of the paraunitary polyphase matrices.

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## ‣ Generic Feasibility of Perfect Reconstruction with Short FIR Filters in Multi-channel Systems

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 04/03/2011
Português

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We study the feasibility of short finite impulse response (FIR) synthesis for
perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis
banks, we focus on the one with the minimum filter length. For filter banks
with oversampling factors of at least two, we provide prescriptions for the
shortest filter length of the synthesis bank that would guarantee PR almost
surely. The prescribed length is as short or shorter than the analysis filters
and has an approximate inverse relationship with the oversampling factor. Our
results are in form of necessary and sufficient statements that hold
generically, hence only fail for elaborately-designed nongeneric examples. We
provide extensive numerical verification of the theoretical results and
demonstrate that the gap between the derived filter length prescriptions and
the true minimum is small. The results have potential applications in synthesis
FB design problems, where the analysis bank is given, and for analysis of
fundamental limitations in blind signals reconstruction from data collected by
unknown subsampled multi-channel systems.; Comment: Manuscript submitted to IEEE Transactions on Signal Processing

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## ‣ Committee Algorithm: An Easy Way to Construct Wavelet Filter Banks

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 07/01/2012
Português

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Given a lowpass filter, finding a dual lowpass filter is an essential step in
constructing non-redundant wavelet filter banks. Obtaining dual lowpass filters
is not an easy task. In this paper, we introduce a new method called committee
algorithm that builds a dual filter straightforwardly from two
easily-constructible lowpass filters. It allows to design a wide range of new
wavelet filter banks. An example based on the family of Burt-Adelson's 1-D
Laplacian filters is given.; Comment: 4 pages, 1 figure, Accepted by ICASSP 2012

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## ‣ Prime Coset Sum: A Systematic Method for Designing Multi-D Wavelet Filter Banks with Fast Algorithms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/07/2014
Português

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As constructing multi-D wavelets remains a challenging problem, we propose a
new method called prime coset sum to construct multi-D wavelets. Our method
provides a systematic way to construct multi-D non-separable wavelet filter
banks from two 1-D lowpass filters, with one of whom being interpolatory. Our
method has many important features including the following: 1) it works for any
spatial dimension, and any prime scalar dilation, 2) the vanishing moments of
the multi-D wavelet filter banks are guaranteed by certain properties of the
initial 1-D lowpass filters, and furthermore, 3) the resulting multi-D wavelet
filter banks are associated with fast algorithms that are faster than the
existing fast tensor product algorithms.

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## ‣ Alias-free, real coefficient m-band QMF banks for arbitrary m

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /12/1987
Português

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Based on a generalized framework for alias free QMF banks, a theory is developed for the design of uniform QMF banks with real-coefficient analysis filters, such that aliasing can be completely canceled by appropriate choice of real-coefficient synthesis filters. These results are then applied for the derivation of closed-form expressions for the synthesis filters (both FIR and IIR), that ensure cancelation of aliasing for a given set of analysis filters. The results do not involve the inversion of the alias-component (AC) matrix.

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## ‣ Theory and design of uniform DFT, parallel, quadrature mirror filter banks

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /12/1986
Português

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In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signalx(n), are also derived using this concept. In general, the reconstructed. signalhat{x}(n)suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, andhat{x}(n)is equal to a delayed version ofx(n))of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general...

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## ‣ Theory and design of two-parallelogram filter banks

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /11/1996
Português

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It is well known that the analysis and synthesis filters of orthonormal DFT filter banks can not have good frequency selectivity. The reason for this is that each of the analysis and synthesis filters have only one passband. Such frequency stacking (or configuration) in general does not allow alias cancellation when the individual filters have good stopband attenuation. A frequency stacking of this nature is called nonpermissible and should be avoided if good filters are desired. In a usual M-channel filter bank with real-coefficient filters, the analysis and synthesis filters have two passbands. It can be shown that the configuration is permissible in this case. Many designs proposed in the past demonstrate that filter banks with such configurations can have perfect reconstruction and be good filters at the same time. We develop the two-parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of two parallelograms. The two-parallelogram filter banks are analyzed from a pictorial viewpoint by exploiting the concept of permissibility. Based on this analysis, we construct and design a special type of two-parallelogram filter banks, namely, cosine-modulated filter banks (CMFB). In two-parallelogram CMFB...

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## ‣ On the study of four-parallelogram filter banks

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /11/1996
Português

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The most commonly used 2-D filter banks are separable filter banks, which can be obtained by cascading two 1-D filter banks in the form of a tree. The supports of the analysis and synthesis filters in the separable systems are unions of four rectangles. The natural nonseparable generalization of such supports are those that are unions of four parallelograms. We study four parallelogram filter banks, which is the class of 2-D filter banks in which the supports of the analysis and synthesis filters consist of four parallelograms. For a given a decimation matrix, there could be more than one possible configuration (the collection of passbands of the analysis filters). Various types of configuration are constructed for four-parallelogram filter banks. Conditions on the configurations are derived such that good design of analysis and synthesis filters are possible. We see that there is only one category of these filter banks. The configurations of four-parallelogram filter banks in this category can always be achieved by designing filter banks of low design cost.

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## ‣ Linear phase cosine modulated maximally decimated filter banks with perfect reconstruction

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /11/1995
Português

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We propose a novel way to design maximally decimated FIR cosine modulated filter banks, in which each analysis and synthesis filter has a linear phase. The system can be designed to have either the approximate reconstruction property (pseudo-QMF system) or perfect reconstruction property (PR system). In the PR case, the system is a paraunitary filter bank. As in earlier work on cosine modulated systems, all the analysis filters come from an FIR prototype filter. However, unlike in any of the previous designs, all but two of the analysis filters have a total bandwidth of 2π/M rather than π/M (where 2M is the number of channels in our notation). A simple interpretation is possible in terms of the complex (hypothetical) analytic signal corresponding to each bandpass subband.
The coding gain of the new system is comparable with that of a traditional M-channel system (rather than a 2M-channel system). This is primarily because there are typically two bandpass filters with the same passband support. Correspondingly, the cost of the system (in terms of complexity of implementation) is also comparable with that of an M-channel system. We also demonstrate that very good attenuation characteristics can be obtained with the new system.

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## ‣ A new class of two-channel biorthogonal filter banks and wavelet bases

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /03/1995
Português

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We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters.

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## ‣ Linear phase paraunitary filter banks: theory, factorizations and designs

Fonte: IEEE
Publicador: IEEE

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /12/1993
Português

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M channel maximally decimated filter banks have been used in the past to decompose signals into subbands. The theory of perfect-reconstruction filter banks has also been studied extensively. Nonparaunitary systems with linear phase filters have also been designed. In this paper, we study paraunitary systems in which each individual filter in the analysis synthesis banks has linear phase. Specific instances of this problem have been addressed by other authors, and linear phase paraunitary systems have been shown to exist. This property is often desirable for several applications, particularly in image processing.
We begin by answering several theoretical questions pertaining to linear phase paraunitary systems. Next, we develop a minimal factorizdion for a large class of such systems. This factorization will be proved to be complete for even M. Further, we structurally impose the additional condition that the filters satisfy pairwise mirror-image symmetry in the frequency domain. This significantly reduces the number of parameters to be optimized in the design process. We then demonstrate the use of these filter banks in the generation of M-band orthonormal wavelets. Several design examples are also given to validate the theory.

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## ‣ Multidimensional multirate filters and filter banks derived from one-dimensional filters

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /05/1993
Português

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A method by which every multidimensional (M-D) filter with an arbitrary parallelepiped-shaped passband support can be designed and implemented efficiently is presented. It is shown that all such filters can be designed starting from an appropriate one-dimensional prototype filter and performing a simple transformation. With D denoting the number of dimensions, the complexity of design and implementation of the M-D filter are reduced from O(ND) to O(N). Using the polyphase technique, an implementation with complexity of only 2N is obtained in the two-dimensional. Even though the filters designed are in general nonseparable, they have separable polyphase components. One special application of this method is in M-D multirate signal processing, where filters with parallelepiped-shaped passbands are used in decimation, interpolation, and filter banks. Some generalizations and other applications of this approach, including M-D uniform discrete Fourier transform (DFT) quadrature mirror filter banks that achieve perfect reconstruction, are studied. Several design example are given.

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## ‣ Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /01/1990
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Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This includes design of decimation and interpolation filters, analysis/synthesis filter banks (also called quadrature mirror filters, or QMFJ, and the development of new sampling theorems. First, the basic concepts and building blocks in multirate digital signal processing (DSPJ, including the digital polyphase representation, are reviewed. Next, recent progress as reported by several authors in this area is discussed. Several applications are described, including the following: subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrow-band filter coefficients. The M-band QMF bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems...

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## ‣ Structures for M-channel perfect-reconstruction FIR QMF banks which yield linear-phase analysis filters

Fonte: Instituto de Tecnologia da Califórnia
Publicador: Instituto de Tecnologia da Califórnia

Tipo: Article; PeerReviewed
Formato: application/pdf

Publicado em /03/1990
Português

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The authors develop structures for FIR (finite impulse response) perfect-reconstruction QMF (quadrature mirror filter) banks, which cover a subclass of systems that yield linear-phase analysis filters for arbitrary M. The parameters of these structures can be optimized to design analysis filters with minimum stopband energy which at the same time have linear phase and satisfy the perfect-reconstruction property. If there are M subbands, then depending on whether the coefficients hk(n) of each analysis filter are symmetric or antisymmetric, several combinations of filter banks are possible. Some of these permit perfect reconstruction and some do not. For a given M, the authors develop a formula for the number of combinations for a subclass of linear-phase perfect-reconstruction structures. As an example, they elaborate on a perfect-reconstruction linear-phase lattice structure for three channels. The lattice structure is such that, regardless of the parameter values, the QMF bank enjoys the perfect-reconstruction property while at the same time the analysis filters have linear phase. A design example is presented, along with tables of impulse response coefficients

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## ‣ Design of Linear Phase IIR Filters with Flat Magnitude Response using Complex Coefficients Allpole Filters

Fonte: Centro de Investigación en computación, IPN
Publicador: Centro de Investigación en computación, IPN

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/06/2007
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This paper presents a new method for the design of linear phase IIR filters with flat magnitude response. The method is based on the design of flat digital allpole filters with complex coefficients. Depending on the parity of the allpole filter order the resulting IIR filter have either real or complex coefficients. The parameters of the design are the same as in traditional IIR filter design, i.e., passband and stopband frequencies, ωp and ωs, passband droop Ap , and stopband attenuation As . Several design examples are provided to illustrate the method. In addition, a design of linear phase modified two-band IIR filter banks and a design of stable IIR filter with an improved group delay are presented as two applications of the proposed method.

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