This thesis introduces spatial filtering, which is a technique to extend the time step size beyond the conventional stability limit for the Finite-Difference Time-Domain (FDTD) method, at the expense of transforming field nodes between the spatial domain and the discrete spatial-frequency domain and removing undesired spatial-frequency components at every FDTD update cycle. The spatially-filtered FDTD method is demonstrated to be almost as accurate as and more efficient than the conventional FDTD method via theories and numerical examples. Then, this thesis combines spatial filtering and an existing subgridding scheme to form the spatially-filtered subgridding scheme. The spatially-filtered subgridding scheme is more efficient than existing subgridding schemes because the former allows the time step size used in the dense mesh to be larger than the dense mesh CFL limit. However, trade-offs between accuracy and efficiency are required in complicated structures.

This dissertation reviews the theory of fast matrix multiplication from a multilinear-algebraic point of view, as well as recent fast matrix multiplication algorithms based on discrete Fourier transforms over nite groups. To this end, the algebraic approach is described in terms of group algebras over groups satisfying the triple product Property, and the construction of such groups via uniquely solvable puzzles. The higher order singular value decomposition is an important decomposition of tensors that retains some of the properties of the singular value decomposition of matrices. However, we have proven a novel negative result which demonstrates that the higher order singular value decomposition yields a matrix multiplication algorithm that is no better than the standard algorithm. / Mathematical Sciences / M. Sc. (Applied Mathematics)

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-05T12:56:54Z No. of bitstreams: 1 arquivototal.pdf: 2044930 bytes, checksum: 05bad0799c40d5bf256cf504f0a8b5ab (MD5) / Approved for entry into archive by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-05T15:29:04Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 2044930 bytes, checksum: 05bad0799c40d5bf256cf504f0a8b5ab (MD5) / Made available in DSpace on 2017-09-05T15:29:04Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2044930 bytes, checksum: 05bad0799c40d5bf256cf504f0a8b5ab (MD5) Previous issue date: 2016-08-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We will do here a theoretical study of the Discrete Fourier Transform on the finite circle ℤ/nℤ. Our main objective is to see if we can get properties analogous to those found in the Fourier transform for the continuous case. In this work we show that ℤ/nℤ has a ring structure, providing conditions for the development of extensively discussed topics in arithmetic, for example, The Chinese Remainder Theorem, Euler’s Phi Function and primitive roots, themes these to be dealt with in first chapter. The main subject of this study is developed in the second chapter, which define the space L2(ℤ/nℤ) and prove that this is a finite-dimensional inner product vector space, with an orthonormal basis. This fact is of utmost importance when we are determining the matrix and demonstrating the properties of the discrete Fourier transform. We will also make geometric interpretations of the Chinese Remainder Theorem and the finite circle ℤ/nℤ as well as give a graphical representation of the DFT of some functions that calculate. During the development of this study we will make recurrent use of definitions and results treated in Arithmetic, Algebra and Linear Algebra. / Faremos, aqui, um estudo teórico sobre a Transformada Discreta de Fourier no círculo finito ℤ/nℤ. Nosso principal objetivo é verificar se podemos obter propriedades análogas às encontradas nas transformadas de Fourier para o caso contínuo. Nesse trabalho mostraremos que ℤ/nℤ tem uma estrutura de anel, dando condições para o desenvolvimento de temas bastante discutidos na Aritmética como, por exemplo, o Teorema Chinês do Resto, função Phi de Euler e raízes primitivas, temas estes que serão tratados no primeiro capítulo. O assunto principal desse estudo é desenvolvido no segundo capítulo, onde definiremos o espaço L2(ℤ/nℤ) e provaremos que este é um espaço vetorial com produto interno, dimensão finita e uma base ortonormal. Tal fato será de extrema importância quando estivermos determinando a matriz e demonstrando as propriedades da transformada discreta de Fourier. Também faremos interpretações geométricas do Teorema Chinês do Resto e do círculo finito ℤ/nℤ assim como daremos a representação gráfica da DFT de algumas funções que calcularemos. Durante o desenvolvimento desse estudo faremos uso recorrente de definições e resultados tratados na Aritmética, Álgebra e Álgebra Linear.

Made available in DSpace on 2016-03-15T19:37:42Z (GMT). No. of bitstreams: 1 Eurico Luiz Prospero Ruivo.pdf: 15234351 bytes, checksum: 5a581041d50f5cbd30ccc684b8112487 (MD5) Previous issue date: 2012-12-11 / Universidade Presbiteriana Mackenzie / The Fourier spectra of cellular automata rules give a characterisation of the limit configurations generated by them at the end of their time evolution. In the present work, the Fourier spectra of each rule of the elementary cellular automata rule space are computed, under periodic and non-periodic boundary conditions, and the space is then partitioned according to the similarity among these computed spectra, what gives the notion of spectral classes in such space. For the partition obtained under periodic boundary condition, each spectral class is analysed in terms of the behaviour of each of its rules and how this behaviour affects the correspondent spectrum. Finally, the spectral classes are related in terms of the similarity among them, for both boundary conditions, what results in graphs depicting the proximity among the spectral classes. / Os espectros de Fourier de regras de autômatos celulares fornecem uma caracterização da configuração limite gerada por elas ao fim de suas evoluções temporais. Neste trabalho, são calculados os espectros de Fourier de todas as regras do espaço dos autômatos celulares elementares, sob condições de contorno periódica e não-periódicas, e o espaço é então particionado de acordo com a similaridade entre os espectros calculados, dando origem à noção de classes espectrais no espaço em questão. Para a participação gerada sob condição de contorno periódica, cada classe espectral é analisada de acordo com o comportamento de cada regra e a implicação deste no espectro obtido. A seguir é analisada a relação de similaridade entre as classes espectrais geradas em cada tipo de condição de contorno, o que d´a origem a grafos representando a proximidade entre as classes espectrais.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-04-25T17:30:25Z No. of bitstreams: 1 carloshenriquenascimentomartins.pdf: 10221613 bytes, checksum: 0d6eef0f715fc0f9f68bf12a390dcd55 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-04-26T12:22:24Z (GMT) No. of bitstreams: 1 carloshenriquenascimentomartins.pdf: 10221613 bytes, checksum: 0d6eef0f715fc0f9f68bf12a390dcd55 (MD5) / Made available in DSpace on 2017-04-26T12:22:24Z (GMT). No. of bitstreams: 1 carloshenriquenascimentomartins.pdf: 10221613 bytes, checksum: 0d6eef0f715fc0f9f68bf12a390dcd55 (MD5) Previous issue date: 2015-03-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Esta tese apresenta as etapas de desenvolvimento de um sistema de monitoramento de parâmentos de qualidade de energia dedicado a análise de harmônicos variantes no tempo através do equipamento denominado AHVT (Analisador de Harmônicos Variantes no Tempo). O desenvolvimento do trabalho é composto por: (i) estudo e implementação MATLAB de algoritmos para processamento em tempo real, com capacidade de sintonização dos componentes harmônicos; (ii) análise e desenvolvimento de estratégias para detecção e validação da presença de interharmônicos próximos à frequência fundamental e suas consequência na estimação de parâmetros como fase, amplitude e frequência para o componente fundamental, (iii) proposta de implementação do dispositivo, sistema de aquisição/ condicionamento de sinais/ filtragem, sistema de conversão analógico digital e plataforma de processamentoDSP/FPGA, sistema de transmissão de dados e plataformas de análise online/offline dos eventos de harmônicos variantes no tempo; (iv) plataforma de simulação do Analisador de Harmônicos Variantes no Tempo (AHVT) para estudo dos métodos de trigger para detecção e captura dos eventos. / In this work is presented the steps of development and implementation of a Power Quality paramaters monitoring system with main goal events denomined ”time arying harmonics”named of Time Varying Harmonic Analyzer. The development is comprises:(i) research and implementation of real time algorithms with capable to tuning harmonic waves,(ii) Analyze and research/development of strategies for detect and validation of interharmonics with frequencies near of fundamental, and conseguencies and challenges to phase, magnitude and frequency estimation with presence interharmonic waveform (iii) The proposal of a hardware design including analog to digital conversion and digital signal processing plataform, broadcast data link and IHM(Interface Human Machine) for online and offline analyzes to time varying harmonic analyzer;(iiii)off-line simulation plataform of Analisador de Harmônicos Variantes no Tempo Time Varying Harmonic Analyzer (TVHA) to trigger detect methods to detection and capture of waveforms.

Modified discrete cosine transform (MDCT) derived from DCT IV has emerged as the most suitable choice for transform domain audio coding applications due to its time domain alias cancellation property and de-correlation capability. In the present research work, we focus on MDCT domain analysis of audio signals for compression and other applications. We have derived algorithms for linear filtering in DCT IV and DST IV domains for symmetric and non-symmetric filter impulse responses. These results are also extended to MDCT and MDST domains which have the special property of time domain alias cancellation. We also derive filtering algorithms for the DCT II and DCT III domains. Comparison with other methods in the literature shows that, the new algorithm developed is computationally MAC efficient. These results are useful for MDCT domain audio processing such as reverb synthesis, without having to reconstruct the time domain signal and then perform the necessary filtering operations. In audio coding, the psychoacoustic model plays a crucial role and is used to estimate the masking thresholds for adaptive bit-allocation. Transparent quality audio coding is possible if the quantization noise is kept below the masking threshold for each frame. In the existing methods, the masking threshold is calculated using the DFT of the signal frame separately for MDCT domain adaptive quantization. We have extended the spectral integration based psychoacoustic model proposed for sinusoidal modeling of audio signals to the MDCT domain. This has been possible because of the detailed analysis of the relation between DFT and MDCT; we interpret the MDCT coefficients as co-sinusoids and then apply the sinusoidal masking model. The validity of the masking threshold so derived is verified through listening tests as well as objective measures. Parametric coding techniques are used for low bit rate encoding of multi-channel audio such as 5.1 format surround audio. In these techniques, the surround channels are synthesized at the receiver using the analysis parameters of the parametric model. We develop algorithms for MDCT domain analysis and synthesis of reverberation. Integrating these ideas, a parametric audio coder is developed in the MDCT domain. For the parameter estimation, we use a novel analysis by synthesis scheme in the MDCT domain which results in better modeling of the spatial audio. The resulting parametric stereo coder is able to synthesize acceptable quality stereo audio from the mono audio channel and a side information of approximately 11 kbps. Further, an experimental audio coder is developed in the MDCT domain incorporating the new psychoacoustic model and the parametric model.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第22448号 / 工博第4709号 / 新制||工||1735(附属図書館) / 京都大学大学院工学研究科電子工学専攻 / (主査)教授 竹内 繁樹, 教授 白石 誠司, 准教授 浅野 卓 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

This master's thesis describes ways of signal processing via digital devices. Major field of interest is an analysis of Doppler radar response and then mining of informations about detected object (e.g. speed, movement direction, length, ...). There was realized too little research, that's why borrowing some procedures from different branches not too much related to the IT is necessary. In case of using very complex methods that are easy to parallel, hardware implementation on the FPGA is supposed. With transceiver there is created a very powerful on-line system able to process most of tasks real-time. Then processed and transformed data are sent to the output so visualization and display can be made.

Cette thèse présente une étude des applications des groupes de réflexion finis aux problems liés aux réseaux bidimensionnels et aux polytopes tridimensionnels. Plusieurs familles de fonctions orbitales, appelées fonctions orbitales de Weyl, sont associées aux groupes de réflexion cristallographique. Les propriétés exceptionnelles de ces fonctions, telles que l’orthogonalité continue et discrète, permettent une analyse de type Fourier sur le domaine fondamental d’un groupe de Weyl affine correspondant. Dans cette considération, les fonctions d’orbite de Weyl constituent des outils efficaces pour les transformées discrètes de type Fourier correspondantes connues sous le nom de transformées de Fourier–Weyl. Cette recherche limite notre attention aux fonctions d’orbite de Weyl symétriques et antisymétriques à deux variables du groupe de réflexion cristallographique A2. L’objectif principal est de décomposer deux types de transformations de Fourier–Weyl du réseau de poids correspondant en transformées plus petites en utilisant la technique de division centrale. Pour les cas non cristallographiques, nous définissons les indices de degré pair et impair pour les orbites des groupes de réflexion non cristallographique avec une symétrie quintuple en utilisant un remplacement de représentation-orbite. De plus, nous formulons l’algorithme qui permet de déterminer les structures de polytopes imbriquées. Par ailleurs, compte tenu de la pertinence de la symétrie icosaédrique pour la description de diverses molécules sphériques et virus, nous étudions la brisure de symétrie des polytopes doubles de type non cristallographique et des structures tubulaires associées. De plus, nous appliquons une procédure de stellation à la famille des polytopes considérés. Puisque cette recherche se concentre en partie sur les fullerènes icosaédriques, nous présentons la construction des nanotubes de carbone correspondants. De plus, l’approche considérée pour les cas non cristallographiques est appliquée aux structures cristallographiques. Nous considérons un mécanisme de brisure de symétrie appliqué aux polytopes obtenus en utilisant les groupes Weyl tridimensionnels pour déterminer leurs extensions structurelles possibles en nanotubes. / This thesis presents a study of applications of finite reflection groups to the problems related to two-dimensional lattices and three-dimensional polytopes. Several families of orbit functions, known as Weyl orbit functions, are associated with the crystallographic reflection groups. The exceptional properties of these functions, such as continuous and discrete orthogonality, permit Fourier-like analysis on the fundamental domain of a corresponding affine Weyl group. In this consideration, Weyl orbit functions constitute efficient tools for corresponding Fourier-like discrete transforms known as Fourier–Weyl transforms. This research restricts our attention to the two-variable symmetric and antisymmetric Weyl orbit functions of the crystallographic reflection group A2. The main goal is to decompose two types of the corresponding weight lattice Fourier–Weyl transforms into smaller transforms using the central splitting technique. For the non-crystallographic cases, we define the even- and odd-degree indices for orbits of the non-crystallographic reflection groups with 5-fold symmetry by using a representation-orbit replacement. Besides, we formulate the algorithm that allows determining the structures of nested polytopes. Moreover, in light of the relevance of the icosahedral symmetry to the description of various spherical molecules and viruses, we study symmetry breaking of the dual polytopes of non-crystallographic type and related tube-like structures. As well, we apply a stellation procedure to the family of considered polytopes. Since this research partly focuses on the icosahedral fullerenes, we present the construction of the corresponding carbon nanotubes. Furthermore, the approach considered for the non-crystallographic cases is applied to crystallographic structures. We consider a symmetry-breaking mechanism applied to the polytopes obtained using the three-dimensional Weyl groups to determine their possible structural extensions into nanotubes.

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