Yes / A multipartite system comprised of n subsystems, each of which is described with ‘local variables’ in Z(d) and with a d-dimensional Hilbert space H(d), is considered. Local Fourier transforms in each subsystem are defined and related phase space methods are discussed (displacement operators, Wigner and Weyl functions, etc). A holistic view of the same system might be more appropriate in the case of strong interactions, which uses ‘global variables’ in Z(dn) and a dn-dimensional Hilbert space H(dn). A global Fourier transform is then defined and related phase space methods are discussed. The local formalism is compared and contrasted with the global formalism. Depending on the values of d, n the local Fourier transform is unitarily inequivalent or unitarily equivalent to the global Fourier transform. Time evolution of the system in terms of both local and global variables, is discussed. The formalism can be useful in the general area of Fast Fourier transforms.

Yes / Two methods for fast Fourier transforms are used in a quantum context. The first method is for systems with dimension of the Hilbert space with d an odd integer, and is inspired by the Cooley-Tukey formalism. The ‘large Fourier transform’ is expressed as a sequence of n ‘small Fourier transforms’ (together with some other transforms) in quantum systems with d-dimensional Hilbert space. Limitations of the method are discussed. In some special cases, the n Fourier transforms can be performed in parallel. The second method is for systems with dimension of the Hilbert space with odd integers coprime to each other. It is inspired by the Good formalism, which in turn is based on the Chinese reminder theorem. In this case also the ‘large Fourier transform’ is expressed as a sequence of n ‘small Fourier transforms’ (that involve some constants related to the number theory that describes the formalism). The ‘small Fourier transforms’ can be performed in a classical computer or in a quantum computer (in which case we have the additional well known advantages of quantum Fourier transform circuits). In the case that the small Fourier transforms are performed with a classical computer, complexity arguments for both methods show the reduction in computational time from to . The second method is also used for the fast calculation of Wigner and Weyl functions, in quantum systems with large finite dimension of the Hilbert space.

QC 351 A7 no. 49 / The use of the two -dimensional Fourier transform to compute the form of the optical image has led to new insights into the form of images. The techniques involved are discussed in some detail, and the application to tolerancing of surface errors is used as an ex- ample of the results.

This paper presents a theory of Fourier transforms of complex-valued functions on a finite abelian group and investigates two applications of this theory. Chapter I is an introduction with remarks on notation. Basic theory, including Pontrvagin duality and the Poisson Summation formula, is the subject of Chapter II. In Chapter III the Fourier transform is viewed as an intertwining operator for certain unitary group representations. The solution of the eigenvalue problem of the Fourier transform of functions on the group Z/n of integers module n leads to a proof of the quadratic reciprocity law in Chapter IV. Chapter V addresses the, use of the Fourier transform in computing.

In this thesis a number of problems in harmonic analysis of a geometric flavour are discussed and, in particular, the Lebesgue space mapping properties of certain averaging and Fourier restriction operators are studied. The first three chapters focus on the perspective afforded by affine-geometrical considerations whilst the remaining chapter considers some discrete variants of these problems. In Chapter 1 there is an overview of the basic affine theory of the aforementioned operators and, in particular, the affine arc-length and surface measures are introduced. Chapter 2 presents work of the author, submitted for publication, concerning an operator which takes averages of functions on Euclidean space over both translates and dilates of a fixed polynomial curve. Moreover, the averages are taken with respect to the affine arc-length; this allows one to prove Lebesgue space estimates with a substantial degree of uniformity in the constants. The sharp range of uniform estimates is obtained in all dimensions except for an endpoint. Chapter 3 presents some work of the author, published in Mathematika, concerning a family of Fourier restriction operators closely related to the averaging operators discussed in Chapter 2. Specifically, a Fourier restriction estimate is obtained for a broad class of conic surfaces by introducing a certain measure which exhibits a special kind of affine invariance. Again, the sharp range of estimates is obtained, but the results are limited to the case of 2-dimensional cones. Finally, Chapter 4 discusses some recent joint work of the author and Jim Wright considering the restriction problem over rings of integers modulo a prime power. The sharp range of estimates is obtained for Fourier restriction to the moment curve in finitely-generated free modules over such rings. This is achieved by lifting the problem to the p-adics and applying a classical argument of Drury in this setting. This work aims to demonstrate that rings of integers offer a simplified model for the Euclidean restriction problem.

Kransalger är en viktig nyckelart i Östersjön. De förökar sig med hjälp av oosporer och denna studie har syftat till att urskilja morfologisk differentiering mellan oosporer inom och mellan individer och populationer. Främst ställde jag mig frågan huruvida skillnader och likheter i morfologi kan associeras med skillnader mellan olika geografiska avstånd och habitat samt i vilken mån oosporer kan återföras till korrekt population och individ. Kransalger av arten Chara aspera har insamlats på lokaler i östra Svealand och elliptiska Fouriertransformationer har använts för att med hjälp av vågfunktioner beskriva oosporernas konturer. Parametrarna i vågfunktioner har sedan använts för statistiska analyser. Resultaten visade att de olika populationerna kunde separeras morfologiskt när oosporernas populationstillhörighet varit känd för analysen. Däremot var det svårare att separera individer från varandra men det fungerade bra i den population där flest oosporer insamlats. Då oosporernas identitet varit okänd för analysen återfördes endast hälften av dem till rätt population. Det gick inte att återföra okända oosporer till individer. De tre populationerna från bräckt vatten grupperades tillsammans i diskriminantanalysen, skilda från de två sötvattenpopulationerna som i sin tur var tydligt skilda från varandra. En spridning mellan de olika populationerna i brackvatten är trolig. Däremot är en spridning mellan populationerna i sött vatten inte sannolik. Det finns inte heller något som talar för en spridning mellan habitaten. Slutligen kan jag konstatera att det finns tillräckligt mycket information att hämta i oosporerna morfologi för att mäta relativa skillnader mellan individer och grupper liksom för att skatta variabilitet. / Charophytes are an important key species in the Baltic Sea. They reproduce by using oospores and this study aims at distinguish morphological differentiation between oospores within and between individuals and populations. Mainly I asked myself the question whether the differences and similarities in morphology could be associated with differences between geographic distance and habitat, and to what extent oospores could be reassigned to the correct population and individual. Charophytes of the genus Chara aspera were collected in eastern Svealand and harmonics from elliptic Fourier transforms have been used to describe the contours of the oospores. The parameters of the harmonics were then used for statistical analyses. The results showed that the different populations could be separated morphologically when the population affiliation of the oospores has been known to the analysis. It was difficult to separate individuals from each other, but it worked well in the population in which most oospores were collected. When the identity of the oospores was unknown to the analysis only half of them were returned to the correct population, and it did not work to reassign unknown oospores to individuals. The three populations from brackish water grouped together in the discriminant analysis, separated from the two freshwater populations, which, in turn, were clearly distinct from one another. Dispersal between the different populations in brackish water is likely. However, dispersal between the populations in fresh water is not likely. There is nothing to indicate dispersal between brackish and freshwater habitats. I can conclude that there is enough information in the morphology of the oospores to measure relative differences between individuals and groups, as well as to estimate variability.

Orthogonal frequency division multiplexing (OFDM) is a multicarrier transmission technique which provides efficient bandwidth utilization and robustness against time dis¬persive channels. A major problem in the RF portion of a multicarrier transmitter is Gaussian-like time-domain signals with relatively high peak-to-average power ratios (PA¬PRs). These peaks can lead to saturation in the power amplifier (PA) which in turn distorts the signal and reduces the PA efficiency. To address this problem, numerous techniques have appeared in the literature based on signal and/or data modification. In the class of distortionless techniques, partial transmit sequences (PTS), selective mapping (SLM), and tone reservation (TR) have received a great deal of attention as they are proven techniques that achieve significant PAPR reduction. However, high compu¬tational complexity is a problem in practical systems. In PTS and SLM, this complexity arises from the computation of multiple inverse fast Fourier transforms (IFFTs), resulting in a complexity proportional to the number of PTS subblocks or SLM sequences. TR has also a high computational complexity related to the computation of the IFFT as it must search for the optimal subsets of reserved subcarriers and generate the peak reduction signal. In addition, most research in the direction of analyzing and improving the above techniques has employed direct computation of the inverse discrete Fourier transform (IDFT), which is not practical for implementation. This thesis focuses on the development and performance analysis of the major distortionless techniques in conjunction with the common IFFT algorithms to reduce the peak-to-power average (PAPR) of the original OFDM signal at the transmitter side. The structure of the IFFT common algorithms is used to propose a class of IFFT-based PAPR reduction techniques to reduce the computational complexity and improve PAPR performance. For IFFT based PTS, two techniques are proposed. A low complexity scheme based on decimation in frequency (DIF) and high radix IFFT algorithm is proposed. Then, a new PTS subblocking technique is proposed to improve PAPR performance. The periodic auto-correlation function (ACF) of time-domain IFFT-based PTS subblocks is derived. To improve the PAPR, we use error-correcting codes (ECCs) in the subblocking. Our approach significantly decreases the computational complexity while providing comparable PAPR reduction to ordinary PTS (O-PTS). With IFFT-based SLM, a technique for reducing computational complexity is proposed. This technique is based on multiplying the phase sequences with a subset of the inputs to identical inverse discrete Fourier transform (IDFTs). These subsets generate the partial SLM sequences using repetition codes. It is also shown how the partial time-domain sub-sets can be combined to generate new SLM sequences. These sequences do not requires any IFFT operations. The proposed scheme outperforms the existing techniques while pro¬viding comparable PAPR reduction to original SLM (O-SLM). Finally, a gradient-based algorithm is proposed for IFFT-based TR. Unlike previous work, non-static channels are considered where the peak reduction tones (PRTs) locations and consequently the peak reduction kernels should be adjusted dynamically for best per¬formance. Two low complexity algorithms with different degrees of computational com¬plexity and PAPR performance are proposed. To generate the peak reduction kernels, the transform matrices of identical IFFTs are used. This provides low complexity solutions to determining the PRTs and computing the peak reduction kernels.

[pt] A geração de cenas realísticas de fenômenos naturais em tempo real é uma das mais importantes áreas de pesquisa para aplicações em jogos e simuladores. No início da computação gráfica para tempo real, a maioria das aplicações tratava a superfície da água como um plano com uma textura. Essa abordagem produz uma visualizaçãomuito pouco realística da superfície da água, além de não reproduzir o comportamento hidrodinâmico correto da água. Nesse contexto, muitos grupos de pesquisa desenvolveram técnicas para a visualização realística da superfície da água, contudo, a maioria desses trabalhos foca no processo off-line e poucos tratam da questão em tempo real. No entanto, os recentes avanços no desempenho do hardware permitiram a utilização de técnicas tradicionalmente usadas emoff-line para o escopo de tempo real, porém não há uma pesquisa-guia que descreva tais técnicas e faça uma análise comparativa das mesmas. Sendo assim, sem tal pesquisa-guia é muito difícil escolher a melhor técnica para um hardware específico ou se determinada técnica provê o controle de simulação necessário para uma aplicação específica.Nesse contexto, a presente pesquisa analisa as técnicas mais importantes para visualização e simulação de oceano em tempo real, utilizando a unidade de processamento gráfico como o processador principal. Além disso, ela realiza uma análise comparativa de desempenho de cada técnica e estuda os prós e contras delas. Ainda, alguns métodos off-line clássicos são adaptados para uso na GPU. / [en] The synthesis of realistic natural scenes in real time is one of the most important research areas for applications in games and simulators. In the beginning of real-time computer graphics, most of the applications treated water surface as a textured plane. This approach produces a very low realistic rendering of the water surface and does not reproduce the correct hydrodynamics behaviour of the water. So, a lot of research groups developed techniques for realistic water rendering, most of them for off-line processes and a few for real-time use. However, current improvementson hardware performance allow the usage oftraditional off-line techniques for real-time proposes, but there is no research work that describesthese techniques and makes a comparative analysis of them. Then, without this comparative analysis, it is very difficult to choose the best technique for a specific hardware or to decide if a particular technique provides the simulation control that a certain application needs.In this context, the present research work analyses the most important techniques for real-time ocean water simulation and visualization using the graphics processor unit as a main processor. Moreover, it makes a performance comparative analysis of each technique and analyses the pros and cons of them. Furthermore, some classic off-line methods are adapted for GPU use.

Orientadores: Araí Augusta Bernárdez Pécora, Emerson dos Reis / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-24T13:04:25Z (GMT). No. of bitstreams: 1 RuedaOrdonez_DiegoAndres_M.pdf: 19506541 bytes, checksum: 0bbc753dfedabd5800a9c9bd05c71077 (MD5) Previous issue date: 2014 / Resumo: Neste trabalho, foi utilizada uma metodologia para a análise dos sinais de flutuações de pressão visando estudar a fluidização e o fenômeno da segregação em leitos fluidizados contendo misturas binárias de partículas de diferentes tamanhos e massas específicas. As medidas foram feitas para caracterizar o comportamento fluidodinâmico do leito fluidizado contendo misturas binárias e encontrar as velocidades inerentes ao fenômeno da segregação. Para tanto, primeiramente foram estudados os comportamentos de cada material isolado para posterior comparação com o comportamento observado para as misturas contendo tais materiais.Três tipos de sólidos particulados foram utilizados neste trabalho: microesferas de plástico (diâmetro médio de Sauter de 971 µm) e microesferas de vidro (diâmetros médios de Sauter de 462 e 959 µm).O sistema experimental utilizado consiste de uma coluna, de 0,1 m de diâmetro e 2,5 m de altura, equipada com um distribuidor de gás tipo placa porosa e possuindo seções de vidro,acrílico e aço carbono intercaladas, o que permitiu acompanhar visualmente o processo, e adquirir imagens por meio de uma câmera fotográfica. Medidas de flutuações de pressão foram feitas em diferentes velocidades superficiais do gás para cada material ou mistura estudados. Os sinais de pressão foram medidos em três pontos na coluna do leito, sendo um no plenum e dois na coluna, situado a 0,035 e a 0,115 m acima da placa distribuidora.Em todos os testes a altura do leito foi mantida fixa em 0,150 m. As flutuações de pressão foram analisadas no domínio do tempo e no domínio da frequência aplicando a transformada rápida de Fourier (FFT) o que permitiu diferenciar o comportamento dinâmico das misturas em cada velocidade superficial do gás estudada.Os resultados permitiram identificar regiões com diferentes comportamentos fluidodinâmicos e velocidades inerentes ao processo de segregação como as velocidades de fluidização inicial, fluidização completa, de segregação e de mistura completa. Este trabalho procura contribuir para melhorar o entendimento sobre a fluidização de misturas binárias e sobre o fenômeno de segregação normalmente presente em tais sistemas / Abstract: A methodology for analysis of pressure fluctuations signals was used, in the present work, to study the ?uidizing and segregation phenomena in fluidized beds containing granular binary mixtures with different sizes and densities. Pressure measurements have been made to characterize the dynamic behavior of fluidized beds and to find the velocities involved in the segregation phenomena. The analysis of each single studied material was made before analyzing of the mixtures containing such materials. Three types of solid particles were used in this work: plastic microspheres (971 µm Sauter mean diameter) and glass microspheres (462 and 959 µm Sauter mean diameters). The experimental system presents a column, 0.1m diameter and 2.5 m height, equipped with a porous plate gas distributor. The column was made by glass, acrylic and carbon-steel sections to allow visual observations of the process and acquiring images by a camera. Measurements of pressure fluctuations were made in different gas superficial velocities for each studied material or mixture. The pressure signals were measured at three points in the column: one at plenum and two above the distributor plate, at 0.035 and 0.115 m above the distributor plate. The height of the bed material was fixed in 0.15 m regarding all performed tests. Pressure fluctuations were analyzed on the time domain and on the frequency domain using the fast Fourier transform (FFT) which allows differentiating the dynamic behavior of the mixtures in each superficial gas velocity studied. The results allowed the identification of regions with different fluid dynamic behaviors as well as the determination of gas velocities inherent to the segregation process as the initial fluidization, complete fluidization, segregation and complete mixing velocities. This paper aims to contribute on understanding the fluidization process of binary mixtures and on the phenomenon of segregation normally present in such systems / Mestrado / Termica e Fluidos / Mestre em Engenharia Mecânica

This thesis is about measuring charger and discharger properties of dielectrics materials in time domain and transformation of acquired characteristics to the frequency domain. For transformation between time and frequency domain are used Fourier transform and Haman approximation. The result is frequency dependent on loss number. Part of this work is about comparison of these methods in theoretical and practical applications on the basis of accuracy, speed and performance.