Η χρήση ταλαντωτών γίνεται σε όλα τα τηλεπικοινωνιακά και στα περισσότερα ψηφιακά κυκλώματα. Αποτελεί βασικό πυλώνα πάνω στον οποίο στηρίζεται η ποιότητα του τηλεπικοινωνιακού σήματος. Για να παράγει έξοδο για διαφορετικά κανάλια μιας τηλεπικοινωνιακής περιοχής, θα πρέπει ο ταλαντωτής μας να αλλάζει την παραγόμενη συχνότητα του. Μια ειδική κατηγορία αυτών είναι οι ταλαντωτές ελεγχόμενοι από τάση, VCO . Οι ταλαντωτές που χρησιμοποιούνται σήμερα ανήκουν σε 2 βασικές κατηγορίες: ● Ταλαντωτές LC, όπου χρησιμοποιείται ένα συντονιζόμενο κύκλωμα, αποτελούμενο από επαγωγή L και χωρητικότητα C, που από κοινού καθορίζουν την συχνότητα λειτουργίας του ταλαντωτή. ● Ταλαντωτές δακτυλίου, χρησιμοποιούν κυκλώματα RC μετάθεσης φάσης Οι πρώτοι υπερέχουν στον χαμηλότερο θόρυβο και κατανάλωση, οι δεύτεροι σε μικρότερη επιφάνεια υλοποίησης και μεγαλύτερη περιοχή συχνοτήτων. Η μελέτη έγινε για ολοκληρωμένο κύκλωμα ASIC, BiCmos 0,35μm της Austriamicrosystems. Η περιοχή συχνοτήτων του VCO είναι 10GHz – 10,5GHz. Η πορεία πέρασε από την εξομοίωση των επιμέρους τμημάτων του ταλαντωτή και σταδιακά στην σύνθεσή τους. Το ζητούμενο ήταν να επιτευχθεί η χαμηλότερη στάθμη θορύβου, στα προδιαγεγραμμένα όρια λειτουργίας. Το γεγονός αυτό οδήγησε σε διαρκείς εξομοιώσεις. Στην συνέχεια μετεξελίχθηκε σε ορθογώνιο ταλαντωτή QVCO με την ίδια περιοχή εξόδου. Η διαδικασία επαναλήφτηκε για την επίτευξη της μέγιστης απόδοσης. Για την εξομοίωση χρησιμοποιήθηκε το Advanced Design System της Agilent. Η τροφοδοσία του κυκλώματος είναι στα 3volts. Η κατανάλωση 42mw για τον ταλαντωτή VCO, 90mW για τον ταλαντωτή QVCO. Ο θόρυβος φάσης είναι χαμηλότερος από -114dBc/Hz στα 10KHz για το VCO και -100dBc/Hz στα 10KHz για το QVCO. / Design of an integrated ASIC Austriamicrosystems (AMS), 0.35mm technology, quadrature voltage controlled oscillator in the range of 10GHz. The design and simulation environment had occurred in the ADS of Agilent. This design was aimed at the lowest possible noise level.

Thesis (MScEng)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: This thesis investigates orthogonal frequency division multiplexing (OFDM) as a viable modulation technique for an ultrasonic acoustic underwater modem. The underwater environment provides a challenging setting for acoustic communications. Long delay spreads due to multipath propagation, severe Doppler frequency shifts, frequency dependent absorption and very limited bandwidth are but some of the challenges to overcome. OFDM essentially provides the parallel transmission of symbols in the frequency domain by simultaneously modulating many closely spaced orthogonal subcarriers. The resulting long parallel symbol rate together with the cyclic extension of symbols render the signal robust against intersymbol interference (ISI) caused by multipath propagation. Intercarrier interference (ICI) between the overlapping frequency responses of subcarriers is mitigated by their property of orthogonality. Doppler spread contributes to the loss of orthogonality and can result in severe ICI. A method of measuring the Doppler shift by means of including a preamble and postamble symbol with each data frame is proposed. The detected frequency offset is corrected by resampling the frame at the desired sample rate. Not only do the ambles serve as a mechanism for timing and frequency synchronisation, but they are also applied in the channel estimation process. The equalisation of channel response is required for the coherent demodulation of the received symbols. An investigation into different phase shift keying (PSK) and quadrature amplitude modulation (QAM) constellations reveal optimal arrangements for minimal symbol errors. The optimised QAM constellations do not lend themselves to Gray-coding, so that an efficient interleaving scheme is needed to mitigate the non-uniform distribution of bit errors among symbol errors. Forward error correction is provided via a Bose Chaudhuri Hocquenghem (BCH) block code. Variable code rates, together with the ability to switch between different constellations, enable the modem to perform so-called variable modulation in an attempt to maximise the throughput under specific channel conditions. The modulation/demodulation scheme is wholly defined in software as to provide flexibility and facilitate experimentation with different signal processing methods. The accompanying hardware platform allows for the transmission of a pre-generated signal and the recording of a received signal for off-line processing. The prototype design serves as a proof of concept and thus provides only simplex communication. Field tests over limited distances demonstrate the successful operation of the prototype modem. We conclude that OFDM is indeed a suitable modulation technique for acoustic underwater communication. / AFRIKAANSE OPSOMMING: Hierdie tesis ondersoek die toepassing van ortogonale frekwensiedeling multipleksering (OFDM) as modulasie tegniek op ʼn onderwater kommunikasie modem. Die onderwater omgewing bied vele uitdagings vir akoestiese kommunikasie. Lang vertraging-verstrooiings as gevolg van multipad voortplanting, Doppler frekwensieskuif, frekwensieafhanklike absorpsie, en beperkte bandwydte is van die uitdagings wat oorkom moet word. In essensie bied OFDM die parallelle versending van ʼn aantal simbole deur die gelyktydige modulasie van verskeie nou-gespasieerde subdraers in die frekwensiegebied. Die gevolglike lang parallelle simboolperiodes, tesame met die sikliese uitbreiding van simbole, verleen immuniteit teen intersimbool steurnisse (ISI) wat ontstaan as gevolg van multipad voortplanting. Die ortogonaliteit van naburige draers in die frekwensiegebied beperk interdraer steuring (ICI) tussen hul oorvleuelende frekwensie weergawes. Doppler frekwensieskuif kan egter lei tot die verlies aan ortogonaliteit en bydra tot ernstige interdraer steurings. ʼn Metode wat gebruik maak van aanhef en slot simbole, ingesluit by elke raam, word voorgestel om die Dopplerskuif te meet. Die bepaalde frekwensieafset word gekorrigeer deur die monstertempo van die raam aan te pas na die verlangde tempo. Buiten die tyd- en frekwensie-sinkronisasie funksies van die aanhef en slot simbole, speel dit ook ʼn belangrike rol in die ontrekking van die frekwensie weergawe van die kanaal. Die effening van die kanaal se frekwensieweergawe is noodsaaklik vir die koherente demodulasie van die ontvangde simbole. ʼn Ondersoek na verskillende fase verskuif sleuteling (PSK) en kwadratuur amplitude modulasie (QAM) konstellasies het optimale rangskikkings opgelewer vir minimale simboolfoute. Hierdie optimale QAM konstellasies verleen hulself egter nie na Gray-kodering nie. ʼn Effektiewe invlegtegniek is nodig om die nie-uniforme verspreiding van bisfoute tussen simboolfoute te beperk. Fout korrigering funksionaliteit word gebied deur ʼn Bose Chaudhuri Hocquenghem (BCH) blokkode. Verstelbare koderingstempo’s en die vermoë om tussen verskillende konstellasies te skakel, stel die modem in staat om sogenaamde verstelbare modulasie te gebruik in ʼn poging om die data deurset te optimeer onder spesifieke kanaal kondisies. Die modulasie en demodulasie skema is volledig in sagteware gedefinieer. Dit verleen buigbaarheid en vergemaklik eksperimentering met verskeie seinverwerkingstegnieke. Die meegaande hardeware platvorm stel die modem in staat om vooraf opgewekte seine uit te saai en rou ontvangde siene op te neem vir na-tydse verwerking. Die prototipe ontwerp dien as ʼn konseptuele bewys en bied dus slegs simplekse kommunikasie. Die suksesvolle werking van die modem is gedemonstreer deur toetsing oor beperkte afstande. Hieruit word afgelei dat OFDM inderdaad geskik is vir akoestiese onderwater kommunikasie.

Thesis (MEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Large close range environmental reflections or poor isolation between the transmit and receive paths of an FMCW radar can overload the receiver. The In phase and Quadrature phase (IQ) Reflected Power Canceller (RPC) provides a solution to the problem by cancelling any close range reflections. In this study a procedure to optimise the design of an RPC is developed and the performance limits of a practical RPC is investigated in depth. There are four focus areas in the evaluation and design of the IQ Reflected Power Canceller. First, an analysis was performed on a theoretical IQ Reflected Power Canceller, which provided insight into how the system functioned and made it possible to identify practical application issues that would arise during the design. The next focus area was the IQ Reflected Power Canceller’s dynamic range. Equations, based on the power and noise characteristics of each component in the canceller, were derived. From these equations, a system, with an optimised dynamic range, could be developed. Next, the IQ Reflected Power Canceller’s feedback loop stability was investigated. The canceller is an active negative feedback control system but, in order to obtain the negative feedback, the feedback signal has to be phase shifted by 180 degrees to the phase of the input signal. An analysis of the canceller’s RF phase contribution resulted in an equation that can be used to manage the nett RF phase in the feedback loop. The evaluation model of the IQ Reflected Power Canceller produced favourable results. The tests performed on the system included measuring the level of cancellation that can be achieved, whether the dynamic range corresponds to the predicted values and the amount of RF phase error that can be introduced in the feedback path while maintaining a stable system. The IQ Reflected Power Canceller was found to perform well in the evaluation. It provided a cancellation of more than 45 dB for close range reflections and the canceller remained stable across a wide range of RF centre frequencies (1 GHz). This means that the FMCW radar’s frequency modulation bandwidth will not be limited because of the IQ Reflected Power Canceller. The evaluation clearly showed that the modulator in the feedback loop is the critical element that determines the dynamic range of the radar with an RPC. / AFRIKAANSE OPSOMMING: Onvoldoende isolasie tussen die sender en ontvanger van ’n Frekwensie Gemoduleerde Kontinu Golf radar, sowel as groot weerkaatsings vanaf voorwerpe in die omgewing van die radar, veroorsaak dat die ontvanger versadig. Hierdie beperking veroorsaak dat die radar ’n verminderde dinamiese bereik het, en daarmee ook dat die radar se maksimum teiken-afstand verminder word. Die IQ Gereflekteerde Drywingskanselleerder kan as ’n oplossing gebruik word teen hierdie ongewenste refleksies. Hierdie navorsing poog om ’n kanselleerder te evalueer met die eind doel gestel daarop om ’n praktiese stelsel aanmekaar te sit. Die kanselleerder word geëvalueer deur na vier fokus areas te kyk. Eerstens word ’n ideale model opgestel, wat ’n beter begrip van die kanselleerder bewerkstellig. Uit hierdie ideale model, is daar praktiese oorwegings wat die kanselleerder affekteer, geïdentifiseer. Ten einde die dinamiese bereik van die radar ontvanger te verbeter, word ’n metode afgelei wat gebruik word om die kanselleerder se dinamiese bereik te optimeer. Hierdie metode neem die maksimum drywingsbeperkinge van die komponente in die kanselleerder in ag. Die kanselleerder is ’n aktiewe terugvoer beheerstelsel, en aangesien ’n sommeerder in die terugvoer lus gebruik word, moet die fase deur die lus met 180 grade geskuif word om sodoende ’n kansellerende sein by die ontvangde sein te tel. Die RF fase foute in die kanselleerder word geanaliseer deur ’n nie-ideale model van die kanselleerder op te stel. Hierdie nie-ideale model maak dit moontlik om die effek van ’n RF fase fout op die kanselleerder se stabiliteit te ondersoek. ’n Praktiese kanselleerder is ontwerp uit die inligting wat versamel is gedurende die evaluasie, en ’n werkende stelsel is aanmekaar gesit. Met hierdie praktiese kanselleerder is die hoeveelheid drywing-onderdrukking wat bereik kan word, gemeet. Die dinamiese bereik van die kanselleerder is ook bepaal en vergelyk met die teoreties berekende waardes. Die aannames oor die effek van die RF fase fout in die kanselleerder, is bevestig deur metings te neem. Goeie resultate is met die kanselleerder behaal. ’n Kansellasie van meer as 45 dB is gemeet vir naby-geleë refleksies. Die kanselleerder het ook stabiel gebly oor ’n wye band van senter-frekwensies (1 GHz). Dus sal die Frekwensie Gemoduleerde Kontinu Golf radar se modulasie bandwydte nie beperk word as gevolg van die kanselleerder nie. Uit die evaluasie is daar gevind dat die modulator die kritieke element in the kanselleerder se terugvoer lus is, dus bepaal die modulator die dinamiese bereik van die radar met ’n kanselleerder.

Made available in DSpace on 2014-12-17T14:55:50Z (GMT). No. of bitstreams: 1 AndersonMCS_DISSERT.pdf: 542550 bytes, checksum: cf969edd5c8c6cd5c0f0dcbf4f8113e0 (MD5) Previous issue date: 2011-07-26 / The modern society depends on an efficient communications system able to of transmitting and receiving information with a higher speed and reliability every time. The need for ever more efficient devices raises optimization techniques of microstrip devices, such as techniques to increase bandwidth: thicker substrates and substrate structures with EBG (Electromagnetic Band Gap) and PBG (Photonic Band Gap). This work has how aims the study of the application of PBG materials on substrates of planar structures in microstrip, more precisely in directional quadrature couplers and in rat-race and impedance of transformers. A study of the planar structures in microstrip and substrates EBG is presented. The PBG substrates can be used to optimize the radiation through the air, thus reducing the occurrence of surface waves and the resulting diffraction edge responsible for degradation of radiation pattern. Through specific programs in FORTRAN Power Station obtained the frequencies and couplings for each structure. Are used the program PACMO - Computer Aided Design in Microwave. Results are obtained of the frequency and coupling devices, ranging the frequency band used (cellular communication and Wimax systems) and the permittivity of the substrate, comparing the results of conventional material and PBG materials in the s and p polarizations. / A sociedade moderna depende de um eficiente sistema de comunica??es, capaz de transmitir e receber informa??es com uma velocidade e confiabilidade maiores a cada momento. A necessidade de dispositivos cada vez mais eficientes faz surgir t?cnicas de otimiza??o dos dispositivos em microfita, como por exemplo, t?cnicas para aumentar a largura de banda: substratos mais espessos e estruturas com substratos de Banda Eletromagn?tica Proibida - EBG (Electromagnetic Band Gap) e Banda Fot?nica Proibida - PBG (Photonic Band Gap). Este trabalho tem como objetivo o estudo da aplica??o de materiais EBG/PBG em substratos de estruturas planares em microfita, mais precisamente em acopladores direcionais em quadratura e em anel e em transformadores de imped?ncias. ? apresentado um estudo das estruturas planares em microfita e dos substratos EBG/PBG. Substratos PBG podem ser usados para otimizar a irradia??o pelo ar, reduzindo assim a ocorr?ncia de ondas superficiais e a conseq?ente difra??o de borda respons?vel pela degrada??o do diagrama de radia??o. Atrav?s de programas espec?ficos em FORTRAN obtiveram-se as freq??ncias e acoplamentos para cada estrutura. Foi utilizado o programa PACMO Projeto Auxiliado por Computador para Microondas. S?o obtidos resultados da freq??ncia e acoplamentos dos dispositivos, variando-se banda de freq??ncia utilizada (sistemas de comunica??o celular e Wimax) e a permissividade do substrato, comparando-se os resultados de materiais convencionais e materiais PBG nas polariza??es s e p.

Orientador: Marco Lucio Bittencourt / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-10T12:57:32Z (GMT). No. of bitstreams: 1 Vazquez_ThaisGodoy_D.pdf: 11719751 bytes, checksum: c6d385d6a6414705c9f468358b8d3bea (MD5) Previous issue date: 2008 / Resumo: Este trabalho tem por objetivo principal o desenvolvimento de funções de interpolaçao e regras de integraçao tensorizaveis para o Metodo dos Elementos Finitos (MEF) de alta ordem hp, considerando os sistemas de referencias locais dos elementos. Para isso, primeiramente, determinam-se ponderaçoes especficas para as bases de funçoes de triangulos e tetraedros, formada pelo produto tensorial de polinomios de Jacobi, de forma a se obter melhor esparsidade e condicionamento das matrizes de massa e rigidez dos elementos. Alem disso, procuram-se novas funçoes de base para tornar as matrizes de massa e rigidez mais esparsas possiveis. Em seguida, escolhe-se os pontos de integraçao que otimizam o custo do calculo dos coeficientes das matrizes de massa e rigidez usando as regras de quadratura de Gauss-Jacobi, Gauss-Radau-Jacobi e Gauss-Lobatto-Jacobi. Por fim, mostra-se a construçao de uma base unidimensional nodal que permite obter uma matriz de rigidez praticamente diagonal para problemas de Poisson unidimensionais. Discute-se ainda extensoes para elementos bi e tridimensionais / Abstract: The main purpose of this work is the development of tensor-based interpolation functions and integration rules for the hp High-order Finite Element Method (FEM), considering the local reference systems of the elements. We first determine specific weights for the shape functions of triangles and tetrahedra, constructed by the tensorial product of Jacobi polynomials, aiming to obtain better sparsity and numerical conditioning for the mass and stiffness matrices of the elements. Moreover, new shape functions are proposed to obtain more sparse mass and stiffness matrices. After that, integration points are chosen that optimize the cost for the calculation of the coefficients of the mass and stiffness matrices using the rules of quadrature of Gauss-Jacobi, Gauss-Radau-Jacobi and Gauss-Lobatto-Jacobi. Finally, we construct an one-dimensional nodal shape function that obtains an almost diagonal stiffness matrix for the 1D Poisson problem. Extensions to two and three-dimensional elements are discussed. / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2014-11-21T14:25:51Z No. of bitstreams: 2 Dissertação - Túlio Guimarães Marques - 2013.pdf: 3490137 bytes, checksum: a39789fad1b421e22443faee08545072 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2014-11-24T10:17:57Z (GMT) No. of bitstreams: 2 Dissertação - Túlio Guimarães Marques - 2013.pdf: 3490137 bytes, checksum: a39789fad1b421e22443faee08545072 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-11-24T10:17:57Z (GMT). No. of bitstreams: 2 Dissertação - Túlio Guimarães Marques - 2013.pdf: 3490137 bytes, checksum: a39789fad1b421e22443faee08545072 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-03-01 / Outras / This paper aims at introducing the science which is behind the most intriguing number known to history, the number . It has challenged generations of researchers who have tried to determine its value and articulate several areas of Mathematics such as Geometry, Algebra and Analysis. The quotient of ratio between the measure of the length of a circumference and the measure of its diameter are what de ne . Some historical references such as Archimedes, Euler, Leibniz and Lindemann have signi cantly contributed with the methods to precise . The rst real academic approach to this ratio was studied by the greatest mathematician of antiquity, Archimedes, when he created an instructive process for the study of the limits. With the unsolvable problem of the quadrature of the circle, ingenious geometrical constructions are born, in order to allow the drawing, with a ruler and compass, of a square having the same area as a previous given circle. The evolution of the forms employed in order to calculate have become more evident with the introduction of Analysis applied under the foundations of Calculus. At that time, the Series come to life, indispensable tools allowing the study of the behaviour of its decimal places. Along with the advances brought by them, the investigations turned towards the classi cation concerning the rationality or the irrationality of the number. In the end, we will present some contextualization and propose exercises with the aim of stimulating the search for knowledge. / O trabalho a seguir apresenta a ciência por trás do número mais intrigante da história, o número . Ele tem desa ado gerações de pesquisadores a determinar o seu valor e articular as várias áreas da matemática, como a Geometria, a Álgebra e a Análise. O quociente da razão entre a medida do comprimento de uma circunferência e a medida de seu diâmetro de ne . Algumas referências históricas, entre eles, Arquimedes, Euler, Leibniz e Lindemann, contribuíram signi cantemente nos métodos para precisar . A primeira abordagem realmente acadêmica dessa razão foi estudada pelo maior matemático da antiguidade, Arquimedes, quando ele criou um processo instrutivo no estudo dos limites. Com o insolúvel problema da quadratura do círculo, surgem construções geométricas engenhosas na tentativa de desenhar, com régua e compasso, um quadrado de mesma área de um círculo dado. A evolução das formas utilizadas para o cálculo do tornou-se mais evidente com a introdução da Análise aplicada nos fundamentos do Cálculo. Neste momento, surgem as Séries, ferramentas indispensáveis para estudar o comportamento de suas casas decimais. Com os avanços obtidos por estas, as investigações voltaram-se para classi cação quanto a racionalidade ou irracionalidade do número . Inicialmente a irracionalidade foi provada e mais tarde sua transcendência. Por m, são apresentadas algumas contextualizações e propostas de exercícios com a tentativa de estimular a busca por conhecimento.

O objetivo principal deste trabalho é introduzir os modelos log-Birnbaum-Saunders mistos (log-BS mistos) e estender os resultados para os modelos log-Birnbaum-Saunders t-Student mistos (log-BS-t mistos). Os modelos log-BS são bastante conhecidos desde o trabalho de Rieck e Nedelman (1991) e particularmente receberam uma grande atenção nos últimos 10 anos com vários trabalhos publicados em periódicos internacionais. Contudo, o enfoque desses trabalhos tem sido em modelos log-BS ou log-BS generalizados com efeitos fixos, não havendo muita atenção para modelos com efeitos aleatórios. Inicialmente, apresentamos no trabalho uma revisão das distribuições Birnbaum-Saunders e Birnbaum-Saunders generalizada (BSG) e em seguida discutimos os modelos log-BS e log-BS-t com efeitos fixos, para os quais revisamos alguns resultados de estimação e diagnóstico. Os modelos log-BS mistos são então apresentados precedidos de uma revisão dos métodos de quadratura de Gauss Hermite (QGH). Embora a estimação dos parâmetros nos modelos log-BS mistos seja efetuada através do procedimento Proc NLMIXED do SAS (Littell et al, 1996), aplicamos o método de quadratura não adaptativa a fim de obtermos aproximações para o logaritmo da função de verossimilhança do modelo log-BS de intercepto aleatório. Com essas aproximações derivamos as funções escore e a matriz hessiana, além das curvaturas normais de influência local (Cook, 1986) para alguns esquemas de perturbação usuais. Os mesmos procedimentos são aplicados para os modelos log-BS-t de intercepto aleatório. Discussões sobre a predição dos efeitos aleatórios, teste para o componente de variância dos modelos com intercepto aleatório e análises de resíduos são também apresentados. Finalmente, comparamos os ajustes de modelos log-BS e log-BS mistos a um conjunto de dados reais. Métodos de diagnóstico são utilizados na comparação dos modelos ajustados. / The aim of this work is to introduce the log-Birnbaum-Saunders mixed models (log-BS mixed models) and to extend the results to log-Birnbaum-Saunders Student-t mixed models (log-BS-t mixed models). The log-BS models are well-known since the work by Rieck and Nedelman (1991) and particularly have received great attention in the last 10 years with various published papers in international journals. However, the emphasis given in such works has been in fixed-effects models with few attention given to random-effects models. Firstly, we present in this work a review on Birnbaum-Saunders and generalized Birnbaum-Saunders distributions and so we discuss log-BS and log-BS-t fixed-effects models for which some results on estimation and diagnostic are presented. Then, we introduce the log-BS mixed models preceded by a review on Gauss-Hermite quadrature. Although the parameter estimation of the marginal log-BS and log-BS-t mixed models are performed in the procedure NLMIXED of SAS (Littell et al., 1996), we apply the quadrature methods in order to obtain approximations for the likelihood function of the log-BS and log-BS-t random intercept models. These approximations are used to derive the respective score functions, observed information matrices as well as the normal curvature of local influence (Cook, 1986) under some usual perturbation schemes. Discussions on the prediction of the random effects, variance component tests and residual analysis are also given. Finally, we compare the fits of log-BS and log-BS-t mixed models to a real data set. Diagnostic methods are used in the comparisons.

Image segmentation is the problem of partitioning an image into meaningful parts, often consisting of an object and background. As an important part of many imaging applications, e.g. face recognition, tracking of moving cars and people etc, it is of general interest to design robust and fast segmentation algorithms. However, it is well accepted that there is no general method for solving all segmentation problems. Instead, the algorithms have to be highly adapted to the application in order to achieve good performance. In this thesis, we will study segmentation methods for blood vessels in medical images. The need for accurate segmentation tools in medical applications is driven by the increased capacity of the imaging devices. Common modalities such as CT and MRI generate images which simply cannot be examined manually, due to high resolutions and a large number of image slices. Furthermore, it is very difficult to visualize complex structures in three-dimensional image volumes without cutting away large portions of, perhaps important, data. Tools, such as segmentation, can aid the medical staff in browsing through such large images by highlighting objects of particular importance. In addition, segmentation in particular can output models of organs, tumors, and other structures for further analysis, quantification or simulation. We have divided the segmentation of blood vessels into two parts. First, we model the vessels as a collection of lines and edges (linear structures) and use filtering techniques to detect such structures in an image. Second, the output from this filtering is used as input for segmentation tools. Our contributions mainly lie in the design of a multi-scale filtering and integration scheme for de- tecting vessels of varying widths and the modification of optimization schemes for finding better segmentations than traditional methods do. We validate our ideas on synthetical images mimicking typical blood vessel structures, and show proof-of-concept results on real medical images.

This thesis is concerned with the analysis of the finite element method and the discontinuous Galerkin method for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. The weak solution loses regularity in a neighbourhood of boundary singularities, which may be at corners or at roots of the weak solution on edges. The main attention is paid to the study of error estimates. It turns out that the order of convergence is not dampened by the nonlinearity, if the weak solution is nonzero on a large part of the boundary. If the weak solution is zero on the whole boundary, the nonlinearity only slows down the convergence of the function values but not the convergence of the gradient. The same analysis is carried out for approximate solutions obtained with numerical integration. The theoretical results are verified by numerical experiments. 1

Approved for public release; distribution is unlimited. / Trellis-Coded Modulation (TCM) is employed with quadrature amplitude modulation (QAM) to provide error correction coding with no expense in bandwidth. There are two common implementations of TCM, namely pragmatic TCM and Ungerboeck TCM. Both schemes employ Viterbi algorithms for decoding but have different code construction. This thesis investigates and compares the performance of pragmatic TCM and Ungerboeck TCM by implementing the Viterbi decoding algorithm for both schemes with 16-QAM and 64-QAM. Both pragmatic and Ungerboeck TCM with six memory elements are considered. Simulations were carried out for both pragmatic and Ungerboeck TCM to evaluate their respective performance. The simulations were done using Matlab software, and an additive white Gaussian noise channel was assumed. The objective was to ascertain that pragmatic TCM, with its reduced-complexity decoding, is more suitable to adaptive modulation than Ungerboeck TCM. / Civilian