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PURPOSE: The purpose of this paper is to use Dynamic Time Warping algorithm along with two statistical tests, Fourier transform and Random permutation, to analyze the similarity of company charts based on stock market data., DESIGN/METHODOLOGY/APPROACH: The analyzed data from the Warsaw Stock Exchange will detect the similarity between different companies at different and the same time, and between different times for the same company. The research has been carried out based on data from the Warsaw Stock Exchange for selected companies on which DTW analysis has been performed, using AAiFT (Fourier transformations) and RP (Random permutations)., FINDINGS: Obtained results indicate that it is possible to detect high similarity between charts by DTW and verify this similarity using statistical tests. Boundary conditions were indicated for the analyses performed and various analysis cases were investigated., PRACTICAL IMPLICATIONS: Conducted research reveals the relevance of the use of DTW in a financial context and the possibility of further development as a tool to support investing., ORIGINALITY/VALUE: Previous analyses using the DTW method have not included the use of statistical tests in the analysis of the resulting similarity. The use of such a solution is of particular importance in stock market data, allowing the analysis and detection of similarity, along with the determination of the probability of its occurrence., peer-reviewed

Orientador: Nancy Lopes Garcia Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica Resumo: Quando novas tecnologias para tingimento de tecidos são desenvolvidas, avaliar a qualidade dessas técnicas envolve a medição da homogeneidade de cores resultante através de imagens. A presença da textura do tecido cria uma estrutura de dependência sofisticada para as cores dos pixels. A transformada de Fourier é utilizada juntamente com técnicas de regularização para separar o efeito da textura das imagens. As imagens são então modeladas por campos aleatórios de Markov ocultos e bases de Fourier como covariáveis possibilitando, assim, uma avaliação da homogeneidade de cores baseada em entropia, utilizando apenas a parte correspondente ao tingimento Abstract: When new textile dyeing technologies are developed, evaluating the quality of these techniques involves measuring the resulting color homogeneity using digital images. The presence of a texture effect caused by the fabric creates a sophisticated dependence structure in pixels coloring. Fourier transform is used with regularization techniques to remove the texture signal from the image. Images are then modeled as a hidden Markov random field and Fourier basis as covariates, allowing an entropy-based evaluation of color homogeneity using the filtered signal that corresponds to the dyeing process only Mestrado Estatística Mestre em Estatística CAPES

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Àlex Haro, [eng] Within the field of dynamical systems, one shall find a special sort of systems, systems that revolve around external perturbations, either periodic or quasi-periodic, the so called skew-product dynamical systems. Even though the study of these systems can be a very helpful source of tools for an engineering or more practical work that may present systems alike, the main focus of this project is of a more theoretical nature. What is about to be presented is an approach to response solutions of such perturbated systems and the proof of existence and uniqueness of invariant fiberwise hyperbolic tori given an approximate torus of such characteristics, and the further expression of the proof’s conditions in computable terms via Fourier transforms. Besides the theoretical part, it is also provided an algorithm and its respective computational implementation that allows to simplify the expression of the linear dynamics of a system under a quasi-periodic perturbation into a diagonal matrix at the cost of an error that will significantly decrease at each step of the algorithm.

In this letter, we present the first detailed numerical comparison of two promising all-optical schemes to demultiplex orthogonal frequency-division multiplexing (OFDM) signals. The investigated schemes are the optical discrete Fourier transformation (O-DFT) and the optical spectral magnification (SM) based on time lenses. In the former scheme, cascaded delay-interferometers (DIs) are used to perform the O-DFT, with subsequent active optical gating to remove the intercarrier interference (ICI). Here, a reduced-complexity partial O-DFT, realized by replacing a number of DIs with optical bandpass filters, is investigated. In the latter scheme, the OFDM spectrum is magnified, allowing for simple optical bandpass filtering of the individual subcarriers with reduced ICI. Ideally, only a single unit consisting of two time lenses is needed, reducing the complexity and potentially the energy consumption compared with the type of O-DFT scheme relying on many active gates. The bit-error-rate is estimated down to $\sim 10^{\mathrm {\mathbf {-6}}}$ by Monte Carlo bit-error counting for a 32-subcarrier OFDM input signal, showing that a performance close to the ideal O-DFT is achievable for both the reduced-complexity O-DFT and the SM scheme.

Agradecimentos: The authors would like to thank the funding agencies for financial aid for research: FAPESP/CEPID (05/51689-2) and (11/51959-0); CNPq/INCT (573.916/2008-0) and (573913/2008-00); CNPq/PQ (312397/2013-5); CAPES/PROCAD (8881.068505/2014-01) and FAPEAM Programa RH-POSGRAD Abstract: Thousands of people die every year from burn injuries. The aim of this study is to evaluate the feasibility of high intensity femtosecond lasers as an auxiliary treatment of skin burns. We used an in vivo animal model and monitored the healing process using 4 different imaging modalities: histology, Optical Coherence Tomography (OCT), Second Harmonic Generation (SHG), and Fourier Transform Infrared (FTIR) spectroscopy. 3 dorsal areas of 20 anesthetized Wistar rats were burned by water vapor exposure and subsequently treated either by classical surgical debridement, by laser ablation, or left without treatment. Skin burn tissues were non-invasively characterized by OCT images and biopsied for further histopathology analysis, SHG imaging and FTIR spectroscopy at 3, 5, 7 and 14 days after burn. The laser protocol was found as efficient as the classical treatment for promoting the healing process. The study concludes to the validation of femtosecond ultra-short pulses laser treatment for skinburns, with the advantage of minimizing operatory trauma FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ COORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPES FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DO AMAZONAS - FAPEAM Aberto

Line shape parameters including the half-widths and the off-diagonal elements of the relaxation matrix have been calculated for self-broadened NH3 lines in the perpendicular nu4 band. As in the pure rotational and the parallel nu1 bands, the small inversion splitting in this band causes a complete failure of the isolated line approximation. As a result, one has to use formalisms not relying on this approximation. However, due to differences between parallel and perpendicular bands of NH3, the applicability of the formalism used in our previous studies of the nu1 band and other parallel bands must be carefully verified. We have found that, as long as potential models only contain components with K1 = K2 = 0, whose matrix elements require the selection rule ∆k = 0, the formalism is applicable for the nu4 band with some minor adjustments. Based on both theoretical considerations and results from numerical calculations, the non-diagonality of the relaxation matrices in all the PP, RP, PQ, RQ, PR, and RR branches is discussed. Theoretically calculated self-broadened half-widths are compared with measurements and the values listed in HITRAN 2012. With respect to line coupling effects, we have compared our calculated intra-doublet off-diagonal elements of the relaxation matrix with reliable measurements carried out in the PP branch where the spectral environment is favorable. The agreement is rather good since our results do well reproduce the observed k and j dependences of these elements, thus validating our formalism.

Agradecimentos: National Institute of Standards and Technology (NIST) Greenhouse Gas and Climate Science Measurements; DARPA SCOUT Program; Fundacao de Amparo a Pesquisa no Estado de Sao Paulo (FAPESP); (2014/10125-8, 2011/13777-8, 2013/19093-9, 2008/57857-2); Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq); (229211/2013-5, 574017/2008); This paper is a contribution of the US government and is not subject to copyright in the US Abstract: Terahertz dual frequency comb spectro scopy (THz-DFCS) yields high spectral resolution without compromising bandwidth. No netheless, the resolution of THz-DFCS is usually limited by the laser repetition rate, which is typically between 80 MHz and 1 GHz. In this paper, we demonstrate a new method to achieve sub-repetition rate resolution in THz-DFCS by adaptively modifying the effective laser repetition rate using integrated Mach-Zehnder electro-optic modulators (MZ-EOMs). Our results demonstrate that it is possible to improve the 100 MHz resolution of a terahertz frequency comb by at least 20x (down to 5 MHz) across the terahertz spectrum without compromising the average output power, and to a large extent, its bandwidth. Our approach can augment a wide range of existing THz-DFCS systems to provide a significant and easily adaptable resolution improvement FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQ Aberto

[spa] El teorema de equidistribución de Bilu establece que, dada una sucesión estricta de puntos en el toro algebraico N-dimensional cuya altura de Weil tiende a cero, las órbitas de Galois de los puntos se equidistribuyen con respecto a la medida de Haar de probabilidad del policírculo unidad. Para el caso unidimensional, versiones cuantitativas de este resultado fueron obtenidas independientemente por Petsche y por Favre y Rivera-Letelier. Se presenta en esta tesis una versión cuantitativa del resultado de Bilu para el caso de dimensión cualquiera. Dado un punto en el toro algebraico de dimensión N de altura de Weil menor que 1, se proporciona una cota para la integral de una determinada función test en P1(C)N con respecto a la medida signada definida como la diferencia de la medida discreta de probabilidad asociada a la órbita de Galois del punto y la medida de probabilidad soportada en el policírculo unidad, donde coincide con la medida de Haar normalizada. Esta cota está dada en términos de una constante que depende únicamente de la función test, de la altura de Weil del punto, y de una noción que generaliza a dimensión superior el grado de un número algebraico. Para la demostración de este resultado se utiliza el análisis de Fourier para la descomposición del problema y, a través de proyecciones, se reduce al caso unidimensional donde aplicamos la versión cuantitativa de Favre y Rivera-Letelier., [cat] El teorema d’equidistribució de Bilu estableix que, donat una successió de punts en el tor algebraic N-dimensional amb altura de Weil que tendeix cap a zero, les òrbites de Galois dels punts es equidistribueixen respecte de la mesura de Haar de probabilitat del policercle unitat. Per al cas unidimensional, versions quantitatives d’aquest resultat van ser obtingudes independentment per Petsche, i per Favre I Rivera-Letelier. Es presenta en aquesta tesi una versió quantitativa del resultat de Bilu per al cas de dimensió qualsevol. Donat un punt en el tor algebraic de dimensió N d’altura de Weil més petita que 1, es proporciona una fita per a l’integral d’una determinada funció test en P1(C)N respecte de la mesura signada definida com la diferència de la mesura discreta de probabilitat associada a l’òrbita de Galois del punt i la mesura de probabilitat suportada en el policercle unitat, on coincideix amb la mesura de Haar normalitzada. Aquesta fita ve donada en termes d’una constant que depèn únicament de la funció test, de l’altura de Weil del punt, i d’una noció que generalitza a dimensió superior el grau d’un nombre algebraic. Per a la demostració d’aquest resultat s’utilitza l’anàlisi de Fourier per la descomposició del problema i, mitjançant projeccions, es redueix al cas unidimensional on apliquem la versió quantitativa de Favre i Rivera-Letelier.

This paper is devoted to the proof of boundedness of bilinear smooth square functions. Moreover, we deduce boundedness of some bilinear pseudo-differential operators associated with symbols belonging to a subclass of $BS^0_{0,0}$., Comment: 27 pages

Starting from the refined Robert-Bonamy formalism [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)], we propose here an extension of line mixing studies to infrared absorptions of linear polyatomic molecules having stretching and bending modes. The present formalism does not neglect the internal degrees of freedom of the perturbing molecules, contrary to the energy corrected sudden (ECS) modelling, and enables one to calculate the whole relaxation matrix starting from the potential energy surface. Meanwhile, similar to the ECS modelling, the present formalism properly accounts for roles played by all the internal angular momenta in the coupling process, including the vibrational angular momentum. The formalism has been applied to the important case of CO2 broadened by N2. Applications to two kinds of vibrational bands (Σ → Σ and Σ → Π) have shown that the present results are in good agreement with both experimental data and results derived from the ECS model.

WOS: 000350191000030, In this study, two different types of Phase Change Materials (PCM) suitable for Thermal Energy Storage (TES) applications were used as a core material in a microencapsulation process. The wall material for these microencapsulated PCM (MPCM) was Poly(styrene-co-ethylacrylate) (PScEA). Microcapsules were prepared using an emulsion co-polymerization technique. The prepared MPCM were characterized as follows: morphology, shape and size were analyzed by Scanning Electron Microscopy (SEM) and Particle Size Distribution (PSD). Besides, Fourier Transformed Infrared spectroscopy (FT-IR) was used to perform the chemical characterization of the shell microcapsules. Moreover, thermophysical properties were analyzed by Differential Scanning Calorimetry (DSC) for the two PCM in usage (paraffin 42-44 and palmitic acid) meanwhile the thermal stability was evaluated by Thermogravimetrical Analysis (TGA). Mechanical characterization of the prepared microcapsules was performed by using the Atomic Force Microscopy (AFM) as indentor. Experiments were performed at two different temperatures 25 degrees C and 70 degrees C, and two parameters were evaluated: the Young's modulus on a punctual area and the vertical force required to plastically deform the MPCM. At the light of the results, it can be considered that these synthesized MPCM were successfully prepared being able to be used in a TES system. (C) 2014 Elsevier Ltd. All rights reserved., Spanish government [ENE2011-28269-C03-02]; European Union's Seventh Framework Programme (FP7) [PIRSES-GA-2013-610692]; Scientific & Technical Research Council of Turkey (TUBITAK) [TUBITAK 111M614], The work is partially funded by the Spanish government (ENE2011-28269-C03-02). The authors would like to thank the Catalan Government for the quality accreditation given to their research group DIOPMA (2014 SGR 1543). The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement no PIRSES-GA-2013-610692 (INNOSTORAGE). Also, preparation of microcapsules funded by The Scientific & Technical Research Council of Turkey (TUBITAK) (The Project Code: TUBITAK 111M614).

This PhD thesis consists of five complementary chapters. Chapters 2 through 4 constitute the basis of research papers to be published subsequently. These three chapters summarize the state of a single crystal undergoing elastoplastic deformation. The studies presented in this thesis primarily deal with experimental and computational concepts that enable the calculation, measurement and extraction of the spatially resolved net Burgers density vector and the geometrically necessary dislocation densities (GNDs), which reveal the small scale continuum characteristics of a single crystal in the elastoplastic state. The calculation methodology of a new validation parameter, β, which is the orientation of the net Burgers density vector, is given in chapter 2. This new parameter, β, enables us to validate the elastic-plastic constitutive relations. Since the existing methods used for validation cannot give direct information about the state of the material, the β-variable is introduced for elastic- plastic constitutive models. β-fields, which are essentially contour maps of β-variables on two dimensional spatial coordinates, are used to monitor the activity regions of effective slip systems. Chapters 2 through 4 present a comprehensive analysis of the spatially resolved net Burgers density vector, along with the length scale characterization of dislocation structures and validation of constitutive relations. The studies presented in this work are the outcome of experimental and computational research. The experimental work consists of the indentation of a nickel single crystal deformed through a quasi-statically applied line load parallel to the [110] crystallographic orientation. The line load was applied onto (001) surface of the single crystal by a tungsten carbide wedge indenter with a 90◦ included angle. A two-dimensional deformation field on an indented single crystal, in which the only non-zero lattice rotation occurs in the plane of deformation and only three effective in-plane slip systems are activated, was investigated. The mid-section of the deformed single crystal was exposed by EDM and polished electrochemically. The in-plane lattice rotations were measured by high-resolution electron backscattered diffraction (HR-EBSD). The Nye's dislocation density components, lattice curvatures, GNDs and net Burgers density vectors were calculated. Therefore, the β- variable and the β-fields are calculated both experimentally, analytically and numerically in Chapter 2. A qualitative comparison of the three methods showed that the β-field obtained from experimental measurements agrees with those obtained from analytical and numerical methods. The directions of the net Burgers density vector, which are used to determine the boundaries of the slip activity regions, are also given in Chapter 2. Chapter 3 mainly deals with the hardening parameters associated with strain hardening rules utilized in finite element simulations, and investigates the sensitivity of the β-variable to parameters such as latent hardening ratio, initial hardening modulus and saturation strength. The study revealed that a change in the saturation strength has a significant effect on both magnitude of the β-variable and the boundary of the slip activity regions. Chapter 4 presents a length scale analysis associated with dislocation structures such as cell size and cell wall width. The methods presented in this chapter employ the SEM- based continuum method and Fourier Analysis. As-measured GNDs are extracted along the local crystallographic traces, and a quasi-periodic arrangement of dislocation structures is obtained. The extracted GND functions are truncated, interpolated, and filtered. Finally, Fourier Transform is applied to obtain a relationship between cell size and cell wall width of the dislocation structures. The results are compared with those obtained by TEM micrographs. Whereas TEM micrographs characterize the dislocation structures in small scale, the method that is presented in this chapter provides multi scale characterization, which is an order of magnitude larger. Concluding remarks and recommendations for future studies are given in Chapter 5.

Background: Complex fractionated atrial electrograms (CFAE) acquired during atrial fibrillation (AF) are commonly assessed using the discrete Fourier transform (DFT), but this can lead to inaccuracy. In this study, spectral estimators derived by averaging the autocorrelation function at lags were compared to the DFT. Method: Bipolar CFAE of at least 16 s duration were obtained from pulmonary vein ostia and left atrial free wall sites (9 paroxysmal and 10 persistent AF patients). Power spectra were computed using the DFT and three other methods: 1. a novel spectral estimator based on signal averaging (NSE), 2. the NSE with harmonic removal (NSH), and 3. the autocorrelation function average at lags (AFA). Three spectral parameters were calculated: 1. the largest fundamental spectral peak, known as the dominant frequency (DF), 2. the DF amplitude (DA), and 3. the mean spectral profile (MP), which quantifies noise floor level. For each spectral estimator and parameter, the significance of the difference between paroxysmal and persistent AF was determined. Results: For all estimators, mean DA and mean DF values were higher in persistent AF, while the mean MP value was higher in paroxysmal AF. The differences in means between paroxysmals and persistents were highly significant for 3/3 NSE and NSH measurements and for 2/3 DFT and AFA measurements (p

Shape Memory Alloys (SMAs) are good candidates for solid-state dampers appropriate for the oscillations of bridge stay cables because of their large recoverable strain, hysteresis and reasonable fatigue-life. This work experimentally analyzes the relevant properties of NiTi SMA and conducts facility measurements, frequency analyzes and simulations of the effects of SMA on stay cables. Appropriate phenomenological SMA models were developed and included in a Finite Element (FE) simulation environment. A complete damping solution for bridge stay cables was developed from these experimental analyzes. This paper detail the required properties for a NiTi SMA and analyzes their performance. For instance, the fatigue-life and several of the thermo-mechanical effects influencing the application of NiTi SMAs are outlined. The damping effect of the SMA was studied in two facilities. The first series of measurements was performed using cable 1 of the ELSA facility (JRC-EU, Ispra, Italy). The second was completed in two campaigns at IFSTTAR (Bouguenais, near Nantes in France). The numeric analyzes and simulated results were completely coherent with these experiments: the SMA dampers also drastically reduce the maximum oscillation amplitude induced by the simulated action. The frequency evolution of the damped cable was studied using direct calculations on the signals, the windowed Fourier transform and Morlet wavelets.

M.Ing. This work comprises the implementation and comparison of five design techniques for the design of gradient-index thin film optical filters: classical rugate, inverse Fourier transform, a wavelet-based design procedure, as well as the flip-flop and the genetic optimization techniques. Designs for a high-reflectance filter, a beamsplitter, a discrete level filter, a distributed filter, and an anti-reflection coating were used to compare the various filter synthesis techniques. The optical thickness of the various examples was maintained below 30 and the refractive index excursion limits were between 1.5 and 3.2. The overall performance of a specific design was evaluated by a weighted merit function. The classical rugate filter uses a sinusoidal refractive index modulation that produces a single reflection band. More complex filters are realized by linear superposition of these elementary profiles. Sidelobe and ripple suppression are obtained by applying quintic windowing functions to the refractive index profile and adding matching layers at the edges of the filter. This filter design procedure has the best figure of merit of 3.73 for the discrete level filter, and the second best of 3.09 for the high-reflectance filter. The inverse Fourier transform links the refractive index profile and reflection spectrum of an optical filter by an approximate relation. It is self-correcting and iterative in nature. It produces filters with the highest optical density. The procedure excels in the design of the distributed filter with a figure of merit of 4.17. Mortlett's wavelet is used as the basis of the wavelet design technique. A single wavelet yields a single reflection band, similar to the classical rugate filter. Sidelobe suppression is an inherent property of the method, but matching layers are needed for passband ripple suppression. The optical density of the high reflection filter is larger for a filter designed with this method than for the equivalent classical rugate filter. The figure of merit of 1.75 for the high-reflectance filter is the best for any of the designs. Flip-flop refinement is a brute force approach to filter design. The layers of a starting design are flipped between two values of refractive index, the change in figure of merit evaluated and the best case saved. This process is repeated for a fixed number of iterations. It is computationally intensive and lacks ripple suppression characteristics. The flip-flop method does not compare well with any of the other techniques. It yields filters with the worst figures of merit for most of the design examples. However, it was applied successfully to the anti-reflection coating. The peak ripple for the anti-reflection filter in the 400 nm to 1100 nm wavelength band is 9.62 % compared to the inverse Fourier transform's 57.30 %. The genetic algorithm operates on the principle of "survival of the fittest". It is a stochastic procedure and yields quasi-random refractive index profiles. It excels with the antireflection coating. The peak ripple in the passband of the anti-reflection coating is 3.29%. The figure of merit for the anti-reflection coating designed with the genetic algorithm is 2.09.

Suppose we are given a video of a rotating object and suppose we want to determine the rate of rotation solely from the video itself and its known frame rate. In this thesis, we present a new mathematical operator called the Geometric Sum Transform (GST) that can help one determine the angular frequency of the object in question. The GST is a generalization of the discrete Fourier transform (DFT) and as such, the two transforms have much in common. However, whereas the DFT is applied to a sequence of scalars, the GST can be applied to a sequence of vectors. Most importantly, we show that the GST, like the DFT, can (1) be used to estimate frequency and (2) can be computed surprisingly quickly. Indeed, we provide a Fast Geometric Sum Transform (FGST) algorithm that computes the GST in O(N logN) matrix-vector multiplications, where N is the number of images in the video sequence. This is a vast improvement over the O(N2) such multiplications required for a direct computation of the GST. The remainder of this thesis is devoted to proving other properties of the GST and giving proof-of-concept numerical examples.

A review of current signal analysis tools show that new techniques are required for an enhanced fidelity or data integrity. Recently, the Hilbert-Huang transform (HHT) and its inherent property, the Empirical Mode Decomposition (EMD) technique, have been formerly investigated. The technique of Complex EMD (CEMD) was also explored. The scope of this work was to assess the CEMD technique as an innovative analysis tool. Subsequent to this, comparisons between applications of the Hilbert transform (HT) and the Fast-Fourier transform (FFT) were analyzed. MATLAB was implemented to model signal decomposition and the execution of mathematical transforms for generating results. The CEMD technique successfully decomposed the data into its oscillatory modes. After comparative graphical analysis of the HT and FFT, application of the HT provided marginal enhancements of the data modeled previously by the FFT. Altogether, the HHT could not be determined as a helpful analysis tool. Nevertheless, the CEMD technique, an inherent component of the HHT, exhibited a possible improvement as an analysis tool for signal processing data. Further evaluation of the CEMD technique and the HHT is needed for ultimate determination of their usefulness as an analysis tool.

M.Ing. Along with the increased use of power-electronic devices, there has been an increase in the magnitudes of distorted currents. Much of the power-theory in use today was devised many decades ago, mostly for AC-systems with clean sinusoidal voltages and currents. Modem loads are more often no longer mostly linear. Against the background of a study in the basic mathematics underlying AC power theory, a few techniques concerned with per-frequency power were examined. In addition certain concerns surrounding the use of correlation indexes for the purposes of load identification were also examined.

In this article part of the techniques and developments we are carrying out within the INCO2 group are reported. Results follow the interdisciplinary approach with which we tackle signal processing applications. Chosen case studies show different stages of development: We present algorithms already completed which are being used in practical applications as well as new ideas that may represent a starting point, and which are expected to deliver good results in a short and medium term.

Conventional approaches for a distributed low probability of detection communications system with a large number of unique transmitters and a single or a few receivers, require receiver complexity proportional to the number of transmitters. To improve efficiency in terms of receiver complexity, two alternative designs are analyzed and compared to a reference receiver, whose complexity grows linearly as the number of transmitters increases. The first alternative system groups the transmitters into clusters whose pseudorandom noise codes have some chips in common. The resulting receiver would then perform two stages of processes: identification of the transmitting cluster and received bit detection. The total number of processes required for any given transmitter would be substantially less than the traditional receiver. The second alternative design would utilize a common long spreading code and a shorter cyclically shifted spreading code in each transmitter. The receiver utilizes the cyclic shift property of the fast Fourier transform to recover efficiently both the identity of active receivers and the data sent using a single branch. The complexity of the two proposed systems is compared to that of the reference system. http://archive.org/details/designofscalable109454577 US Navy (USN) author. Approved for public release; distribution is unlimited.

Future mobile communications systems reaching for ever increasing data rates require higher bandwidths than those typical used in todays cellular systems. By going to higher bandwidth the (for low bandwidth) at fading radio channel becomes frequency selective and time dispersive. Due to its inherent robustness against time dispersion Orthogonal Frequency Division Multiplex (OFDM) is an attractive candidate for such future mobile communication systems. OFDM partitions he available bandwidth into many subchannels with much lower bandwidth. Such a narrowband subchannel experiences now almost at fading channel. However, one potential drawback with OFDM modulation is the high Peak to Average power Ratio (PAPR) of the transmitted signal: The signal transmitted by the OFDM system is the superposition of all signals transmitted in the narrowband subchannels. The transmit signal has then due to the central limit theorem a Gaussian distribution leading to high peak values compared to the average power. system design not taking this into account will have a high clip rate. Each signal sample that is beyond the saturation limit of the power amplier suersither clipping to this limit value or other non- linear distortion, both creating additional bit errors in the receiver. One possibility to avoid clipping is to design he system for very high signal peaks. However, this approach leads to very high power consumption (since the power amplifier must have high supply rails) and also complex power amplifiers. The preferred solution is therefore to apply digital signal processing that reduces such high peak values in the transmitted signal thus voiding clipping. These methods are commonly referred to as PAPR reduction. APR reduction methods can be categorized into transparent methods here the receiver is not aware of the reduction scheme applied by the transmitter and on-transparent methods where the receiver needs to know the PAPR algorithm applied by the transmitter. This master thesis would focus on transparent PAPR reduction algorithms. The pulse shaping mechanism is used to reduce PAPR. he ct is analyzed in terms of BER.

Fast Fourier Transform (FFT) processors are today one of the most important blocks in communication systems. They are used in every communication system from broadband to 3G and digital TV to Radio LANs. This master’s thesis project deals with the pipelined, radix-2 algorithmic exploration and the hardware solution for the FFT processor with the FFT size of 2N points, the selection of the scaling schemes based on application requirement is discussed. The designed architecture is functionally verified in Simulink® and the Xilinx® ISE simulator. How to encapsulate the C++ coded algorithms or functions into the Simulink. This FFT processor is used in OFDM based BPSK modulated communication system for the WHD WVAN standard at the Low Rate Physical (LRP) lay. This thesis project presents the design of the 128 point fixed–point F streaming processor. The final architecture used is the SDF (single path with delay feedback) that implements the radix-2 FFT algorithm. Since the FFT processor can’t be used standalone, so in this thesis it is employed in an OFDM Transmitter and the performance is measured for SNR over a range of PAPRs. The goal of this report is to outline the knowledge gained during the master’s thesis project, to describe a design methodology for the fixed point pipelined FFT processors, the scaling choices and how to encapsulate the existing C code into the Simulink environment to measure the performance of fixed-point systems.

Bu tezde doğrusal doğal ve kesirli Fourier dönüşümleri ile ilgili bir çok temel konu ve problem ele alındı. İlkolarak, genelleştirilmiş sonlu kaplam kısıtları altında sinyalin temsil edilmesi üzerine çalışıldı. Sonra birden çok dönüşüm bölgesinde kısmi ve artık bilgiler verildiğinde, sinyalin geri çatılması problemiyle uğraşıldı. Sinyalin temsili kısmında, herhangi iki doğrusal doğal bölgede sonlu aralıklara hapis olan sinyallerin örnekleme, serbestlik derecesi, ve zaman-sıklık tanım alanı konularına odaklanıldı. Bu sinyallerin serbestlik derecesi için zaman-bant genişliği çarpımının genellenmesi olan ikili doğrusal doğal genişlik çarpımı kavramı geliştirildi. İkili doğrusal doğal genişlik çarpımının bu sinyallerin paralelkenar şeklindeki zaman-sıklık tanım alanına karşılık geldiği ispatlandı. Ayrıca, bu sinyaller ikili doğrusal doğal genişlik çarpımına eşit sayıdaki en az örnek sayısı ile bu iki doğrusal doğal bölgede temsil edilebilir. Bu örneklerle hesaplanan ayrık doğrusal doğal dönüşümünün, sürekli doğrusal dönüşüm için oldukça iyi bir yaklaşım verdiği aralarındaki tam ilişki verilerek ispatlandı. Bunun yanısıra, rastgele sinyallerin en az örnek ile temsil edilmesi problemine, doğrusal doğal dönüşüm örnekleme teoremi kullanılarak bakıldı. Bu problemin zaman-sıklık tanım alanını içine alan en küçük paralelkenarı bulma problemine karşılık geldiği ispatlandı. Bundan yararlanılarak, ikili doğrusal doğal genişlik çarpımının sinyallerin serbestlik derecesine zaman-bant genişliği çarpımından daha çok yaklaştığı görüldü. Bu yaklaşımın temsili verimliliği için kuramsal sınırlar verildi. Ayrıca, doğrusal doğal bölgelerin zaman-sıklık düzlemi ile ilişkisi kuruldu. Her doğrusal doğal bölgenin aslında ölçeklenmiş kesirli Fourier bölgelerine karşılık geldiği ve herhangi bir doğrusal doğal bölgenin ilişkili olduğu kesir değeri ile etiketlenebileceği ispatlandı. Bu kavramlar açıklıklı optik sistemlerin incelenmesi konusunda kullanıldı. Sistemin serbestlik derecesinin bulanabilmesini sağlayan bir method geliştirildi. Bunun yanı sıra, dalganın herhangi bir düzlemde en az ne kadar örnek ile temsil edilebileceği araştırıldı. Tezin diğer kısmında ise, iki yada daha çok kesirli Fourier bölgelerinde kısmi bilgiler verildiğinde sinyalin geri çatılması üzerine çalışıldı. Bu problem için yeni bir doğrusal cebirsel yaklaşım sunuldu ve kararsızlık oranı verilen noktalar arasındaki artık bilgi miktarının ölçüsü olarak kullanıldı. Kararsızlık oranının bilinen nokta sayısı ve diziliminden nasıl etkilendiği incelenerek, verilen noktalararasındaki artıklık ve bilgi ilişkileri araştırıldı. We study a number of fundamental issues and problems associated with linear canonical transforms (LCTs) and fractional Fourier transforms (FRTs). First, we study signal representation under generalized finite extent constraints. Then we turn our attention to signal recovery problems under partial and redundant information in multiple transform domains. In the signal representation part, we focus on sampling issues, the number of degrees of freedom, and the time-frequency support of the set of signals which are confined to finite intervals in two arbitrary linear canonical domains. We develop the notion of bicanonical width product, which is the generalization of the ordinary time-bandwidth product, to refer to the number of degrees of freedom of this set of signals. The bicanonical width product is shown to be the area of the time-frequency support of this set of signals, which is simply given by a parallelogram. Furthermore, these signals can be represented in these two LCT domains with the minimum number of samples given by the bicanonical width product. We prove that with these samples the discrete LCT provides a good approximation to the continuous LCT due to the underlying exact relation between them. In addition, the problem of finding the minimum number of samples to represent arbitrary signals is addressed based on the LCT sampling theorem. We show that this problem reduces to a simple geometrical problem, which aims to find the smallest parallelogram enclosing a given time-frequency support. By using this equivalence, we see that the bicanonical width product provides a better fit to the actual number of degrees of freedom of a signal as compared to the time-bandwidth product. We give theoretical bounds on the representational efficiency of this approach. In the process, we accomplish to relate LCT domains to the time-frequency plane. We show that each LCT domain is essentially a scaled FRT domain, and thus any LCT domain can be labeled by the associated fractional order, instead of its three parameters. We apply these concepts knowledge to the analysis of optical systems with arbitrary numbers of apertures. We propose a method to find the largest number of degrees of freedom that can pass through the system. Besides, we investigate the minimum number of samples to represent the wave at any plane in the system. In the signal recovery part of this thesis, we study a class of signal recovery problems where partial information in two or more fractional Fourier domains are available. We propose a novel linear algebraic approach to these problems and use the condition number as a measure of redundant information in given samples. By analyzing the effect of the number of known samples and their distributions on the condition number, we explore the redundancy and information relations between the given data under different partial information conditions. 166

This dissertation presents two extensions to the phase vocoder method of sound analysis and synthesis, as well as an examination of the author's spectral subtraction audio works based on the phase vocoder. The phase vocoder technique has proved to be an effective method of "time stretching" musical sounds, however, some musical features of the original sounds are not maintained during the transformation. We consider here maintaining two of these aspects: noise levels, and sub-audio (vibrato and tremolo) characteristics within the phase vocoder. The noise levels are maintained by determining the "sinusoidality" of each spectral component, separating the spectral energy into sinusoidal and noise energy based on these sinusoidality measurements, and modulating the noise based spectrum before re-synthesizing with the traditional IFFT method. The vibrato and tremolo (sub-audio modulation) rates of a sound are maintained by modeling each channel of the phase vocoder in a higher order spectral domain, removing the modulations in this domain, and re-imposing them after time-dilation. Finally, several of the author's audio works involve use of the phase vocoder representation of sound to subtract spectral components from a long term average of a time varying sound. These works will be considered along with their aesthetic motivations and technical implementations

This thesis present a fully parallel novel fixed point 16-bit word width 512 point FFT processor architecture. The 512 point FFT is realized by decomposing it into three 8 point FFT units. This approach reduces the number of required complex multiplication compared to the conventional radix-2 512 point FFT algorithm. It uses an ROM unit for storing the twiddle factor. The proposed architecture is designed in XILINX 8.2i using Verilog and it is functionally verified with the MATLAB. The floorplanning and timing estimation of each basic module of the proposed architecture is done based on the macro element at 0.25 CMOS technology. The core area of this chip is 99.02 mm2. The processor compute one parallel to parallel (i.e. when all input data are available in parallel and all output data are generated in parallel) 512-point FFT computation in 422 clock pulse in 4.69sec at 90 MHz operation.

This work presents the design and ASIC implementation of Discrete Fourier Transform Processing Module. The performance of designed DFT processing module is better than radix-2 and radix-4 FFT algorithms, and is comparable to Split radix FFT algorithm, in terms of computational requirements. Different architectures are proposed for DFT processing module, and their comparative analysis is done. ASIC implementation of Discrete Fourier Transform processing module includes, its modelling using Verilog HDL, gate level synthesis of the modelled design and physical synthesis of netlist generated by gate level synthesis. The functionality of Design after physical synthesis is verified. Designed DFT processing module is retargetable and can be used as an IP.

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

We report real wave packet (WP) calculations of reaction probabilities, cross sections, rate constants, and product distributions of the reaction N(4S) + O2(X3 ) → NO(X2Π) + O(3P). We propagate initial WPs corresponding to several O2 levels, and employ reactant coordinates and a flux method for calculating initial-state-resolved observables, or product coordinates and an asymptotic analysis for calculating state-to-state quantities. Exact or J-shifting calculations are carried out at total angular momentum J=0 or J>0, respectively. We employ the recent X 2A' S3 potential energy surface (PES) by Sayós et al. and the earlier a 4A' PES by Duff et al. In comparing S3 results with the WP ones of a previous X 2A' S2 PES, we find lower S3 energy thresholds and larger S3 probabilities, despite the higher S3 barrier. This finding is due to the different features of the doublet PESs in the reactant and product channels, at the transition state, and in the NO2 equilibrium region. We analyze the effects of the O2 initial level and discuss Cs abstraction or insertion mechanisms. Tunnel effects through the S3 barrier enhance the room-temperature rate constant by ~ 3.7 times with respect to the previous S2 WP rate, thus improving the agreement with the experimental result. The NO vibrational distribution is inverted and the rotational ones are strongly oscillating. We explain these non-statistical results showing that the reaction partners approach each other with a large impact parameter. The WP vibrational distribution is however different from that observed, which is oscillating. WP calculations show that the new S3 PES describes accurately several features of the X 2A' state, although a lowering of its barrier height by ~ 0.56 kcal/mol should bring calculated and observed rate constants in full agreement.

[spa] A lo largo de este trabajo se han estudiado la estructura y propiedades del SiO(2) y de su interficie con el silicio. La estructura del sistema depende de la tecnología empleada en el crecimiento del óxido y de los tratamientos anteriores y posteriores al proceso de oxidación. Se ha realizado un análisis comparativo entre los óxidos crecidos en horno convencional y RTO. Se ha estudiado el influjo de los tratamientos térmicos de recocido. Se ha analizado la influencia de las limpiezas de la superficie del silicio anteriores al proceso de oxidación. Por ejemplo, un análisis comparativo del estado de la superficie del silicio después de un tratamiento de la superficie con limpiezas RCA con etapa final de HF diluido en agua y HF diluido en etanol. Los análisis confluyen en la presencia de una capa de óxido nativo de mayor espesor en el primer caso. La microscopia de fuerzas atómicas revela mayor rugosidad de la superficie tratada con HF diluido en agua. Se ha verificado que la ley de evolución del estrés en el óxido con respecto al tiempo de recocido sigue una ley exponencial con un tiempo de relajación característico. Se han estudiado los efectos de degradación y dañado de capas gruesas de óxido de silicio amorfo irradiadas con AR. Se han crecido capas de óxido y después se ha procedido a su implantación con dosis de iones de argón con energías entre 130 Y 150 KeV. Se ha estudiado también la recuperación de las estructuras después de un proceso de recocido. Son muchas las técnicas de análisis que se han utilizado: XPS, TEM, SEM, AFM, elipsometría, medidas eléctricas, etc. Sin embargo, nuestro trabajo ha estado en gran parte dedicado al desarrollo y aplicación de nuevas técnicas experimentales y técnicas de manipulación y de análisis relacionadas con la espectroscopia infrarroja por transformada de Fourier, para la cual se han desarrollado programas de simulación y de obtención de la función dieléctrica de las capas.

An Asynchronous Fourier Transformer [1] does not require synchronisation with multiplying chirp waveforms. This is achieved by passing a signal through a chirp delay line without first multiplying by a pre-multiplying chirp and following this with envelope detection to recover the output. The output envelope then represents a distorted Fourier Transform of the input envelope. Errors produced by the absence of the pre-multiplying chirp, envelope detection and differentiation of the detected envelope, where all phase information has been lost, have been shown [1],[4] to be derivatives of the true Fourier Transform, the first error term being the second derivative. The compensation scheme [1] thus takes the output of the delay line, differentiates it twice and subtracts the result of the differentiation from the original output, after applying to it an appropriate weighting factor. While this earlier work showed the Asynchronous Fourier Transformer to be a robust and useful device, it represented only an initial study of its practical applications. This thesis presents a more detailed study on the uses and limitations of this potentially very useful device. Results using two SAW devices are presented. The devices have centre frequencies of 107 MHz and 172 MHz, bandwidths of 20 MHz and 40 MHz, and delay lengths of 3 microseconds and 6.8 microseconds respectively. The thesis discusses the accuracy that the Asynchronous Fourier Transformer can achieve, the range of pulse widths that it can usefully be applied to and in particular its use as a simple robust frequency discriminator for radar and similar applications.

The special affine Fourier transformation (SAFT) is a generalization of the fractional Fourier transformation (FRT) and represents the most general lossless inhomogeneous linear mapping, in phase space, as the integral transformation of a wave function. Here we first summarize the most well-known optical operations on lightwave functions (i.e., the FRT, lens transformation, free-space propagation, and magnification), in a unified way, from the viewpoint of the one-parameter Abelian subgroups of the SAFT. Then we present a new operation, which is the Lorentz-type hyperbolic transformation in phase space and exhibits squeezing. We also show that the SAFT including these five operations can be generated from any two independent operations. Other funder Futaba Electronics Memorial Foundation European Commission pe, la, sp, ke, is, en - TS 22.11.11

When generating musical sound on a digital computer, it is important to have a good model whose parameters provide a rich source of meaningf ul sound transformations. Three basic model types are used widely today far musical sound generation: instrument models, spectrum models, and abstract models. Instrument models attempt to parameterize a sound at its source, such as a violin, clarinet, or vocal tract. Spectrum models attempt to parameterize a sound at the basilar membrane of the ear, discarding whatever information the ear seems to discard in the spectrum. Abstract models, such as FM, attempt to provide musically useful parameters in an abstract formula. This paper addresses the second category of synthesis technique: spectrum modeling. It describes a technique called spectral modeling synthesis (SMS), that models time-varying spectra as ( 1) a collection of sinusoids controlled through time by piecewise linear amplitude and frequency envelopes ( the de- terministic part), and (2) a time-varying filtered noise component ( the stochastic part). The analysis procedure first extracts the sinusoidal trajectories by tracking peaks in a sequence of short-time Fourier transforms. These peaks are then removed by spectral subtraction. The remaining "noise floor" is then modeled as white noise through a time- varying filter. A piecewise linear approximation to the upper spectral envelope of the noise is computed far each successive spectrum, and the stochastic part is synthesized by means of the overlap- add technique. The SMStechnique has proved to give general, high quality transformations far a wide variety ofmusical signals.

Projecte realitzat en el marc d’un programa de mobilitat amb Fraunhofer Institut Produktionsanlagen und Konstruktionstechnik (Berlin) [ANGLÈS] Many industrial machines use screws and other small tools to fix smaller components that compose the whole structure of the machine. To ensure that these tools withstand the pressures that can be subjected at, a correct design of the tool is a necessary job and must be done accurately. It is quite true that the companies that manufacture the tools design them regarding to certain parameters of resistance to temperature, pressure, torque, etc.. But once they have been used for real purposes may be desirable to apply concrete measures to them in order to ensure that no deformation has been suffered and that the design has been done properly. In this project we focus on the analysis of screws of known geometry, but the main ideas and methods that we will develop can be also be applied on other objects with certain changes and considerations. The aim of this project is to design an algorithm that measures concrete distances for given screws and compares the obtained distances with the already known theoretical measurements so that we can achieve to conclude if the screw is between the parameters of normality or if that screw has suffered bending, for example. The task of measurement, that can be done physically, is called to be improved by using digital image processing methods in order to make the process faster and automatic. But not only this, we also have to deal with the fact that the screws to be analyzed might contain dirt produced by their previous usage, as rust, embedded oil... Therefore, a previous task to the measurement step must be a process of cleaning the contour of the screw, which will be carried out using Fourier Descriptors in a particular way that we will explain deeply in section 3. But since the method has to return the measures in a physical unit of measure, a process that deals with a conversion between the measurements found in pixels ant turns them into millimeters has to be also carried out. We are provided by a high precision camera (μEye UI-1540-M) and with a platform specifically designed for this purpose which contains a support for the camera and system to hold the screw from its base, and that allows us to move the support forward and backward, sideways, up and down in order to achieve a good approach in terms of resolution of the image. The system that holds the screw has also a mechanism to hold a high precision point grid (Low Reflect Grid Distortion Targ 3X3 0.5mm Dot, Edmund Optics) at the same place than the screw, which will allow us to compute a factor of conversion that will be valid as soon as the picture of the screw is taken at the same exact distance that the picture of the point grid. And also as soon as we handle the problem that comes from the radial distortion that presents the camera, which brings us to realize that not all distances in the image are equally reliable. [CASTELLÀ] Muchas máquinas industriales utilizan tornillos y otras herramientas pequeñas para fijar componentes más pequeños que componen toda la estructura de una máquina. Para asegurarse de que estas herramientas van a soportar las presiones a las que se pueden someter, es necesario un preciso y buen diseño de la herramienta en cuestión. Es cierto que las empresas que fabrican las herramientas, las diseñan teniendo en cuenta ciertos parámetros de resistencia a la temperatura, presión, torsión, etc. Pero una vez que se han utilizado para los propósitos reales puede ser necesario medir distancias concretas con el fin de garantizar que no a sufrido ninguna deformación y que el diseño se ha hecho correctamente. En este proyecto nos centramos en el análisis de tornillos de geometría ya conocida, pero las ideas principales y los métodos que vamos a desarrollar también pueden ser aplicados en otros objetos con ciertas modificaciones y consideraciones. El objetivo de este proyecto es diseñar un algoritmo que mida distancias concretas en los tornillos y compararlas luego con las distancias teóricas, a fin de valorar y llegar a la conclusión de si las medidas del tornillo en cuestión están entre los parámetros de la normalidad o si ha sufrido algún tipo de deformación. La tarea de medición se puede hacer físicamente, pero puede ser mejorada mediante el uso de métodos de procesamiento de imágenes digitales con el fin de hacerlo más rápido y automático. Pero no sólo eso, también tenemos que tener en cuenta que los tornillos que se analizarán pueden contener suciedad producida por su uso anterior, ya sea óxido, aceite incrustado ... Por lo tanto, una tarea previa a la de medición debe ser un proceso de limpieza del contorno de la rosca, que se llevará a cabo utilizando descriptores de Fourier de una manera particular que vamos a explicar en profundidad en la sección 3. Sin embargo, dado que el método tiene que devolver las medidas en una unidad física y real de medida, es necesario también un proceso para convertir las medidas digitales obtenidas, que se encuentran en píxeles, a milímetros. Para la realización del proyecto contamos con una cámara de alta precisión (μEye UI-1540-M), con una plataforma diseñada específicamente para este propósito, con un soporte para la cámara y con un sistema para mantener el tornillo sujeto en la base. Esto nos permite mover el tornillo hacia adelante y hacia atrás, hacia los lados, hacia arriba y abajo con el fin de lograr un buen enfoque en términos de resolución de la imagen. El sistema que sujeta el tornillo tiene también un mecanismo para mantener una red de puntos de alta precisión (Low Reflexion Grid Distortion Targ 3X3 0.5mm Dot, Edmund Optics) en el mismo lugar que el tornillo, lo que nos permitirá calcular un factor de conversión que será válido siempre y cuando se tomen las imagenes del tornillo a la misma distancia que la imagen de la red de puntos. Además debemos solucionar el problema que viene dado por la distorsión radial que presenta la cámara, ya que no todas las distancias en la imagen tienen la misma fiabilidad. [CATALÀ] Moltes màquines industrials utilitzen cargols i altres eines petites per fixar components més petits que componen tota l'estructura d'una màquina. Per assegurar que aquestes eines suportaran les pressions a què es poden sotmetre, cal un precís i bon disseny de l'eina en qüestió. És cert que les empreses que fabriquen les eines, les dissenyen tenint en compte certs paràmetres de resistència a la temperatura, pressió, torsió, etc. Però una vegada que s'han utilitzat per als propòsits reals pot ser necessari mesurar distàncies concretes per tal de garantir que no a sofert cap deformació i que el disseny s'ha fet correctament. En aquest projecte ens centrem en l'anàlisi de cargols de geometria ja coneguda, però les idees principals i els mètodes que desenvoluparem també poden ser aplicats en altres objectes amb certes modificacions i consideracions. L'objectiu d'aquest projecte és dissenyar un algorisme que mesuri distàncies concretes en els cargols i comparar després amb les distàncies teòriques, a fi de valorar i arribar a la conclusió de si les mesures del cargol en qüestió estan entre els paràmetres de la normalitat o si ha patit algun tipus de deformació. La tasca de mesura es pot fer físicament, però pot ser millorada mitjançant l'ús de mètodes de processament d'imatges digitals per tal de fer-lo més ràpid i automàtic. Però no només això, també hem de tenir en compte que els cargols que s'analitzaran poden contenir brutícia produïda pel seu ús anterior, ja sigui òxid, oli incrustat ... Per tant, una tasca prèvia a la de mesurar ha de ser un procés de neteja del contorn de la rosca, que es durà a terme utilitzant descriptors de Fourier d'una manera particular que explicarem en profunditat a la secció 3. No obstant això, atès que el mètode ha de retornar les mesures en una unitat física i real de mesura, cal també un procés per convertir les mesures digitals obtingudes, que es troben en píxels, a milímetres. Per a la realització del projecte comptem amb una càmera d'alta precisió (μEye UI-1540-M), amb una plataforma dissenyada específicament per a aquest propòsit, amb un suport per a la càmera i amb un sistema per mantenir el cargol subjecte a la base. Això ens permet moure el cargol cap endavant i cap enrere, cap als costats, cap amunt i avall per tal d'aconseguir un bon enfocament en termes de resolució de la imatge. El sistema que subjecta el cargol té també un mecanisme per mantenir una xarxa de punts d'alta precisió (Low Reflexion Grid Distortion Targ 3X3 0.5mm Dot, Edmund Optics) en el mateix lloc que el cargol, el que ens permetrà calcular un factor de conversió que serà vàlid sempre que es prenguin les imatges del cargol a la mateixa distància que la imatge de la xarxa de punts. A més hem de solucionar el problema que ve donat per la distorsió radial que presenta la càmera, ja que no totes les distàncies en la imatge tenen la mateixa fiabilitat.

This work describes the use of constraints in variational procedures for spectral analysis. It is reported how the designer in a variational approach for spectral estimation has to select a set of constraints. At the same time it is shown that the selected set of constraints becomes more relevant, as concerns with the resulting quality of the estimate, than the objective function minimized or maximized in the procedure. Finally, some examples are presented which are the result of considering correlation and envelope constraints and minimizing the correlation extrapolation energy.

Nowadays, the amount of information that communications networks support due to its rise, makes necessary the distribution of different information flows, to avoid saturation and information lose. This project aims to improve the traffic data forecast and its variation on a particular point of the network for a specific moment. In this way, it is possible to perform data distribution proportionally, preventing the saturation of network nodes and thus enjoying a higher quality of service. It will be proved, that by using the Wavelet Transform, the long dependency that some series manifest can be broken. Moreover, to achieve our target, autoregressive models will be applied, improving the results obtained without using Wavelet Transform up to 50 times. Hoy en día, la cantidad de información que soportan las redes de comunicaciones debido su auge, hace necesario la distribución de distintos flujos de información para que no se saturen las redes ni se pierda información. Este proyecto trata de mejorar la previsión de datos de tráfico y su variación en un punto de la red durante unos instantes concretos. Con ello, es posible realizar la distribución de datos de forma proporcional, evitando que los nodos de red se saturen y así poder disfrutar de una mayor calidad de servicio. Se demostrará que mediante la Transformada Wavelet se puede romper la larga dependencia que algunas series manifiestan. Además, para alcanzar nuestro objetivo, se aplicarán los modelos autorregresivos, mejorando hasta en 50 veces los resultados obtenidos sin la utilización de la Transformada Wavelet. Actualment, la quantitat d’informació que circula a través de les xarxes de comunicació degut a l’augment d’aquestes, crea la necessitat de distribuir diferents fluxos d’informació, perquè no es saturin les xarxes ni es perdi informació. Aquest treball tracta de millorar la previsió de dades de tràfic i la seva variació en un punt de la xarxa durant uns instants concrets. Amb això, es possible realitzar la distribució de tràfic de forma proporcional, evitant que els nodes de la xarxa es saturin y així poder gaudir d’una major qualitat de servei. Es demostrarà que mitjançant la Transformada Wavelet es pot trencar la llarga dependència que manifesten algunes series. A més, per aconseguir el nostre objectiu, s’aplicaran models autoregressius, millorant fins a 50 vegades els resultats aconseguits sense la utilització de la Transformada Wavelet.

In this work, we investigate the challenging problem of estimating credit risk measures of portfolios with exposure concentration under the multi-factor Gaussian and multi-factor t-copula models. It is well-known that Monte Carlo (MC) methods are highly demanding from the computational point of view in the aforementioned situations. We present efficient and robust numerical techniques based on the Haar wavelets theory for recovering the cumulative distribution function (CDF) of the loss variable from its characteristic function. To the best of our knowledge, this is the first time that multi-factor t-copula models are considered outside the MC framework. The analysis of the approximation error and the results obtained in the numerical experiments section show a reliable and useful machinery for credit risk capital measurement purposes in line with Pillar II of the Basel Accords.

It is very well known that the first succesful valuation of a stock option was done by solving a deterministic partial differential equation (PDE) of the parabolic type with some complementary conditions specific for the option. In this approach, the randomness in the option value process is eliminated through a no-arbitrage argument. An alternative approach is to construct a replicating portfolio for the option. From this viewpoint the payoff function for the option is a random process which, under a new probabilistic measure, turns out to be of a special type, a martingale. Accordingly, the value of the replicating portfolio (equivalently, of the option) is calculated as an expectation, with respect to this new measure, of the discounted value of the payoff function. Since the expectation is, by definition, an integral, its calculation can be made simpler by resorting to powerful methods already available in the theory of analytic functions. In this paper we use precisely two of those techniques to find the well-known value of a European call, La primera valoració, generalment acceptada, d'una opció sobre una acció es feu solucionant una equació diferencial, en derivades parcials, determinista, del tipus parabòlic introduint algunes condicions de contorn específiques de l'opció. En aquest plantejament, la aleatorietat inherent en la valoració de l'opció s'elimina introduint l'hipòtesi l'inexistència de possibilitats d'arbitratge. Un plantejament alternatiu és construir una cartera que repliqui els resultats de l'opció. Des d'aquest punt de vista la funció de pagament per l'opció es un procés aleatori que, sota una nova mesura de probabilitat, converteix el procés en una martingala. El valor de la cartera replicant, equivalent al valor de l'opció, es calcula com a esperança del valor descomptat dels pagaments, respecte aquesta nova mesura. Com que l'esperança matemàtica és, per definició, una integral, el seu càlcul es pot fer de forma més simple utilitzant mètodes procedents de la teoria de funcions analítiques.