Uma fundamentação matemática para processamento digital de sinais intervalares

This work deals with a mathematical fundament for digital signal processing under point view of interval mathematics. Intend treat the open problem of precision and repesention of data in digital systems, with a intertval version of signals representation. Signals processing is a rich and complex area, therefore, this work makes a cutting with focus in systems linear invariant in the time. A vast literature in the area exists, but, some concepts in interval mathematics need to be redefined or to be elaborated for the construction of a solid theory of interval signal processing. We will construct a basic fundaments for signal processing in the interval version, such as basic properties linearity, stability, causality, a version to intervalar of linear systems e its properties. They will be presented interval versions of the convolution and the Z-transform. Will be made analysis of convergences of systems using interval Z-transform , a essentially interval distance, interval complex numbers , application in a interval filter.

Localização e mapeamento simultâneos de ambientes planos usando visão monocular e representação híbrida do ambiente

The goal of this work is to propose a SLAM (Simultaneous Localization and Mapping) solution based on Extended Kalman Filter (EKF) in order to make possible a robot navigates along the environment using information from odometry and pre-existing lines on the floor. Initially, a segmentation step is necessary to classify parts of the image in floor or non floor . Then the image processing identifies floor lines and the parameters of these lines are mapped to world using a homography matrix. Finally, the identified lines are used in SLAM as landmarks in order to build a feature map. In parallel, using the corrected robot pose, the uncertainty about the pose and also the part non floor of the image, it is possible to build an occupancy grid map and generate a metric map with the obstacle s description. A greater autonomy for the robot is attained by using the two types of obtained map (the metric map and the features map). Thus, it is possible to run path planning tasks in parallel with localization and mapping. Practical results are presented to validate the proposal

Uma fundamentação para sinais e sistemas intervalares

In this work we use Interval Mathematics to establish interval counterparts for the main tools used in digital signal processing. More specifically, the approach developed here is oriented to signals, systems, sampling, quantization, coding and Fourier transforms. A detailed study for some interval arithmetics which handle with complex numbers is provided; they are: complex interval arithmetic (or rectangular), circular complex arithmetic, and interval arithmetic for polar sectors. This lead us to investigate some properties that are relevant for the development of a theory of interval digital signal processing. It is shown that the sets IR and R(C) endowed with any correct arithmetic is not an algebraic field, meaning that those sets do not behave like real and complex numbers. An alternative to the notion of interval complex width is also provided and the Kulisch- Miranker order is used in order to write complex numbers in the interval form enabling operations on endpoints. The use of interval signals and systems is possible thanks to the representation of complex values into floating point systems. That is, if a number x 2 R is not representable in a floating point system F then it is mapped to an interval [x;x], such that x is the largest number in F which is smaller than x and x is the smallest one in F which is greater than x. This interval representation is the starting point for definitions like interval signals and systems which take real or complex values. It provides the extension for notions like: causality, stability, time invariance, homogeneity, additivity and linearity to interval systems. The process of quantization is extended to its interval counterpart. Thereafter the interval versions for: quantization levels, quantization error and encoded signal are provided. It is shown that the interval levels of quantization represent complex quantization levels and the classical quantization error ranges over the interval quantization error. An estimation for the interval quantization error and an interval version for Z-transform (and hence Fourier transform) is provided. Finally, the results of an Matlab implementation is given

Mapeamento robótico 2,5-D com representação em grade de ocupação-elevação

This work introduces a new method for environment mapping with three-dimensional information from visual information for robotic accurate navigation. Many approaches of 3D mapping using occupancy grid typically requires high computacional effort to both build and store the map. We introduce an 2.5-D occupancy-elevation grid mapping, which is a discrete mapping approach, where each cell stores the occupancy probability, the height of the terrain at current place in the environment and the variance of this height. This 2.5-dimensional representation allows that a mobile robot to know whether a place in the environment is occupied by an obstacle and the height of this obstacle, thus, it can decide if is possible to traverse the obstacle. Sensorial informations necessary to construct the map is provided by a stereo vision system, which has been modeled with a robust probabilistic approach, considering the noise present in the stereo processing. The resulting maps favors the execution of tasks like decision making in the autonomous navigation, exploration, localization and path planning. Experiments carried out with a real mobile robots demonstrates that this proposed approach yields useful maps for robot autonomous navigation

Extração e Representação de Conhecimento de Séries Temporais de Demanda de Energia Elétrica Usando TSKR

The opening of the Brazilian market of electricity and competitiveness between companies in the energy sector make the search for useful information and tools that will assist in decision making activities, increase by the concessionaires. An important source of knowledge for these utilities is the time series of energy demand. The identification of behavior patterns and description of events become important for the planning execution, seeking improvements in service quality and financial benefits. This dissertation presents a methodology based on mining and representation tools of time series, in order to extract knowledge that relate series of electricity demand in various substations connected of a electric utility. The method exploits the relationship of duration, coincidence and partial order of events in multi-dimensionals time series. To represent the knowledge is used the language proposed by Mörchen (2005) called Time Series Knowledge Representation (TSKR). We conducted a case study using time series of energy demand of 8 substations interconnected by a ring system, which feeds the metropolitan area of Goiânia-GO, provided by CELG (Companhia Energética de Goiás), responsible for the service of power distribution in the state of Goiás (Brazil). Using the proposed methodology were extracted three levels of knowledge that describe the behavior of the system studied, representing clearly the system dynamics, becoming a tool to assist planning activities

Números complexos: uma proposta de mudança metodológica para uma aprendizagem significativa no ensino médio

This work presents a proposal of a methodological change to the teaching and learning of the complex numbers in the Secondary education. It is based on the inquiries and difficulties of students detected in the classrooms about the teaching of complex numbers and a questioning of the context of the mathematics teaching - that is the reason of the inquiry of this dissertation. In the searching for an efficient learning and placing the work as a research, it is presented a historical reflection of the evolution of the concept of complex numbers pointing out their more relevant focuses, such as: symbolic, numeric, geometrical and algebraic ones. Then, it shows the description of the ways of the research based on the methodology of the didactic engineering. This one is developed from the utilization of its four stages, where in the preliminary analysis stage, two data surveys are presented: the first one is concerning with the way of presenting the contents of the complex numbers in math textbooks, and the second one is concerning to the interview carried out with High school teachers who work with complex numbers in the practice of their professions. At first, in the analysis stage, it is presented the prepared and organized material to be used in the following stage. In the experimentation one, it is presented the carrying out process that was made with the second year High school students in the Centro Federal de Educação tecnológica do Rio Grande do Norte CEFET-RN. At the end, it presents, in the subsequent and validation stages, the revelation of the obtained results from the observations made in classrooms in the carrying out of the didactic sequence, the students talking and the data collection

Uma análise dos questionamentos dos alunos nas aulas de números complexos

This work presents a contribution for the studies reffering to the use of the History of Mathematics focusing on the improvement of the Teaching and Learning Process. It considers that the History of Matematics, as a way of giving meaning to the discipline and improve the quality of the Teaching and Learning Process. This research focuses on the questions of the students, classified in three categories of whys: the chronological, the logical and the pedagogical ones. Therefore, it is investigated the teaching of the Complex Numbers, from the questions of the students of the Centro Federal de Educação Tecnológica do Rio Grande do Norte (Educational Institution of Professional and Technology Education from Rio Grande do Norte). The work has the following goals: To classify and to analyse the questions of the students about the Complex Numbers in the classes of second grade of the High School, and to collate with the pointed categories used by Jones; To disccus what are the possible guidings that teachers of Mathematics can give to these questions; To present the resources needed to give support to the teacher in all things involving the History of Mathematics. Finally, to present a bibliographic research, trying to reveal supporting material to the teacher, with contents that articulate the Teaching of Mathematics with the History of Mathematics. It was found that the questionings of the pupils reffers more to the pedagogical whys, and the didatic books little contemplate other aspects of the history and little say about the sprouting and the evolution of methods of calculations used by us as well

A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

O uso pedagógico de uma seqüência didática para a aquisição de algumas idéias relacionadas ao conceito de números complexos

The aim of the present work is to contribute to the teaching-learning process in Mathematics through an alternative which tries to motivate the student so that he/she will learn the basic concepts of Complex Numbers and realize that they are not pointless. Therefore, this work s general objective is to construct a didactic sequence which contains structured activities that intends to build up, in each student s thought, the concept of Complex Numbers. The didactic sequence is initially based on a review of the main historical aspects which begot the construction of those numbers. Based on these aspects, and the theories of Richard Skemp, was elaborated a sequence of structured activities linked with Maths history, having the solution of quadratic equations as a main starting point. This should make learning more accessible, because this concept permeates the students previous work and, thus, they should be more familiar with it. The methodological intervention began with the application of that sequence of activities with grade students in public schools who did not yet know the concept of Complex Numbers. It was performed in three phases: a draft study, a draft study II and the final study. Each phase was applied in a different institution, where the classes were randomly divided into groups and each group would discuss and write down the concepts they had developed about Complex Numbers. We also use of another instrument of analysis which consisted of a recorded interview of a semi-structured type, trying to find out the ways the students thought in order to construct their own concepts, i.e. the solutions of the previous activity. Their ideas about Complex Numbers were categorized according to their similarities and then analyzed. The results of the analysis show that the concepts constructed by the students were pertinent and that they complemented each other this supports the conclusion that the use of structured activities is an efficient alternative for the teaching of mathematics

Euler e os números pentagonais

The present investigation includes a study of Leonhard Euler and the pentagonal numbers is his article Mirabilibus Proprietatibus Numerorum Pentagonalium - E524. After a brief review of the life and work of Euler, we analyze the mathematical concepts covered in that article as well as its historical context. For this purpose, we explain the concept of figurate numbers, showing its mode of generation, as well as its geometric and algebraic representations. Then, we present a brief history of the search for the Eulerian pentagonal number theorem, based on his correspondence on the subject with Daniel Bernoulli, Nikolaus Bernoulli, Christian Goldbach and Jean Le Rond d'Alembert. At first, Euler states the theorem, but admits that he doesn t know to prove it. Finally, in a letter to Goldbach in 1750, he presents a demonstration, which is published in E541, along with an alternative proof. The expansion of the concept of pentagonal number is then explained and justified by compare the geometric and algebraic representations of the new pentagonal numbers pentagonal numbers with those of traditional pentagonal numbers. Then we explain to the pentagonal number theorem, that is, the fact that the infinite product(1 x)(1 xx)(1 x3)(1 x4)(1 x5)(1 x6)(1 x7)... is equal to the infinite series 1 x1 x2+x5+x7 x12 x15+x22+x26 ..., where the exponents are given by the pentagonal numbers (expanded) and the sign is determined by whether as more or less as the exponent is pentagonal number (traditional or expanded). We also mention that Euler relates the pentagonal number theorem to other parts of mathematics, such as the concept of partitions, generating functions, the theory of infinite products and the sum of divisors. We end with an explanation of Euler s demonstration pentagonal number theorem

Os artigos de Euler sobre os números amigáveis

Among the many methodological resources that the mathematics teacher can use in the classroom, we can cite the History of Mathematics which has contributed to the development of activities that promotes students curiosity about mathematics and its history. In this regard, the present dissertation aims to translate and analyze, mathematically and historically, the three works of Euler about amicable numbers that were writed during the Eighteenth century with the same title: De numeris amicabilibus. These works, despite being written in 1747 when Euler lived in Berlin, were published in different times and places. The first, published in 1747 in Nova Acta Eruditorum and which received the number E100 in the Eneström index, summarizes the historical context of amicable numbers, mentions the formula 2nxy & 2nz used by his precursors and presents a table containing thirty pairs of amicable numbers. The second work, E152, was published in 1750 in Opuscula varii argument. It is the result of a comprehensive review of Euler s research on amicable numbers which resulted in a catalog containing 61 pairs, a quantity which had never been achieved by any mathematician before Euler. Finally, the third work, E798, which was published in 1849 at the Opera postuma, was probably the first among the three works, to be written by Euler

Forró eletrônico: uma análise sobre a representação da figura feminina

Understanding music as a social manifestation, able to represent the time and culture along with their uses and mores, we look at the female figure in the electronic forró genre. Through a reading of the two genres musical and feminine we seek to identify the discourses present in the compositions, which refer to the feminine with thematic and/or terms referring to women. The study focuses on the compositions between 2009 to 2010 which became hits, ie.: those which have attained the highest number of listeners to 96 FM in a program named Paradão 96, broadcasted daily in the city of Natal/RN. Grounded in such concepts as cultural industry, mass culture, folkcommunication and gender, we analyze the processes of meaning production as a result of using the female figure and more accurately, about the representation of women through the discourse of this specific genre. We have chose the descriptive research with a qualitative approach and Discourse Analysis as a technique to identify the terms that refer to women, reflecting on what would be the possible meanings found in these speeches. We point out that in our investigation the female figure turned into a sexual object, erotic and submissive, in their turn, attributes usually given to women, was not a predominant result in the speech of electronic forró gender. With a variant thematic some playful and others about the betrayal of women we have identified that, to the surprise of many, including ourselves, romantic love was the one who led the audience requests during our time frame and that the female figure has several facets within the studied genre

A Representação discursiva da figura feminina no jornal O Porvir (Currais Novos/Rio Grande do Norte - 1926-1929)

The objective of this paper is to analyze how the female figure was portrayed in discursive narratives in the bi-weekly newspaper O PORVIR , which circulated in Currais Novos, in the state of Rio Grande do Norte, Brazil, between May 2, 1926 and January 20, 1929. Our analysis was based on the semantics of the text, by applying one of the primary concepts used in Textual Analysis of Speeches, Discursive Representation (ADAM, 2011; RODRIGUES; PASSEGGI; SILVA NETO, 2010). Textual Analysis of Speeches has its roots in Textual Linguistics and consists of a theoretical and descriptive approach (ADAM, 2011). This research is characterized as documentary (SEVERINO, 2007) and its corpus includes a review of 39 editions of the aforementioned newspaper, of which we extracted 292 articles that dealt with the female figure and 396 statements for analysis. We used the following semantic categories: referencing (CASTILHO, 2010; NEVES, 2007; KOCH; MARCUSCHI, 1998; MARCUSCHI, 2008; KOCH, 2009); predication (NEVES, 2007; RODRIGUES; PASSEGGI; SILVA NETO, 2010); modification (ADAM, 2011); and spacial and temporal localization (RODRIGUES; PASSEGGI; SILVA NETO, 2010). Our analysis revealed that lady, mother, wife and homemaker were most represented, and always combined with questions about motherhood, marriage and devotion to the home. Such representation does not diverge from pre-colonial models in the early twentieth century, which served as a standard for the female figure

Produção em revista : Representação do moderno e do regional na experiência potiguar anos 1920

This work brings some reading about a few Norte-rio-grandenses writers collaborations published in literary papers which circulated during the third decade of the twentieth century in Brazil, in a way of enlarging the understanding of how the cultural debate was carried out in the years of the definition of the Brazilian Modernism, based on the relationships between literature and culture. Under the genres of prose and poetry, the selected textual collaborations for analysis have brought the traces of a small group of articulated authors in the Brazilian cultural scenery from the 1920 s, concerning the issues of the modern (linked to the modernist renovation) and the regional (under the aspects of the tradition). The set of the analyzed collaborations is representative of a modern-regional cultural practice marked by a tendency either local or cosmopolitan, thus, sharing a large dimension of the formation of the modern literary tradition, marked by different kinds of practices which give form to the project of a collective national awareness. The characterization of the existence of an intellectual field with big links, however with its own characteristics and a certain autonomy, which also gets integrated to the cultural debate of the so-called modernist years through the literary vehicles, gives to these intellectual people a co-participation in the renewing movement in the formation context of the brazilian cultural modernity of the early twentieth century

Forró eletrônico: uma análise sobre a representação da figura feminina

Entendiendo la música como una manifestación social, capaz de representar el tiempo y la cultura, junto con sus usos y costumbres, dirigimos nuestra mirada en la figura femenina presente en el género forró electrónico. A través de la lectura de los dos géneros musical y femenino buscamos identificar los discursos, presentes en las composiciones, que se refieren a lo femenino con temática y/o términos que se refieren a las mujeres. El estudio se centra en las composiciones en el período 2009 a 2010 y que se convirtieron en éxitos, es decir, aquellos que han alcanzado el mayor número de oyentes de Radio 96 FM a través del programa Paradão 96, transmitido diariamente en la ciudad de Natal/RN. Basado en conceptos tales como industria cultural, cultura de masas, folkcomunicación y género, se analizan los procesos de producción de sentido como resultado del uso de la figura femenina y con mayor precisión, sobre la representación de las mujeres a través de discursos del forró electrónico. Elegimos el enfoque descriptivo cualitativo y análisis del discurso como una técnica para identificarlos términos que se refieren a las mujeres, reflexionando sobre los posibles significados que se encuentran en estos discursos. Se señala que en nuestra investigación no predominó una figura femenina convertida en un objeto sexual, erótico y sumisa, atributos dados para las mujeres, en los discursos de forró electrónico. Con variaciones en las temáticas algunas juguetones y otras acerca de la traición de la mujer identificamos que, para sorpresa de muchos, incluidos nosotros, el amor romántico fue el que llevó las solicitudes de audiencia durante nuestro período de tiempo y que la figura femenina tiene varias facetas dentro del forró electrónico