A transformada wavelet contínua constitui poderosa ferramenta para análise multiescala de dados. Ela tem amplas aplicações na Física, na Matemática, nas Ciências Naturais e, inclusive, grande apelo nas engenharias, computação eáreas de tecnologia e inovação. Do ponto de vista introdutório, a transformada wavelet tem sido abordada amplamente em trabalhos anteriores. Assim, esta apresentação dáênfase ao uso dessa técnica em situações teóricas e práticas que normalmente não são exploradas; porém fundamentais para um uso mais adequado, ou mesmo correto, dessa ferramenta. Um embasamento consistente possibilita, sobretudo, uma extensão de sua aplicação para novas pesquisas, facilitadas pela disponibilidade de programas e ferramentas gratuitas e, até, várias dessas sob a forma de recursos de livre distribuição (free softwares). Por critério de escolha dos autores, apresentam-se, neste artigo, conceitos e exemplos de técnicas que podem ser de grande interesse para vários tipos de estudos na Física e em outrasáreas correlatas. Este texto destina-se a pesquisadores, professores e estudantes de pós-graduação, com a possibilidade de atender ainda necessidades de estudantes dosúltimos anos de graduação. Palavras-chave: wavelet, sinais multiescala, análise de sinais.The continuous wavelet transform is a powerful tool for multiscale data analysis. It has wide applications in physics, mathematics, natural sciences and even great appeal in engineering, computing and areas of technology and innovation. As an introductory point of view, the wavelet transform has been widely addressed in previous works. Thus, this presentation emphasizes the use of this technique in theoretical and practical situations that are not usually explored, but situations that are fundamental to a better use, or even a correct use, of this tool. Consistent bases enable mainly extensions of wavelet application to new investigations, that are facilitated by the availability of free programs and tools, and even several of these in completely available distribution of resources (free softwares). The content of this article, by the authors' choice criteria, presents concepts and examples of techniques that can be of great interest for various studies in physics and other related areas. This text is aimed at researchers, teachers and graduate students, with the possibility of still meet the preparation needs of students at last undergraduation stage. Keywords: wavelet, multiscale signals, signal analysis. IntroduçãoA teoria wavelet causou um frenesi na comunidade científica nasúltimas décadas e gerou um fenômeno de interesse, na pesquisa e na aplicação, com crescimento exponencial, gerando dezenas de milhares * Endereço de correspondência: margarete.domingues@inpe.br.de publicações, patentes e prêmios internacionais associados [8]. O leitor e sua família já participam e conhecem os efeitos desse fenômeno, tanto ao utilizar as imagens jpeg de um celular que podem ser enviadas por internet, quanto ao assistir os filmes de animação 3D, ou mesmo a ter seus dados bio...
Indoor positioning systems are facing to the demand of large-scale industrial applications in mobile robotics. It is still challenging to create an indoor positioning system that is easily embeddable, accurate, robust and power efficient. We constructed an easily embeddable, low-power optical sensor named InLock without lens to localize a mobile robot indoors moving at 0.20 m/s with an accuracy inferior to 10cm for the position and 0.1rad for the heading by using only three photo-detectors (PDs) and two infrared Light-Emitting Diodes (LEDs). (i) We modelled the optical sensor based on only three photo-detectors and two infrared LEDs by taking into account radiometric properties. (ii) We constructed the optical sensor by optimizing the geometry of the beacon and the receiver. (iii) We implemented and validated online estimation algorithms for an operating range at a height up to 3m by using an extended Kalman filter and a complementary filter. Our results showed that modelling the optical sensor so that it takes into account radiometric properties and it optimizes the geometry of the beacon can enhance the accuracy of the indoor positioning system.
Current methods of the conversion between a rotation quaternion and Euler angles are either a complicated set of multiple sequence-specific implementations, or a complicated method relying on multiple matrix multiplications. In this paper a general formula is presented for extracting the Euler angles in any desired sequence from a unit quaternion. This is a direct method, in that no intermediate conversion step is required (no quaternion-to-rotation matrix conversion, for example) and it is general because it works with all 12 possible sequences of rotations. A closed formula was first developed for extracting angles in any of the 12 possible sequences, both “Proper Euler angles” and “Tait-Bryan angles”. The resulting algorithm was compared with a popular implementation of the matrix-to-Euler angle algorithm, which involves a quaternion-to-matrix conversion in the first computational step. Lastly, a single-page pseudo-code implementation of this algorithm is presented, illustrating its conciseness and straightforward implementation. With an execution speed 30 times faster than the classical method, our algorithm can be of great interest in every aspect.
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