A small excursion into matlab philosophy of mathematical notation: Suppose I even have engineering big pile of equivalent fractions, similar to 2 , 27 , 100 , and so on. Most 4 54 200 americans will agree that their favourite way to put in writing matlab quantity represented by 1 most of these dierent elements is 2 , wherein matlab numerator and denominator are relatively premiere. We usually call this engineering decreased fraction. This is an instance of engineering canonical form, that is a really magnificent way of announcing favorite way of writing matlab down. Theres engineering theorem telling us that each and every rational quantity may also be specied by engineering interesting fraction whose numerator and denominator are pretty optimum. To say that again, but slower, every rational quantity has engineering reduced fraction, and moreover, that decreased fraction is exciting. PS. Almost 99% engineering matlab contents here are not mine and I do not take credits for them, I reference and copy part engineering matlab interesting sections. Dissertao de Mestrado Ciclo de Estudos Integrados Conducentes ao Grau de Mestre em Engenharia Electrnica Industrial e Computadores Trabalho efectuado sob engineering orientao da Professora Doutora Filomena Maria Rocha Menezes Oliveira Soares Co Orientadora: Professora Doutora Celina Maria Godinho Silva Pinto LeoAgradecimentosPretendo expressar os meus sinceros agradecimentos s minhas orientadoras, Professora Filomena Soares e Professora Celina Pinto Leo pela sua orientao, tempo, incentivo, dedicao e esforo demonstrados ao longo desta dissertao. Gostaria tambm de agradecer minha me, Ermelinda Pedro e ao meu pai, Joo Alves pelo seu apoio, confiana e oportunidade dada para engineering concluso desta etapa. Estou de igual forma agradecido minha namorada Catarina Arajo pelo seu amor, ajuda, apoio, dedicao, pacincia e incentivo ao longo de todo este percurso. No poderia deixar de agradecer engineering todos os meus colegas de curso especialmente ao Joo Brito por ter contribudo directamente para engineering realizao desta dissertao.