Optimisation of multiplier-less FIR filter design techniques

This thesis is concerned with the design of multiplier-less (ML) finite impulse response (FIR) digital filters. The use of multiplier-less digital filters results in simplified filtering structures, better throughput rates and higher speed. These characteristics are very desirable in many DSP systems. This thesis concentrates on the design of digital filters with power-of-two coefficients that result in simplified filtering structures. Two distinct classesof ML FIR filter design algorithms are developed and compared with traditional techniques. The first class is based on the sensitivity of filter coefficients to rounding to power-of-two. Novel elements include extending of the algorithm for multiple-bands filters and introducing mean square error as the sensitivity criterion. This improves the performance of the algorithm and reduces the complexity of resulting filtering structures. The second class of filter design algorithms is based on evolutionary techniques, primarily genetic algorithms. Three different algorithms based on genetic algorithm kernel are developed. They include simple genetic algorithm, knowledge-based genetic algorithm and hybrid of genetic algorithm and simulated annealing. Inclusion of the additional knowledge has been found very useful when re-designing filters or refining previous designs. Hybrid techniques are useful when exploring large, N-dimensional searching spaces. Here, the genetic algorithm is used to explore searching space rapidly, followed by fine search using simulated annealing. This approach has been found beneficial for design of high-order filters. Finally, a formula for estimation of the filter length from its specification and complementing both classes of design algorithms, has been evolved using techniques of symbolic regression and genetic programming. Although the evolved formula is very complex and not easily understandable, statistical analysis has shown that it produces more accurate results than traditional Kaiser's formula. In summary, several novel algorithms for the design of multiplier-less digital filters have been developed. They outperform traditional techniques that are used for the design of ML FIR filters and hence contributed to the knowledge in the field of ML FIR filter design

Algoritmos genéticos: aplicação na síntese de alguns algoritmos de controlo

Mestrado em Engenharia Electrotécnica e de Computadores. Área de Especialização de Automação e Sistemas.Esta dissertação fornece uma visão global da computação evolutiva, nomeadamente dos algoritmos evolutivos e da inteligência dos enxames. De entre os algoritmos evolutivos dá-se um destaque especial aos algoritmos genéticos. Assim, apresentam-se os aspectos principais de construção e implementação dos algoritmos genéticos, os problemas teóricos e práticos e algumas das vantagens destes algoritmos relativamente a outros algoritmos de optimização e pesquisa. Este trabalho inclui uma aplicação dos algoritmos genéticos ao cálculo fraccionário, mais concretamente à optimização de fracções racionais que constituem uma aproximação de derivadas fraccionárias no cálculo em tempo discreto. Inicialmente, faz-se uma análise às técnicas usuais baseadas em expansões por séries de Taylor e fracções de Padé. Numa segunda fase, o problema é reavaliado numa perspectiva de optimização aproveitando a flexibilidade dos algoritmos genéticos.This thesis supplies a global vision of the evolutionary computation, with emphasis in evolutionary algorithms and swarm intelligence. Among the evolutionary algorithms a particular attention is given to the genetic algorithms. In this line of thought the main aspects of construction and implementation of genetic algorithms are presented. Also theoretical and practical problems, as well as some of the advantages of these algorithms are compared with other algorithms of search and optimization. This work includes an application of the genetic algorithms to the fractional calculus, namely to the optimization of rational fraction approximations for the discrete time calculation of fractional derivatives. Initially, it is addressed the analysis to the standard techniques based on Taylor series and Padé fraction expansions. In a second phase, the problem is reevaluated in an optimization perspective by taking advantage of the flexibility of the genetic algorithms

NATURAL ALGORITHMS IN DIGITAL FILTER DESIGN

Digital filters are an important part of Digital Signal Processing (DSP), which plays vital roles within the modern world, but their design is a complex task requiring a great deal of specialised knowledge. An analysis of this design process is presented, which identifies opportunities for the application of optimisation. The Genetic Algorithm (GA) and Simulated Annealing are problem-independent and increasingly popular optimisation techniques. They do not require detailed prior knowledge of the nature of a problem, and are unaffected by a discontinuous search space, unlike traditional methods such as calculus and hill-climbing. Potential applications of these techniques to the filter design process are discussed, and presented with practical results. Investigations into the design of Frequency Sampling (FS) Finite Impulse Response (FIR) filters using a hybrid GA/hill-climber proved especially successful, improving on published results. An analysis of the search space for FS filters provided useful information on the performance of the optimisation technique. The ability of the GA to trade off a filter's performance with respect to several design criteria simultaneously, without intervention by the designer, is also investigated. Methods of simplifying the design process by using this technique are presented, together with an analysis of the difficulty of the non-linear FIR filter design problem from a GA perspective. This gave an insight into the fundamental nature of the optimisation problem, and also suggested future improvements. The results gained from these investigations allowed the framework for a potential 'intelligent' filter design system to be proposed, in which embedded expert knowledge, Artificial Intelligence techniques and traditional design methods work together. This could deliver a single tool capable of designing a wide range of filters with minimal human intervention, and of proposing solutions to incomplete problems. It could also provide the basis for the development of tools for other areas of DSP system design