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Sleep staging is a crucial step before the scoring the sleep apnoea, in subjects that are tested for this condition. These patients undergo a whole night polysomnography recording that includes EEG, EOG, ECG, EMG and respiratory signals. Sleep staging refers to the quantification of its depth. Despite the commercial sleep software being able to stage the sleep, there is a general lack of confidence amongst health practitioners of these machine results. Generally the sleep scoring is done over the visual inspection of the overnight patient EEG recording, which takes the attention of an expert medical practitioner over a couple of hours. This contributes to a waiting list of two years for patients of the Portuguese Health Service. In this work we have used a spectral comparison method called Itakura distance to be able to make a distinction between sleepy and awake epochs in a night EEG recording, therefore automatically doing the staging. We have used the data from 20 patients of Hospital Pulido Valente, which had been previously visually expert scored. Our technique results were promising, in a way that Itakura distance can, by itself, distinguish with a good degree of certainty the N2, N3 and awake states. Pre-processing stages for artefact reduction and baseline removal using Wavelets were applied.

The design and optimization of fractional filters is considered in this paper. Some of the classic filter architectures are presented and their performances relatively to an ideal amplitude spectrum evaluated. The fractional filters are designed using the differential evolution optimization algorithm for computing their parameters. To evaluate the performances of all the filters the quadratic error between the computed amplitude is calculated against an ideal (goal) response. The fractional filters have a better behavior, both in the pass and reject-band.

The quantum fractional derivative is defined using formulations analogue to the common Grünwald?Letnikov derivatives. While these use a linear variable scale, the quantum derivative uses an exponential scale and is defined in R? or R?. Two integral formulations similar to the usual Liouville derivatives are deduced with the help of the Mellin transform.

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A software tool for the analysis of the High-Resolution Electrocardiogram (HR-ECG) for Arrhythmia detection is introduced. New algorithms based on Wavelet analysis are presented and compared with the classic Simson protocol over the P and QRS segments of the Electrocardiogram (EEG). A novel procedure based on a two step wavelet analysis and synthesis is performed in order to obtain a frequency description of the P, T or QRS segments. This frequency ?signature? is useful for the detection of otherwise asymptomatic Arrhythmia patients. The tool has been developed in Matlab, and deployed for a standalone C application.

The linear scale invariant systems are introduced for both integer and fractional orders. They are defined by the generalized Euler-Cauchy differential equation. The quantum fractional derivatives are suitable for dealing with this kind of systems, allowing us to define impulse response and transfer function with the help of the Mellin transform. It is shown how to compute the impulse responses corresponding to the two half plane regions of convergence of the transfer function.

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Rail corrugation is a phenomenon that leads to a waving in the rails with wavelengths typically between 3 cm and 100 cm and amplitude levels of several microns. The genesis of this waving is complex. Rail corrugation is a recognized problem that leads to excess vibration on the rails and vehicles to a point of reducing their life span and compromising safety. In urban areas excess vibration noise is also a problem. A software tool was developed to analyze accelerometer signals acquired in the boggies of rail vehicles in order to quantify the rail corrugation according to their frequency and amplitude. A wavelet packet methodology was used in this work and compared with the One Third Octave Filter (OTOF) power representations, which is currently used in the industry. It is shown that the former produces better results.

The alternative system initial conditions versus the derivative initial conditions is focused in this paper. It is shown that Riemann?Liouville and Caputo initial conditions result from the corresponding derivative and not necessarily from the system at hand. To setup the correct system initialization, a formulation generalizing the integer order approach is presented. This is based on a generalization to the fractional environment of the well known jump formula. The obtained scheme is very general and does not depend on any transform. Besides, it can also be used in the time variant case. The Riemann?Liouville and Caputo initial conditions are interpreted in terms of this general framework and deduced equations where they are correct.

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Neste trabalho pretende-se estudar a variabilidade da frequência cardíaca através da implementação de vários métodos de análise de electrocardiogramas. Na primeira parte descrevem-se os métodos de análise espectral, bem como a representação tempo-frequência. A decomposição de sinais para detectar e isolar os batimentos cardíacos do electrocardiograma é implementada. Descrevem-se algoritmos de isolamento para detecção dos eventos interessantes e pontos fiduciais que os constituem. Na segunda parte estima-se a variação da frequência cardíaca e estabelece-se a sua relação com as variações temporais e espectrais das características encontradas pelos métodos implementados na primeira parte do trabalho.

O desenvolvimento de um pacote de software para lidar facilmente com electrocardiogramas de alta resolução tornou-se importante para pesquisa na área de electrocardiografia. O desenvolvimento de novas técnicas para detecção de potenciais tardios e outros problemas associados a arritmias cardíacas têm sido objecto de estudo ao longo dos anos. No entanto, ainda existe a lacuna de um pacote de software que facilmente permita implementar algumas destas inovadoras técnicas de uma forma integrada, possibilitando avaliar técnicas clássicas como o protocolo de Simson para a detecção de sinais não estacionários (potenciais tardios). Algumas destas inovadoras técnicas envolvem a detecção tempo-frequência usando escalogramas ou a análise espectral usando metodologias wavelet-packet, sendo implementadas no software desenvolvido com flexibilidade e versatilidade suficientes para que futuramente sirva de plataforma de pesquisa para o refinamento destas mesmas técnicas no que toca ao processamento de sinais de electrocardiogramas de alta resolução. O software aqui desenvolvido foi também desenhado de forma a suportar dois tipos de ficheiros diferentes provenientes de outros tantos sistemas de aquisição. Os sistemas suportados são o ActiveTwo da Biosemi e o USBamp da g.tec.

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Some results presented in the paper ?Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions? ?I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999? are discussed in this paper. The slightly modified Grünwald-Letnikov derivative proposed there is used to deduce some interesting results that are in contradiction with those proposed in the referred paper.