Most signal processing methods were developed for continuous signals. Digital devices, such as the computer, process only discrete signals. This dissertation proposes new techniques to accurately define and efficiently implement an important signal processing method---the time--frequency distribution (TFD)---using discrete signals. The TFD represents a signal in the joint time--frequency domain. Because these distributions are a function of both time and frequency they, unlike traditional signal processing methods, can display frequency content that changes over time. TFDs have been used successfully in many signal processing applications as almost all real-world signals have time-varying frequency content. Although TFDs are well defined for continuous signals, defining and computing a TFD for discrete signals is problematic. This work overcomes these problems by making contributions to the definition, computation, and application of discrete TFDs. The first contribution is a new discrete definition of TFDs. A discrete TFD (DTFD) should be free from the sampling-related distortion known as aliasing and satisfy all the important mathematical properties that the continuous TFD satisfies. Many different DTFD definitions exist but none come close to attaining this ideal. I propose three new components which make up the DTFD: 1) a new discrete Wigner--Ville distribution (DWVD) definition which satisfies all properties, 2) a new discrete analytic signal which minimises aliasing in the DWVD, and 3) a new method to define and convolve the discrete kernel with the DWVD to produce the DTFD. The result: a DTFD definition that, relative to the existing definitions, better approximates the ideal DTFD. The second contribution is two sets of computationally efficient algorithms to compute the proposed DTFD. The first set of algorithms computes the DTFD exactly; the second set requires less memory than the first set by computing time- and, or frequency-decimated versions of the DTFD. Both sets of algorithms reduce the computational load by exploiting symmetries in the DTFD and by constructing kernel-specific algorithms for four different kernel types. The third, and final, contribution is a biomedical application for the proposed DTFD and algorithms. This application is to accurately detect seizure events in newborn electroencephalogram (EEG) signals. Existing detection methods do not perform well enough for use in a clinical setting. I propose a new method which is more robust than existing methods and show how using the proposed DTFD, comparative to an existing DTFD, improves detection performance for this method. In summary, this dissertation makes practical contributions to the area of time--frequency signal processing by proposing an improved DTFD definition, efficient DTFD algorithms, and an improved newborn EEG seizure detection method using DTFDs.

Most signal processing methods were developed for continuous signals. Digital devices, such as the computer, process only discrete signals. This dissertation proposes new techniques to accurately define and efficiently implement an important signal processing method---the time--frequency distribution (TFD)---using discrete signals. The TFD represents a signal in the joint time--frequency domain. Because these distributions are a function of both time and frequency they, unlike traditional signal processing methods, can display frequency content that changes over time. TFDs have been used successfully in many signal processing applications as almost all real-world signals have time-varying frequency content. Although TFDs are well defined for continuous signals, defining and computing a TFD for discrete signals is problematic. This work overcomes these problems by making contributions to the definition, computation, and application of discrete TFDs. The first contribution is a new discrete definition of TFDs. A discrete TFD (DTFD) should be free from the sampling-related distortion known as aliasing and satisfy all the important mathematical properties that the continuous TFD satisfies. Many different DTFD definitions exist but none come close to attaining this ideal. I propose three new components which make up the DTFD: 1) a new discrete Wigner--Ville distribution (DWVD) definition which satisfies all properties, 2) a new discrete analytic signal which minimises aliasing in the DWVD, and 3) a new method to define and convolve the discrete kernel with the DWVD to produce the DTFD. The result: a DTFD definition that, relative to the existing definitions, better approximates the ideal DTFD. The second contribution is two sets of computationally efficient algorithms to compute the proposed DTFD. The first set of algorithms computes the DTFD exactly; the second set requires less memory than the first set by computing time- and, or frequency-decimated versions of the DTFD. Both sets of algorithms reduce the computational load by exploiting symmetries in the DTFD and by constructing kernel-specific algorithms for four different kernel types. The third, and final, contribution is a biomedical application for the proposed DTFD and algorithms. This application is to accurately detect seizure events in newborn electroencephalogram (EEG) signals. Existing detection methods do not perform well enough for use in a clinical setting. I propose a new method which is more robust than existing methods and show how using the proposed DTFD, comparative to an existing DTFD, improves detection performance for this method. In summary, this dissertation makes practical contributions to the area of time--frequency signal processing by proposing an improved DTFD definition, efficient DTFD algorithms, and an improved newborn EEG seizure detection method using DTFDs.

Most signal processing methods were developed for continuous signals. Digital devices, such as the computer, process only discrete signals. This dissertation proposes new techniques to accurately define and efficiently implement an important signal processing method---the time--frequency distribution (TFD)---using discrete signals. The TFD represents a signal in the joint time--frequency domain. Because these distributions are a function of both time and frequency they, unlike traditional signal processing methods, can display frequency content that changes over time. TFDs have been used successfully in many signal processing applications as almost all real-world signals have time-varying frequency content. Although TFDs are well defined for continuous signals, defining and computing a TFD for discrete signals is problematic. This work overcomes these problems by making contributions to the definition, computation, and application of discrete TFDs. The first contribution is a new discrete definition of TFDs. A discrete TFD (DTFD) should be free from the sampling-related distortion known as aliasing and satisfy all the important mathematical properties that the continuous TFD satisfies. Many different DTFD definitions exist but none come close to attaining this ideal. I propose three new components which make up the DTFD: 1) a new discrete Wigner--Ville distribution (DWVD) definition which satisfies all properties, 2) a new discrete analytic signal which minimises aliasing in the DWVD, and 3) a new method to define and convolve the discrete kernel with the DWVD to produce the DTFD. The result: a DTFD definition that, relative to the existing definitions, better approximates the ideal DTFD. The second contribution is two sets of computationally efficient algorithms to compute the proposed DTFD. The first set of algorithms computes the DTFD exactly; the second set requires less memory than the first set by computing time- and, or frequency-decimated versions of the DTFD. Both sets of algorithms reduce the computational load by exploiting symmetries in the DTFD and by constructing kernel-specific algorithms for four different kernel types. The third, and final, contribution is a biomedical application for the proposed DTFD and algorithms. This application is to accurately detect seizure events in newborn electroencephalogram (EEG) signals. Existing detection methods do not perform well enough for use in a clinical setting. I propose a new method which is more robust than existing methods and show how using the proposed DTFD, comparative to an existing DTFD, improves detection performance for this method. In summary, this dissertation makes practical contributions to the area of time--frequency signal processing by proposing an improved DTFD definition, efficient DTFD algorithms, and an improved newborn EEG seizure detection method using DTFDs.

Most signal processing methods were developed for continuous signals. Digital devices, such as the computer, process only discrete signals. This dissertation proposes new techniques to accurately define and efficiently implement an important signal processing method---the time--frequency distribution (TFD)---using discrete signals. The TFD represents a signal in the joint time--frequency domain. Because these distributions are a function of both time and frequency they, unlike traditional signal processing methods, can display frequency content that changes over time. TFDs have been used successfully in many signal processing applications as almost all real-world signals have time-varying frequency content. Although TFDs are well defined for continuous signals, defining and computing a TFD for discrete signals is problematic. This work overcomes these problems by making contributions to the definition, computation, and application of discrete TFDs. The first contribution is a new discrete definition of TFDs. A discrete TFD (DTFD) should be free from the sampling-related distortion known as aliasing and satisfy all the important mathematical properties that the continuous TFD satisfies. Many different DTFD definitions exist but none come close to attaining this ideal. I propose three new components which make up the DTFD: 1) a new discrete Wigner--Ville distribution (DWVD) definition which satisfies all properties, 2) a new discrete analytic signal which minimises aliasing in the DWVD, and 3) a new method to define and convolve the discrete kernel with the DWVD to produce the DTFD. The result: a DTFD definition that, relative to the existing definitions, better approximates the ideal DTFD. The second contribution is two sets of computationally efficient algorithms to compute the proposed DTFD. The first set of algorithms computes the DTFD exactly; the second set requires less memory than the first set by computing time- and, or frequency-decimated versions of the DTFD. Both sets of algorithms reduce the computational load by exploiting symmetries in the DTFD and by constructing kernel-specific algorithms for four different kernel types. The third, and final, contribution is a biomedical application for the proposed DTFD and algorithms. This application is to accurately detect seizure events in newborn electroencephalogram (EEG) signals. Existing detection methods do not perform well enough for use in a clinical setting. I propose a new method which is more robust than existing methods and show how using the proposed DTFD, comparative to an existing DTFD, improves detection performance for this method. In summary, this dissertation makes practical contributions to the area of time--frequency signal processing by proposing an improved DTFD definition, efficient DTFD algorithms, and an improved newborn EEG seizure detection method using DTFDs.

Most signal processing methods were developed for continuous signals. Digital devices, such as the computer, process only discrete signals. This dissertation proposes new techniques to accurately define and efficiently implement an important signal processing method---the time--frequency distribution (TFD)---using discrete signals. The TFD represents a signal in the joint time--frequency domain. Because these distributions are a function of both time and frequency they, unlike traditional signal processing methods, can display frequency content that changes over time. TFDs have been used successfully in many signal processing applications as almost all real-world signals have time-varying frequency content. Although TFDs are well defined for continuous signals, defining and computing a TFD for discrete signals is problematic. This work overcomes these problems by making contributions to the definition, computation, and application of discrete TFDs. The first contribution is a new discrete definition of TFDs. A discrete TFD (DTFD) should be free from the sampling-related distortion known as aliasing and satisfy all the important mathematical properties that the continuous TFD satisfies. Many different DTFD definitions exist but none come close to attaining this ideal. I propose three new components which make up the DTFD: 1) a new discrete Wigner--Ville distribution (DWVD) definition which satisfies all properties, 2) a new discrete analytic signal which minimises aliasing in the DWVD, and 3) a new method to define and convolve the discrete kernel with the DWVD to produce the DTFD. The result: a DTFD definition that, relative to the existing definitions, better approximates the ideal DTFD. The second contribution is two sets of computationally efficient algorithms to compute the proposed DTFD. The first set of algorithms computes the DTFD exactly; the second set requires less memory than the first set by computing time- and, or frequency-decimated versions of the DTFD. Both sets of algorithms reduce the computational load by exploiting symmetries in the DTFD and by constructing kernel-specific algorithms for four different kernel types. The third, and final, contribution is a biomedical application for the proposed DTFD and algorithms. This application is to accurately detect seizure events in newborn electroencephalogram (EEG) signals. Existing detection methods do not perform well enough for use in a clinical setting. I propose a new method which is more robust than existing methods and show how using the proposed DTFD, comparative to an existing DTFD, improves detection performance for this method. In summary, this dissertation makes practical contributions to the area of time--frequency signal processing by proposing an improved DTFD definition, efficient DTFD algorithms, and an improved newborn EEG seizure detection method using DTFDs.

Σκοπός της παρούσας διπλωματικής εργασίας είναι η μελέτη του αντίστροφου καθορισμού πηγής (inverse source localization problem) και του ρυθμού μ (mu). Έχοντας ως δεδομένο το σήμα του ΗΕΓ γίνεται προσπάθεια µέσω της εφαρμογής της μεθόδου Ανάλυσης Ανεξάρτητων συνιστωσών (ICA) να προσδιοριστούν οι συνιστώσες οι οποίες σχετίζονται με τις περιοχές του εγκεφάλου που ενεργοποιούνται από την κίνηση των χεριών. Με βάση τη λειτουργία της αισθητηριοκινητικής περιοχής του εγκεφάλου και τις ιδιότητες του ρυθμού μ, γίνεται μια μελέτη πάνω στις συνιστώσες που προκύπτουν από την ICA τόσο σε δεδομένα από πραγματική κίνηση, όσο και σε δεδομένα από νοερή κίνηση, καθώς και στην εφαρμογή που μπορεί να υπάρχει σε συστήματα Διεπαφής Εγκεφάλου – Υπολογιστή. / The subject of this diploma thesis is the study of the inverse source localization problem and the mu rhythm. Performing Independent Component Analysis (ICA) on EEG data, we try to specify the components that are related to the brain areas activated by hand movement. By focusing on the function of the somatosensory brain area and the properties or mu rhythm, we study the components resulting from Independent Component Analysis on data of both real and imaginary movement, as well as the possible implementations on Brain – Computer Interface systems.

H προβολή υποσυνείδητων μηνυμάτων είναι η διαδικασία έκθεσης ερεθισμάτων κάτω από το κατώφλι της συνειδητοποίησης. Με τον τρόπο αυτό μπορεί να επηρεαστούν οι σκέψεις, τα συναισθήματα και ενέργειες του ανθρώπου. Η υποσυνείδητη αντίληψη συμβαίνει όταν οι πληροφορίες αποθηκεύονται στο ανθρώπινο μυαλό, χωρίς ο δέκτης να έχει συνειδητά επίγνωση του προβλήματος. Οι πληροφορίες φτάνουν στο μυαλό, γιατί ενώ δεν είναι συνειδητά αντιληπτές, γίνονται αντιληπτές από το υποσυνείδητο κομμάτι του εγκεφάλου. Αντικείμενο της παρούσας διπλωματικής εργασίας είναι η αποτίμηση των πιθανών διαφορών στις καταγραφές ηλεκτροεγκεφαλογραφήματος (ΕΕG) και προκλητών δυναμικών (ERPs) κατά την υποβολή ενός ατόμου σε οπτικά υποσυνείδητα ερεθίσματα σε σύγκριση με καταγραφές χωρίς ερέθισμα. Στην εργασία χρησιμοποιήθηκε ένα ερευνητικό πρωτόκολλο το οποίο εξετάζει το πώς επηρεάζουν τα υποσυνείδητα ερεθίσματα τη λήψη αποφάσεων και την εγκεφαλική λειτουργία. Στο πρώτο μέρος της εργασίας (κεφάλαια 1 και 2) γίνεται μια συνοπτική αναφορά στις κυριότερες μεθόδους απεικόνισης εγκεφάλου, όπως το ηλεκτροεγκεφαλογράφημα και την λειτουργική απεικόνιση Μαγνητικού Συντονισμού καθώς και στον συνδυασμό τους για πιο ικανοποιητικά αποτελέσματα. Το κεφάλαιο 3 αναφέρεται κυρίως σε θέματα σχετικά τα προκλητά δυναμικά, καθώς και την υποσυνείδητη αντίληψη. Στο κεφάλαιο 4 περιγράφεται η πειραματική διαδικασία και η μετρητική διάταξη που χρησιμοποιήθηκε καθώς και η παρουσίαση της επεξεργασίας των μετρήσεων μέσω του eeglab. Τέλος, στο κεφάλαιο 5 παρουσιάζονται τα αποτελέσματα της επεξεργασίας σε διαγράμματα προκλητών δυναμικών και φασματικής ισχύος καθώς επίσης και τα συμπεράσματα της εργασίας αυτής. / The display of subliminal messages is the process of stimuli exposure below the threshold of awareness. Through this procedure the thoughts, feelings and actions of a human can be influenced. The subliminal perception occurs when information stored in the human mind without the receiver being consciously aware of it. The information reaching the brain is perceived by the subconscious part of the brain. The object of this diploma thesis is to assess the possible differences in electroencephalogram (EEG) and event - related potentials (ERPs) recordings during the presentation of visual subliminal stimuli compared to non – subliminal conditions. A protocol that examines how subliminal stimuli influence the decision making and the cerebral operation is used. In the first part of the thesis (chapters 1 and 2) there is a brief review of the main brain imaging methods such as EEG and fMRI as well as the combination of them. Chapter 3 reveals issues about event - related potentials and mostly about subliminal perception. In chapter 4, the experiment and the measuring devices used are described, and there is also a presentation of the analysis by using the eeglab. Finally, chapter 5 includes the results of analysis on event - related potential and spectral power graphs, as well as the conclusions of this work.

O uso de sistemas denominados Brain Computer Interface, ou simplesmente BCI, para controle de dispositivos tem gerado cada vez mais trabalhos de análise de sinais de EEG, principalmente devido ao fato do desenvolvimento tecnológico dos sistemas de processamento de dados, trazendo novas perspectiva de desenvolvimento de equipamentos que auxiliem pessoas com debilidades motoras. Neste trabalho é abordado o comportamento dos classificadores LDA (Discriminante Linear de Fisher) e o classificador Naive Bayes para classificação de movimento de mão direita e mão esquerda a partir da aquisição de sinais eletroencefalográficos. Para análise destes classificadores foram utilizadas como características de entrada a energia de trechos do sinal filtrados por um passa banda com frequências dentro dos ritmos sensório-motor e também foram utilizadas componentes de energia espectral através do periodograma modificado de Welch. Como forma de pré-processamento também é apresentado o filtro espacial Common Spatial Pattern (CSP) de forma a aumentar a atividade discriminativa entre as classes de movimento. Foram obtidas taxas de acerto de até 70% para a base de dados geradas neste trabalho e de até 88% utilizando a base de dados do BCI Competition II, taxas de acertos compatíveis com outros trabalhos na área. / Brain Computer Interface (BCI) systems usage for controlling devices has increasingly generated research on EEG signals analysis, mainly because the technological development of data processing systems has been offering a new perspective on developing equipment to assist people with motor disability. This study aims to examine the behavior of both Fisher's Linear Discriminant (LDA) and Naive Bayes classifiers in determining both the right and left hand movement through electroencephalographic signals. To accomplish this, we considered as input feature the energy of the signal trials filtered by a band pass with sensorimotor rhythm frequencies; spectral power components from the Welch modified periodogram were also used. As a preprocessing form, the Common Spatial Pattern (CSP) filter was used to increase the discriminative activity between classes of movement. The database created from this study reached hit rates of up to 70% while the BCI Competition II reached hit rates up to 88%, which is consistent with the literature.

The epilepsy is not a recent phenomenon, even its has being approached and Inves- tigated, this area still demands several researches and it is far away from being totally explained. The obtaining of the primordial features to di®erentiate the epileptic events of the others, in coming signs EEG of scalp, it represents a great challenge, since exist to many artifacts, and these are confused with epileptic events. In this sense, this study presents the development of architectures destined to detect events of epilepsy in coming signs EEG of scalp, capable to aid the professionals of the health in the study of this pathology To accomplish the objectives, ¯rstly was developed an application capable to visualize EEG and to segment the electroencephalogram plan to form the base of data Concerning to the detection of the pathological signs, four architectures were proposed. The architecture with analysis multi-resolution used the \ wavelet " (WT) for extraction of features, as well as neural networks and specialist system for recognition. For that architecture the best gotten results obtained a rate of 71,6 % of success, with 28,3 % of error. The sensibility was around 83,3 %, the speci¯city 70,5 % and the precision 76,9 %. The statistical architecture is directly composed of tools for features extraction of the sign. The best success rate was around 85,3 %, the obtained error was of 14,3 % and the inde¯nite ones around 1 %. The sensibility was of 97,4 %, the speci¯city 82,1 % and the precision 89,75 %. The architecture of analysis multi-resolution and AR possesses two stages for extraction of feature: the \ wavelet ", following by the AR models. For that architecture they used two AR models . The best success rate for the \ Yule-Walker"model was around 87,9 %, with order 10. Already in the results of the \ Burg"model, the best success rate was of 88,5 % with order 7. For the last architecture is a hybrid model with several tools of extraction of features in the domain of the time, frequency (FFT) and time-frequency (WT). In that architecture the success rate was in 95,1 %, the error 4,1 % the inde¯nite ones 5,5 %. The speci¯city was of 91,5 %, the obtained sensibility was of 90,5 % and the precision around 91,1 %. Therefore all of the developed systems presented quite coherent results among the phenomena demarcated by the professionals of the medical area and those revealed by the architectures, mainly for the case of the hybrid architecture that presented the best rates. / A identificação de fenômenos epileptogênicos por meio de registros eletroencefalográficos (EEG) não invasivos se constitui numa área de pesquisa que apresenta grandes desafios devido µa presença de diversos distúrbios (artefatos) que dificultam a análise destes registros. Tal tarefa é de extrema importância uma vez que o diagnóstico e o tratamento da epilepsia requer uma avaliação clínica baseada no EEG do paciente. Neste contexto, este trabalho apresenta alguns sistemas para melhorar a identificação dos sinais de crise epilépticas baseados em técnicas de processamento de sinais e de inteligência artificial. Estas propostas são baseadas em uma plataforma que permite a visualização e análise dos arquivos de EEG. Para a detecção de eventos patológicos, são propostas quatro arquiteturas. Na arquitetura com análise multi-resolução foram utilizadas duas famílias wavelet (WT) para a extração de características, redes neurais artificiais e sistema especialista para o reconhecimento dos sinais de crise. Com essa arquitetura, o melhor resultado conseguido foi uma taxa de acerto de 71,6% no reconhecimento dos sinais patológicos. A sensibilidade ficou em torno de 83,3%, a especificidade 70,5% e a precisão 76,9%. Já a arquitetura estatística é composta de ferramentas para extração de características diretamente do sinal. A melhor taxa de acerto ficou em torno de 85,3%, o erro obtido foi de 14,3% e os indefinidos em torno de 1%. A sensibilidade foi de 97,4%, a especificidade 82,1% e a precisão 89,75%. A arquitetura de análise multi-resolução com modelo auto-regressivo (AR) possui duas etapas para extração de características: a \wavelet" (WT), seguida do modelo AR. Para essa arquitetura foram utilizados dois modelos AR. A melhor taxa de acerto para o modelo \Yule-Walker" ficou em torno de 87,9%, com ordem 10. Já para os resultados do modelo\Burg", a melhor taxa de acerto foi de 88,5% com ordem 7. A última arquitetura é um modelo híbrido com várias ferramentas de extração de características no domínio do tempo, freqüência (FFT) e tempo-freqüência (WT). Nessa arquitetura a taxa de acerto ficou em 95,1%, o erro em 4,1% e os indefinidos em 5,5%. A especificidade foi de 91,5%, a sensibilidade obtida foi de 90,5% e a precisão em torno de 91,1%. Todos os sistemas desenvolvidos apresentaram resultados coerentes com os fenômenos demarcados pelos eletroencefalografistas e aqueles revelados pelas arquiteturas. Dentre as propostas, a arquitetura híbrida apresentou o melhor desempenho. / Doutor em Ciências

O uso de sistemas denominados Brain Computer Interface, ou simplesmente BCI, para controle de dispositivos tem gerado cada vez mais trabalhos de análise de sinais de EEG, principalmente devido ao fato do desenvolvimento tecnológico dos sistemas de processamento de dados, trazendo novas perspectiva de desenvolvimento de equipamentos que auxiliem pessoas com debilidades motoras. Neste trabalho é abordado o comportamento dos classificadores LDA (Discriminante Linear de Fisher) e o classificador Naive Bayes para classificação de movimento de mão direita e mão esquerda a partir da aquisição de sinais eletroencefalográficos. Para análise destes classificadores foram utilizadas como características de entrada a energia de trechos do sinal filtrados por um passa banda com frequências dentro dos ritmos sensório-motor e também foram utilizadas componentes de energia espectral através do periodograma modificado de Welch. Como forma de pré-processamento também é apresentado o filtro espacial Common Spatial Pattern (CSP) de forma a aumentar a atividade discriminativa entre as classes de movimento. Foram obtidas taxas de acerto de até 70% para a base de dados geradas neste trabalho e de até 88% utilizando a base de dados do BCI Competition II, taxas de acertos compatíveis com outros trabalhos na área. / Brain Computer Interface (BCI) systems usage for controlling devices has increasingly generated research on EEG signals analysis, mainly because the technological development of data processing systems has been offering a new perspective on developing equipment to assist people with motor disability. This study aims to examine the behavior of both Fisher's Linear Discriminant (LDA) and Naive Bayes classifiers in determining both the right and left hand movement through electroencephalographic signals. To accomplish this, we considered as input feature the energy of the signal trials filtered by a band pass with sensorimotor rhythm frequencies; spectral power components from the Welch modified periodogram were also used. As a preprocessing form, the Common Spatial Pattern (CSP) filter was used to increase the discriminative activity between classes of movement. The database created from this study reached hit rates of up to 70% while the BCI Competition II reached hit rates up to 88%, which is consistent with the literature.