A Terapia Fotodinâmica (TFD) é uma modalidade terapêutica promissora que tem mostrado resultados clínicos efetivos, a lém de custo benefício favorável ao sistema de saúde. Embora a TFD esteja associada à indução de morte celular por necrose e, ou apoptose, pesquisas recentes comprovam a ativação da autofagia. Visando entender a relação entre a quantidade de espécies reativas de oxigênio (EROs), produzidas após fotoativação dos fotossensibilizadores (FSs), com a indução de morte autofágica, foram utilizados os FSs fenotiazínicos estruturalmente semelhantes, azul de metileno (MB) e 1,9-dimetil azul de metileno (DMMB); as linhagens celulares HeLa e HaCat, como modelos biológicos e LEDs emitindo em 633 nm, como fonte luminosa. Os ensaios de viabilidade em função da dose de luz e da concentração dos FSs verificaram que o aumento de morte celular está diretamente relacionado ao aumento da concentração e ao aumento da dose de luz, para ambos FSs. Verificou-se que nas condições de IC50 a concentração do DMMB (10 nmol/L) é menor que a do MB (2,0 µmol/L) em duas ordens de grandeza, e essa diferença também se reflete no grau de desbalanço oxidativo gerado após fotossensibilização. Foi verificado que para o MB, a elevada geração de EROs está fortemente correlacionada com a perda de viabilidade, enquanto que para o DMMB essa correlação é fraca, uma vez que há perda de sobrevida sem grandes gerações de EROs. No entanto, a diminuição de sobrevida causada pelo DMMB se correlaciona forte e significativamente ao aumento da autofagia, indicando ocorrência de morte celular autofágica tanto em células HaCaT quanto em células HeLa. As análises de dano em organelas indicaram que ambos FSs, após serem fotoativados, causam danos em lisossomas e em mitocôndrias de células HaCaT. E confirmou-se, por ensaio de localização subcelular, que ambos FSs estão nessas organelas. Uma vez que a localização subcelular do FS influencia no mecanismo de morte celular foto desenvolvido, verificou-se que o MB nas mesmas concentrações nanomolares do DMMB não induz autofagia, pois o mesmo encontra-se fotoquimicamente inativo nas mitocôndrias, devido à redução pelas coenzimas presentes nesta organela. O DMMB possui um potencial de redução menor que o MB, o que impede a redução deste FS nas mitocôndrias, e, mesmo em baixas concentrações, o DMMB é capaz de comprometer a integridade de mitocôndrias e lisossomas, e induz ir autofagia como um mecanismo de morte celular. As condições em que o MB não se encontra totalmente reduzido no ambiente celular são em concentrações mais elevadas, nas quais a geração do nível de estresse oxidativo é maior e não se observa resposta autofágica após fotossensibilização. Esses resultados mostram que a eficiência de morte celular causada por TFD não está necessariamente relacionada ao nível de estresse oxidativo gerado, uma vez que o DMMB induziu estresse oxidativo em menor extensão do que MB e, no entanto, induziu morte celular em maior extensão. Confirmou-se o conceito de que, fotossensibilizadores mais eficazes para a TFD devem resultar da melhoria na especificidade das reações de fotossensibilização nos alvos celulares e não apenas em melhoria na eficiência de geração de ERO. / Photodynamic Therapy (PDT) is a promising therapeutic modality that has shown effective clinical outcomes and benefits in terms of costs to the national health system. Although PDT is associated with induction of cell death by necrosis or apoptosis, recent data suggest the activation of autophagy. In order to understand the relationship between reactive oxygen species (ROS), generated after light activation of photosensitizers (PSs), and the autophagic cell death induction, we have used two phenothiazines with similar structure - methylene blue (MB) and 1,9-dimethyl methylene blue (DMMB); HaCaT and HeLa cells were used as biological models and LEDs emitting at 633 nm were used as light source. Cell viability assays as function of light dose and PS concentration showed that the increase in cell death was directly proportional to the PS concentration and light dose, to the both PSs. At IC50 was verified that DMMB concentration (10 nmol/L) is lower than MB concentration (2,0 µmol/L) in two order of magnitude, and this difference is reflected in degree of oxidative stress promoted by photosensitizers . Only for MB the amount of detected ROS is highly correlated with loss of cell viability, while for DMMB this correlation is weak, because there is loss of viability without large generation of ROS. Nevertheless, the viability decreased for DMMB is highly correlated with the increase of autophagy, indicating occurrence of autophagic cell death in both HaCaT cells and in HeLa cells. The analyses of damaged cell organelles indicated that both PSs, after be photoactivated, induce lysosomal and mithochondrial damage in HaCaT cells. And the subcellular localization assay confirmed that DMMB and MB are localized in these organelles. Because the subcellular localization of PSs influences cell death mechanisms, this research identified that MB, in the same nanomolar concentration of DMMB, does not induce autophagy, because it is photochemically inactive in mitochondria due the reducing coenzymes present in this organelle. DMMB has a lower reduction potential than MB, which hinders PS reduction in mitochondria, and possibly generate a mild oxidative stress that compromise the integrity of mitochondria and lysosomes, and justify autophagy induction as a cell death mechanism. The conditions that MB is not fully reduced in the cellular environment are at higher concentrations, in which was detected high level of oxidative stress and autophagic cell death was not observed after photosensitization. These results show that the efficiency of cell death induced by PDT is not necessarily related with oxidative stress level, since the oxidative stress induced by DMMB was lesser than by MB, however, the cell death was greater. This research confirms the concept that more effective photosensitizers for PDT means greater specificity of photosensitization reactions, and not only improvement of the efficiency of ROS generation.

Melanoma is a pigmented tumor that originates from the melanocytes; pigmented cells present throughout the body, including skin and iris. The cutaneous form is the most common type, and it represents about 5% of the skin tumors diagnosed in Brazil. Although it does not have a high incidence, it represents about 80% to 85% of all skin tumor deaths. The second most frequent type of melanoma is ocular. It represents 5% of all melanoma cases and is a potentially lethal disease, especially when it causes metastasis. The main therapeutic approach for melanomas, in general, is surgery, with resection of the cutaneous lesion or enucleation in the case of ocular melanoma. Other techniques such as adjuvant immunotherapy, palliative chemotherapy, and radiotherapy are also used. However, they have low efficacy and several side effects. Photodynamic therapy is a therapeutic modality based on the interaction of light at specific wavelength and photosensitizer, in the presence of molecular oxygen, leading the cell to death. As melanoma is a pigmented cancer, it usually does not respond well to photodynamic therapy due to the high absorption of light on the surface of the tumor, making volumetric eradication impossible. This project investigated optical strategies for the diagnosis and treatment of melanoma. For the diagnosis, it was evaluated the fluorescence lifetime technique to differentiate melanoma and normal skin. A sensitivity of 99.4%, specificity of 97.4% and accuracy of 98.4% were achieved using linear discrimination analysis. For the cutaneous melanoma treatment, PDT combined to optical clearing agents (OCAs) was investigated. Vascular and cell-target photosensitizers were evaluated combined or not to OCAs. OCA improved PDT response in all pigmented tumors treated, but the best results were achieved when a dual-photosensitizer treatment combined to OCA was performed. The treatment of conjunctival melanoma was conducted using 2-photon excitation photodynamic therapy. The advantage of this technique is the use of infrared light, in a wavelength that melanin has a low absorption, improving the light penetration into the tumor. The tumor histology shows that apoptosis was induced only at the treatment site, with no damage to the surrounding tissue. Additionally, a single TPE-PDT session could treat the entire tumor. / O melanoma é um tumor pigmentado que surge dos melanócitos, células pigmentadas presentes em todo o corpo, incluindo a pele e a íris. A forma cutânea é a mais comum e representa cerca de 5% dos tumores cutâneos diagnosticados no Brasil. Embora não tenha uma alta incidência, representa cerca de 80% a 85% de todas as mortes por tumor de pele. O segundo tipo de melanoma mais frequente é o ocular. Representa 5% de todos os casos de melanoma e é uma doença potencialmente letal, especialmente em casos de metástase. A principal abordagem terapêutica para melanomas, em geral, é a cirurgia, com ressecção da lesão cutânea ou enucleação no caso do melanoma ocular. Outras técnicas, como imunoterapia adjuvante, quimioterapia paliativa e radioterapia também são usadas, porém, apresentam baixa eficiência e muitos efeitos colaterais. A terapia fotodinâmica é uma modalidade terapêutica baseada na interação da luz em um comprimento de onda específico e um fotossensibilizador, na presença de oxigênio molecular, levando a célula à morte. Como o melanoma é um câncer pigmentado, geralmente não responde bem à terapia fotodinâmica devido à alta absorção de luz na superfície do tumor, impossibilitando a erradicação volumétrica. Este projeto investigou estratégias ópticas para o diagnóstico e tratamento do melanoma. Para o diagnóstico, foi avaliada a técnica de tempo de vida de fluorescência para distinguir melanoma de pele normal. Utilizando análise de discriminação linear, obteve-se uma sensibilidade de 99,4%, especificidade de 97,4% e precisão de 98,4%. Para o tratamento de melanoma cutâneo, a PDT combinada com clareadores ópticos (OCAs) foi investigada. Um fotossensibilizador que tem como alvo vaso sanguíneo e um fotossensibilizador de alvo celular foram avaliados combinados ou não com OCAs. OCAs são soluções hiperosmóticas que desidratam o tecido, diminuindo o espalhamento da luz e melhorando a penetração de luz em profundidade. OCA melhorou a resposta de PDT em todos os tumores melanóticos tratados, mas os melhores resultados foram obtidos quando a PDT foi realizada com a combinação dos fotossensibilizadores e clareador óptico em uma única sessão. O tratamento do melanoma conjuntival foi realizado utilizando a terapia fotodinâmica por excitação de 2 fótons (TPE-PDT). A vantagem desta técnica é o uso de luz na região do infravermelho, em um comprimento de onda que melanina tem baixa absorção, melhorando a penetração de luz no tumor. A histologia do tumor mostrou que a apoptose foi induzida apenas no local do tratamento, sem danos no tecido adjacente. Além disso, uma única sessão de TPE-PDT foi capaz de tratar todo o tumor.

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.

En microscopie à force atomique (AFM), l'étude des échantillons est réalisée à l'aide d'une pointe montée sur un microlevier. Le coeur de la technique est la mesure de la force d'interaction pointe-surface, directement proportionnelle à la déflexion du levier. Plus généralement, la compréhension profonde des propriétés mécaniques des microstructures joue un rôle significatif dans le développement des microsystèmes électromécaniques (MEMS), ou encore de capteurs chimiques ou biologiques miniatures.<br /><br />Au delà du dispositif traditionnel de mesure de déflexion angulaire, nous avons conçu et réalisé un AFM avec une détection interférométrique différentielle (entre la base encastrée et l'extrémité libre du levier). La résolution ultime est de 10^-14 m/Hz^1/2, la mesure est de plus intrinsèquement calibrée, indifférente aux dérives thermiques lentes et sans limitation de la plage d'amplitude de la déflexion. <br /><br />Grâce à notre dispositif, nous mesurons le bruit thermique le long du levier. Une reconstruction de la forme spatiale des quatre premiers modes propres en flexion révèle un excellent accord avec le modèle de poutre de Euler-Bernoulli. Un ajustement simultané sur les quatre résonances thermiquement excitées est réalisé à l'aide d'un seul paramètre libre : la raideur du levier, qui est ainsi mesurée avec une grande précision et robustesse. <br /><br />Les fluctuations thermiques de déflexion à basse fréquence démontrent qu'un modèle d'oscillateur harmonique avec dissipation visqueuse n'est plus pertinent hors résonance. De plus, on observe des différences substantielles entre les leviers avec et sans revêtement métallique. Pour ces derniers, l'approche hydrodynamique de Sader rend compte fidèlement du comportement des fluctuations en dessous de la résonance dans l'air. La présence du revêtement introduit une deuxième source de dissipation : la viscoélasticité. Elle se manifeste comme un bruit en 1/f à basse fréquence. L'utilisation du Théorème Fluctuation-Dissipation (TFD) et des relations de Kramers-Kronig permettent une caractérisation complète de la réponse du levier à l'aide des spectres de fluctuations. Une estimation quantitative de la viscoélasticité et de sa dépendance en fréquence est notamment obtenue.

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.

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.