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.

This thesis studies the application of the wavelet filter bank (WFB) in perceptual audio coding by providing brief overviews of perceptual coding, psychoacoustics, wavelet theory, and existing wavelet coding algorithms. Furthermore, it describes the poor frequency localization property of the WFB and explores one filter design method, in particular, for improving channel separation between the wavelet bands. A wavelet audio coder has also been developed by the author to test the new filters. Preliminary tests indicate that the new filters provide some improvement over other wavelet filters when coding audio signals that are stationary-like and contain only a few harmonic components, and similar results for other types of audio signals that contain many spectral and temporal components. It has been found that the WFB provides a flexible decomposition scheme through the choice of the tree structure and basis filter, but at the cost of poor localization properties. This flexibility can be a benefit in the context of audio coding but the poor localization properties represent a drawback. Determining ways to fully utilize this flexibility, while minimizing the effects of poor time-frequency localization, is an area that is still very much open for research.

Echolocation in bats is a subject that has received much attention over the last few decades. Bat echolocation calls have evolved over millions of years and can be regarded as well suited to the task of active target-detection. In analysing the time-frequency structure of bat calls, it is hoped that some insight can be gained into their capabilities and limitations. Most analysis of calls is performed using non-parametric techniques such as the short time Fourier transform. The resulting time-frequency distributions are often ambiguous, leading to further uncertainty in any subsequent analysis which depends on the time-frequency distribution. There is thus a need to develop a method which allows improved time-frequency characterisation of bat echolocation calls. The aim of this work is to develop a parametric approach for signal analysis, specifically taking into account the varied nature of bat echolocation calls in the signal model. A time-varying harmonic signal model with a polynomial chirp basis is used to track the instantaneous frequency components of the signal. The model is placed within a Bayesian context and a particle filter is used to implement the filter. Marginalisation of parameters is considered, leading to the development of a new marginalised particle filter (MPF) which is used to implement the algorithm. Efficient reversible jump moves are formulated for estimation of the unknown (and varying) number of frequency components and higher harmonics. The algorithm is applied to the analysis of synthetic signals and the performance is compared with an existing algorithm in the literature which relies on the Rao-Blackwellised particle filter (RBPF) for online state estimation and a jump Markov system for estimation of the unknown number of harmonic components. A comparison of the relative complexity of the RBPF and the MPF is presented. Additionally, it is shown that the MPF-based algorithm performs no worse than the RBPF, and in some cases, better, for the test signals considered. Comparisons are also presented from various reversible jump sampling schemes for estimation of the time-varying number of tones and harmonics. The algorithm is subsequently applied to the analysis of bat echolocation calls to establish the improvements obtained from the new algorithm. The calls considered are both amplitude and frequency modulated and are of varying durations. The calls are analysed using polynomial basis functions of different orders and the performance of these basis functions is compared. Inharmonicity, which is deviation of overtones away from integer multiples of the fundamental frequency, is examined in echolocation calls from several bat species. The results conclude with an application of the algorithm to the analysis of calls from the feeding buzz, a sequence of extremely short duration calls emitted at high pulse repetition frequency, where it is shown that reasonable time-frequency characterisation can be achieved for these calls.

<p>This dissertation focuses on two vital challenges in relation to whale acoustic signals: detection and classification.</p><p>In detection, we evaluated the influence of the uncertain ocean environment on the spectrogram-based detector, and derived the likelihood ratio of the proposed Short Time Fourier Transform detector. Experimental results showed that the proposed detector outperforms detectors based on the spectrogram. The proposed detector is more sensitive to environmental changes because it includes phase information.</p><p>In classification, our focus is on finding a robust and sparse representation of whale vocalizations. Because whale vocalizations can be modeled as polynomial phase signals, we can represent the whale calls by their polynomial phase coefficients. In this dissertation, we used the Weyl transform to capture chirp rate information, and used a two dimensional feature set to represent whale vocalizations globally. Experimental results showed that our Weyl feature set outperforms chirplet coefficients and MFCC (Mel Frequency Cepstral Coefficients) when applied to our collected data.</p><p>Since whale vocalizations can be represented by polynomial phase coefficients, it is plausible that the signals lie on a manifold parameterized by these coefficients. We also studied the intrinsic structure of high dimensional whale data by exploiting its geometry. Experimental results showed that nonlinear mappings such as Laplacian Eigenmap and ISOMAP outperform linear mappings such as PCA and MDS, suggesting that the whale acoustic data is nonlinear.</p><p>We also explored deep learning algorithms on whale acoustic data. We built each layer as convolutions with either a PCA filter bank (PCANet) or a DCT filter bank (DCTNet). With the DCT filter bank, each layer has different a time-frequency scale representation, and from this, one can extract different physical information. Experimental results showed that our PCANet and DCTNet achieve high classification rate on the whale vocalization data set. The word error rate of the DCTNet feature is similar to the MFSC in speech recognition tasks, suggesting that the convolutional network is able to reveal acoustic content of speech signals.</p> / Dissertation

Time-Frequency (TF) masking is an audio processing technique useful for isolating an audio source from interfering sources. TF masking has been applied and studied in monaural and binaural applications, but has only recently been applied to distributed microphone arrays. This work focuses on evaluating the TF masking technique's ability to isolate human speech and improve speech intelligibility in an immersive "cocktail party" environment. In particular, an upper-bound on TF masking performance is established and compared to the traditional delay-sum and general sidelobe canceler (GSC) beamformers. Additionally, the novel technique of combining the GSC with TF masking is investigated and its performance evaluated. This work presents a resource-efficient method for studying the performance of these isolation techniques and evaluates their performance using both virtually simulated data and data recorded in a real-life acoustical environment. Further, methods are presented to analyze speech intelligibility post-processing, and automated objective intelligibility measurements are applied alongside informal subjective assessments to evaluate the performance of these processing techniques. Finally, the causes for subjective/objective intelligibility measurement disagreements are discussed, and it was shown that TF masking did enhance intelligibility beyond delay-sum beamforming and that the utilization of adaptive beamforming can be beneficial.

This paper analyzes the return connectedness between the biotechnology sector and other financial assets for 1 January 2000 to 31 December 2018, using an empirical approach from both time- and frequency-domain. The results reveal that the connectedness between the biotechnology sector and other financial assets are decreasing with time, entailing high diversification opportunities in the long-run. Our results also suggest that the spillover effect from the biotechnology sector is higher than the spillover effect to the biotechnology sector, proposing that the sector affects other financial assets to a greater extent than they affect the biotechnology sector. Concurrently, we found that the net directional connectedness is negative for the sector, which means that it does not transmit shocks to others since it is not subject to significant return or volatility shocks. This implies that the systematic risk connected to the biotechnology sector is lower than previous studies argue for. Thus, our main finding is that investments in the sector has safe haven properties, indicating that they are independent towards other sectors. By investing in the biotechnology sector, investors contribute to society and supports the R&amp;D, leading to development of vital drugs. In light of this, we argue that investments in the sector are socially beneficial. Building on these insights, investments in the biotechnology sector are of importance when investing in a prosperous world.

Escoamentos turbulentos têm sido por muitos anos o objetivo de importantes estudos para descobrir sua dinâmica. Dentre as características mais significativas, destaca-se a multiplicidade de escalas que os caracterizam, desde as maiores estruturas (baixas freqüências) controladas pela geometria que as geram, até as menores estruturas (altas freqüências) limitadas pela viscosidade do fluido. Uma idéia importante é o conceito de vórtices que está ligado a melhorias nas técnicas de visualização, tanto em laboratório quanto em experimentos numéricos. Estes vórtices têm um importante papel em numerosas aplicações tecnológicas, sendo necessário entender a dinâmica da organização de seus movimentos para controlar mecanicamente sua produção ou supressão. Neste contexto, a análise de um misturador de ar em um escoamento em tê é o principal objetivo de estudo deste trabalho. A geometria em tê é bastante simples, mas propicia o aparecimento de um escoamento com passagem de vórtices. Testes experimentais do escoamento, com duas entradas de ar com temperaturas diferentes, foram realizados no Laboratório de Engenharia Térmica e Fluidos da Escola de Engenharia de São Carlos da Universidade de São Paulo (LETeF - EESC - USP). As medidas de temperatura foram obtidas com termopares instalados ao longo da tubulação. Com o software CFX foram realizados estudos com métodos numéricos LES e DES aplicados ao escoamento. Estes resultados computacionais foram comparados com os dados experimentais, através da análise tempo-freqüência. Estudos preliminares do escoamento mostram regiões com passagem de vórtices, e a habilidade da técnica de análise tempo-freqüência em caracterizar a existência e a forma destas estruturas turbulentas. / Turbulent flows have been the objective of important studies to discover its dynamics. One important characteristic of these flows is the multiplicity of scales, since the large structures (low frequencies) controlled by the geometry that generates them, until the small structures (high frequencies) limited by the fluid viscosity. An important idea is the concept of vortices that it is associated with the improvements in the visualization techniques, in laboratory or numerical experiments. These vortices have an important function in many technological applications. In each one of these fields, it is necessary to understand the dynamics of its movements to control the mechanisms for producing or suppressing these vortices. In this context, the analysis of an air mixing in a tee junction is the main objective of this work. The tee geometry is sufficiently simple, but contributes for the appearance of a flow with vortices transition. Experimental tests with two different air temperatures inlets were done at the Thermal and Fluid Engineering Laboratory of the University of São Paulo at São Carlos (LETeF - EESC - USP). The measures of temperature were acquired with thermocouples installed along the pipe. Numerical studies with LES and DES methods using CFX software were applied to the flow. These computational results were compared with the experimental data through the time-frequency analysis. Preliminary studies of the flow show vortices transition regions and the ability of time-frequency technique in describing the existence and shape of turbulent structures.

Um dos atributos fundamentais associados aos escoamentos multifásicos é a existência de estruturas características segundo as quais as diferentes fases do líquido escoam. O surgimento de uma dessas estruturas, conhecidas como configurações ou regimes de escoamento, é determinado pelas vazões e propriedades físicas dos componentes, além de parâmetros geométricos como diâmetro e inclinação do conduto. O desenvolvimento de metodologias de caracterização de regimes, bem como a caracterização e o diagnóstico da transição destes regimes de escoamento são de fundamental importância. Este trabalho utiliza a análise tempo-frequência da transformada de Gabor para caracterizar os regimes de escoamento horizontais gás-líquido intermitentes. Mais especificamente, o principal objetivo está em investigar a existência de sub-regimes dentro do regime intermitente, para tanto recorremos à covariância tempo-frequência da transformada de Gabor, que é capaz de detectar transições através da não-estacionaridade associada com as correspondentes transições. Testes experimentais foram conduzidos no circuito TALC em CEA-Grenoble e uma extensiva base de dados foi obtida, cobrindo diversos tipos de escoamento intermitente. Uma sonda de condutividade elétrica, consistindo de dois anéis de eletrodos montados junto à tubulação, produziu sinais dos quais a covariância tempo-frequência foi calculada através da correspondente transformada de Gabor. / One of the main features associated to multiphase flows is the existence of characteristic dynamic structures according to which the different phases of a mixture of immiscible fluids can flow. The manifestation of one of these structures, known a flow pattern or regime, is determined by the flow rates as well as by physical and geometrical properties of the fluids and piping. The development of flow pattern characterization and diagnostic methods, and the associated transitions in between, is of crucial importance for an efficient engineering of such phenomena. Time-frequency analysis based on the Gabor transform is used in this work to characterize horizontal air-water intermittent flow regimes. More specifically, our main objective is to reveal the existence of sub-regimes inside the intermittent regimes region with the help of the corresponding time-frequency covariance based on the Gabor transform, which is capable of detecting transitions by assessing the unstationarity associated with the corresponding transitions. Experimental tests were conducted at the TALC facility at CEA-Grenoble and an extensive database was obtained, covering several types of intermittent flow. A conductivity probe, consisting in two ring electrodes flush mounted to the pipe, delivered signals from which the time-frequency covariance were calculated from the corresponding Gabor transform.