In many scenarios, events such as singularities and transients that carry important information about a signal undergo spreading during acquisition or transmission and it is important to localize the events. For example, edges in an image, point sources in a microscopy or astronomical image are blurred by the point-spread function (PSF) of the acquisition system, while in a speech signal, the epochs corresponding to glottal closure instants are shaped by the vocal tract response. Such events can be extracted with the help of techniques that promote sparsity, which enables separation of the smooth components from the transient ones. In this thesis, we consider development of such sparsity promoting techniques. The contributions of the thesis are three-fold: (i) an auditory-motivated continuous wavelet design and representation, which helps identify singularities; (ii) a sparsity-driven deconvolution technique; and (iii) a sparsity-driven deconvolution technique for reconstruction of nite-rate-of-innovation (FRI) signals. We use the speech signal for illustrating the performance of the techniques in the first two parts and super-resolution microscopy (2-D) for the third part. In the rst part, we develop a continuous wavelet transform (CWT) starting from an auditory motivation. Wavelet analysis provides good time and frequency localization, which has made it a popular tool for time-frequency analysis of signals. The CWT is a multiresolution analysis tool that involves decomposition of a signal using a constant-Q wavelet filterbank, akin to the time-frequency analysis performed by basilar membrane in the peripheral human auditory system. This connection motivated us to develop wavelets that possess auditory localization capabilities. Gammatone functions are extensively used in the modeling of the basilar membrane, but the non-zero average of the functions poses a hurdle. We construct bona de wavelets from the Gammatone function called Gammatone wavelets and analyze their properties such as admissibility, time-bandwidth product, vanishing moments, etc.. Of particular interest is the vanishing moments property, which enables the wavelet to suppress smooth regions in a signal leading to sparsi cation. We show how this property of the Gammatone wavelets coupled with multiresolution analysis could be employed for singularity and transient detection. Using these wavelets, we also construct equivalent lterbank models and obtain cepstral feature vectors out of such a representation. We show that the Gammatone wavelet cepstral coefficients (GWCC) are effective for robust speech recognition compared with mel-frequency cepstral coefficients (MFCC). In the second part, we consider the problem of sparse blind deconvolution (SBD) starting from a signal obtained as the convolution of an unknown PSF and a sparse excitation. The BD problem is ill-posed and the goal is to employ sparsity to come up with an accurate solution. We formulate the SBD problem within a Bayesian framework. The estimation of lter and excitation involves optimization of a cost function that consists of an `2 data- fidelity term and an `p-norm (p 2 [0; 1]) regularizer, as the sparsity promoting prior. Since the `p-norm is not differentiable at the origin, we consider a smoothed version of the `p-norm as a proxy in the optimization. Apart from the regularizer being non-convex, the data term is also non-convex in the filter and excitation as they are both unknown. We optimize the non-convex cost using an alternating minimization strategy, and develop an alternating `p `2 projections algorithm (ALPA). We demonstrate convergence of the iterative algorithm and analyze in detail the role of the pseudo-inverse solution as an initialization for the ALPA and provide probabilistic bounds on its accuracy considering the presence of noise and the condition number of the linear system of equations. We also consider the case of bounded noise and derive tight tail bounds using the Hoe ding inequality. As an application, we consider the problem of blind deconvolution of speech signals. In the linear model for speech production, voiced speech is assumed to be the result of a quasi-periodic impulse train exciting a vocal-tract lter. The locations of the impulses or epochs indicate the glottal closure instants and the spacing between them the pitch. Hence, the excitation in the case of voiced speech is sparse and its deconvolution from the vocal-tract filter is posed as a SBD problem. We employ ALPA for SBD and show that excitation obtained is sparser than the excitations obtained using sparse linear prediction, smoothed `1=`2 sparse blind deconvolution algorithm, and majorization-minimization-based sparse deconvolution techniques. We also consider the problem of epoch estimation and show that epochs estimated by ALPA in both clean and noisy conditions are closer to the instants indicated by the electroglottograph when with to the estimates provided by the zero-frequency ltering technique, which is the state-of-the-art epoch estimation technique. In the third part, we consider the problem of deconvolution of a specific class of continuous-time signals called nite-rate-of-innovation (FRI) signals, which are not bandlimited, but specified by a nite number of parameters over an observation interval. The signal is assumed to be a linear combination of delayed versions of a prototypical pulse. The reconstruction problem is posed as a 2-D SBD problem. The kernel is assumed to have a known form but with unknown parameters. Given the sampled version of the FRI signal, the delays quantized to the nearest point on the sampling grid are rst estimated using proximal-operator-based alternating `p `2 algorithm (ALPAprox), and then super-resolved to obtain o -grid (O. G.) estimates using gradient-descent optimization. The overall technique is termed OG-ALPAprox. We show application of OG-ALPAprox to a particular modality of super-resolution microscopy (SRM), called stochastic optical reconstruction microscopy (STORM). The resolution of the traditional optical microscope is limited by di raction and is termed as Abbe's limit. The goal of SRM is to engineer the optical imaging system to resolve structures in specimens, such as proteins, whose dimensions are smaller than the di raction limit. The specimen to be imaged is tagged or labeled with light-emitting or uorescent chemical compounds called uorophores. These compounds speci cally bind to proteins and exhibit uorescence upon excitation. The uorophores are assumed to be point sources and the light emitted by them undergo spreading due to di raction. STORM employs a sequential approach, wherein each step only a few uorophores are randomly excited and the image is captured by a sensor array. The obtained image is di raction-limited, however, the separation between the uorophores allows for localizing the point sources with high precision. The localization is performed using Gaussian peak- tting. This process of random excitation coupled with localization is performed sequentially and subsequently consolidated to obtain a high-resolution image. We pose the localization as a SBD problem and employ OG-ALPAprox to estimate the locations. We also report comparisons with the de facto standard Gaussian peak- tting algorithm and show that the statistical performance is superior. Experimental results on real data show that the reconstruction quality is on par with the Gaussian peak- tting.

Les océans subissent des pressions d'origine anthropique particulièrement fortes comme la surpêche, la pollution physico-chimique, et le bruit rayonné par les activités industrielles et militaires. Cette thèse se place dans un contexte de compréhension de l'impact du bruit rayonné dans les océans sur les mammifères marins. L'acoustique passive joue donc un rôle fondamental dans ce problème. Ce travail aborde la tâche de détection de signatures acoustiques de mammifères marins dans le spectrogramme. Cette tâche est difficile pour deux raisons : 1. le bruit océanique a une structure complexe (non-stationnaire, coloré), 2. les signaux de mammifères marins sont inconnus et possèdent eux aussi une structure complexe (non-stationnaires bande étroite et/ou impulsionnels). Le problème doit donc être résolu de manière locale en temps-fréquence, et ne pas faire d'hypothèse a priori sur le signal. Des détecteurs statistiques basés uniquement sur la connaissance des statistiques du bruit dans le spectrogramme existent, mais souffrent deux lacunes : 1. leurs performances en terme de probabilité de fausse alarme/ probabilité de détection se dégradent fortement à faible rapport signal à bruit, et 2. ils ne sont pas capables de séparer les signaux à bande étroite des signaux impulsionnels. Ce travail apporte des pistes de réflexion sur ces problèmes.L'originalité de ce travail de thèse repose dans la formulation d'un test d'hypothèse binaire prenant explicitement en compte l'organisation spatiale des pics temps-fréquence. Nous introduisons une méthode d'Analyse de la Densité des Fausses Alarmes (FADA) qui permet de discriminer les régions temps-fréquence abritant le signal de celles n'abritant que du bruit. Plus précisément,le nombre de fausses alarmes dans une région du plan est d'abord modélisé par une loi binomiale, puis par une loi binomiale corrélée, afin de prendre en considération la redondance du spectrogramme. Le test d'hypothèse binaire est résolu par une approche de Neyman-Pearson. Nous démontrons numériquement la pertinence de cette approche et nous la validons sur données réelles de mammifères marins disposant d'une grande variété de signaux et de conditions de bruit. En particulier, nous illustrons la capacité de FADA à discriminer efficacement le signal du bruit en milieu fortement impulsionnel. / The oceans experience heavy anthropogenic pressure due to overfishing, physico-chemical pollution, and noise radiated by industrial and military activities. This work focuses on the use of passive acoustic monitoring of the oceans, as a tool to understand the impact of radiated noise on marine ecosystems, and particularly on marine mammals. This work tackles the task of detection of acoustical signals of marine mammals using the spectrogram. This task is uneasy for two reasons : 1. the ocean noise structure is complex (non-stationary and colored) and 2. the signals of interest are unknown and also shows a complex structure (non-stationary narrow band and/or impulsive). The problem therefore must be solved locally without making a priori hypothesis on the signal. Statistical detectors only based on the local analysis of the noise spectrogram coefficients are available, making them suitable for this problem. However, these detectors suffer two disadvantages : 1. the trade-offs false alarm probability/ detection probability that are available for low signal tonoise ratio are not satisfactory and 2. the separation between narrow-band and impulsive signals is not possible. This work brings some answers to these problems.The main contribution of this work is to formulate a binary hypothesis test taking explicitly in account the spatial organization of time-frequency peaks. We introduce the False Alarm Density Analysis (FADA) framework that efficiently discriminates time-frequency regions hosting signal from the ones hosting noise only. In particular the number of false alarms in regions of the binary spectrogram is first modeled by a binomial distribution, and then by a correlated binomial distribution to take in account the spectrogram redundancy. The binary hypothesis test is solved using a Neyman-Pearson criterion.We demonstrate the relevance of this approach on simulated data and validate the FADA detector on a wide variety of real signals. In particular we show the capability of the proposed method to efficiently detect signals in highly impulsive environment.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-02-16T09:52:46Z No. of bitstreams: 1 alamsilvamenezes.pdf: 8301590 bytes, checksum: aed618e30f38206da4bf4f329924f87e (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-02-26T12:30:53Z (GMT) No. of bitstreams: 1 alamsilvamenezes.pdf: 8301590 bytes, checksum: aed618e30f38206da4bf4f329924f87e (MD5) / Made available in DSpace on 2016-02-26T12:30:53Z (GMT). No. of bitstreams: 1 alamsilvamenezes.pdf: 8301590 bytes, checksum: aed618e30f38206da4bf4f329924f87e (MD5) Previous issue date: 2014-09-01 / A presente tese propõe soluções ao problema da explicitação do conteúdo espectral de processos estacionários e não estacionários, com aplicações na estimação de frequência, estimação da densidade espectral de potência e no monitoramento do espectro. A técnica de estimação de frequência proposta nesta tese, baseada na warped discrete Fourier transform, apresenta, de acordo com as simulações computacionais, o melhor desempenho frente às demais técnicas comparadas, atingindo o Cramer-Rao bound para uma ampla faixa de relação sinal ruído. Em relação a estimação da densidade espectral de potência, a Hartley Multitaper method, proposta nesta tese, apresenta desempenho similar à multitaper method, em termos da variância de estimação e da polarização do espectro, mas simpli cação de implementação. Uma técnica para monitoramento do espectro para sistemas power line communication é proposta, levando em consideração o conceito de quanta e a diversidade observada quando os sinais são aquisitados a partir da rede de energia elétrica e do ar. Baseando-se em sinais sintéticos, gerados em computador, assim como dados de medição do espectro, obtidos utilizando uma antena e o cabo de energia elétrica como elementos sensores, veri fica-se que o desempenho da técnica proposta supera a monitoração padrão, sobretudo quando a diversidade gerada pelo cabo e pela antena sobre o sinal monitorado é explorada na detecção. / This dissertation aims at discussing solutions to deal with spectral analysis of stationary and non-stationary processes for frequency estimation, power spectral density estimation and spectral monitoring applications. The frequency estimation techniques are assessed through computer simulations. The proposed technique for frequency estimation is based on warped discrete Fourier transform outperforms other techniques, achieving the Cramer-Rao Bound for a wide range of signal to noise ratio. Regarding the power spectral density estimation, the proposed Hartley Multitaper Method shows similar performance, in terms of variance of estimates and polarization spectrum; however, it can simplify the implementation complexity. The introduced spectrum sensing technique is based on quanta de nition and the diversity o ered by the signals acquired from the electric power grids and the air. Based on computer-generation data and those one obtained during a measurement campaign, which one in this thesis is evaluated using synthetic signals, generated by computer, as well as measurement data of the spectrum. The numerical results show that the proposed technique outperforms a previous technique and can attain the very detection ratio and the very low false alarm when the diversity yielded by electric power grid and air is exploited.

The aim of the dissertation was to design a realistic, low-complexity non-binary (NB) low density parity check (LDPC) coded space-time-frequency (STF) coded multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system with an iterative joint decoder and detector structure at the receiver. The goal of the first part of the dissertation was to compare the performance of different design procedures for NB-LDPC codes on an additive white Gaussian noise (AWGN) channel, taking into account the constraint on the code length. The effect of quantisation on the performance of the code was also analysed. Different methods for choosing the NB elements in the parity check matrix were compared. For the STF coding, a class of universal STF codes was used. These codes use linear pre-coding and a layering approach based on Diophantine numbers to achieve full diversity and a transmission rate (in symbols per channel use per frequency) equal to the number of transmitter antennas. The study of the system considers a comparative performance analysis of di erent ST, SF and STF codes. The simulations of the system were performed on a triply selective block fading channel. Thus, there was selectivity in the fading over time, space and frequency. The effect of quantisation at the receiver on the achievable diversity of linearly pre-coded systems (such as the STF codes used) was mathematically derived and verified with simulations. A sphere decoder (SD) was used as a MIMO detector. The standard method used to create a soft-input soft output (SISO) SD uses a hard-to-soft process and the max-log-map approximation. A new approach was developed which combines a Hopfield network with the SD. This SD-Hopfield detector was connected with the fast Fourier transform belief propagation (FFT-BP) algorithm in an iterative structure. This iterative system was able to achieve the same bit error rate (BER) performance as the original SISO-SD at a reduced complexity. The use of the iterative Hopfield-SD and FFT-BP decoder system also allows performance to be traded off for complexity by varying the number of decoding iterations. The complete system employs a NB-LDPC code concatenated with an STF code at the transmitter with a SISO-SD and FFT-BP decoder connected in an iterative structure at the receiver. The system was analysed in varying channel conditions taking into account the effect of correlation and quantisation. The performance of different SF and STF codes were compared and analysed in the system. An analysis comparing different numbers of FFT-BP and outer iterations was also done. AFRIKAANS : Die doel van die verhandeling was om ’n realistiese, lae-kompleksiteit nie-binˆere (NB) LDPC gekodeerde ruimte-tyd-frekwensie-gekodeerde MIMO-OFDM-sisteem met iteratiewe gesamentlike dekodeerder- en detektorstrukture by die ontvanger te ontwerp. Die eerstem deel van die verhandeling was om die werkverrigting van verskillende ontwerpprosedures vir NB-LDPC kodes op ’n gesommeerde wit Gausruiskanaal te vergelyk met inagneming van die beperking op die lengte van die kode. Verskillende metodes om die nie-bineêre elemente in die pariteitstoetsmatriks te kies, is gebruik. Vir die ruimte-tyd-frekwensiekodering is ’n klas universele ruimte-tyd-frekwensiekodes gebruik. Hierdie kodes gebruik lineêre pre-kodering en ’n laagbenadering gebaseer op Diofantiese syfers om volle diversiteit te bereik en ’n oordragtempo (in simbole per kanaalgebruik per frekwensie) gelyk aan die aantal senderantennes. Die studie van die sisteem oorweeg ’n vergelykende werkverrigtinganalisie van verskillende ruimte-tyd-, ruimte-freksensie- en ruimte-tyd-frekwensiekodes. Die simulasies van die sisteem is gedoen op ’n drievoudig selektiewe blokwegsterwingskanaal. Daar was dus selektiwiteit in die wegsterwing oor tyd, ruimte en frekwensie. Die effek van kwantisering by die ontvanger op die bereikbare diversiteit van lineêr pre-gekodeerde sisteme (soos die ruimte-tyd-frekwensiekodes wat gebruik is) is matematies afgelei en bevestig deur simulasies. ’n Sfeerdekodeerder (SD) is gebruik as ’n MIMO-detektor. Die standaardmetode wat gebuik is om ’n sagte-inset-sagte-uitset (SISO) SD te skep, gebruik ’n harde-na-sagte proses en die maksimum logaritmiese afbeelding-benadering. ’n Nuwe benadering wat ’n Hopfield-netwerk met die SD kombineer, is ontwikkel. Hierdie SD-Hopfield-detektor is verbind met die FFT-BP-algoritme in iteratiewe strukture. Hierdie iteratiewe sisteem was in staat om dieselfde bisfouttempo te bereik as die oorspronklike SISO-SD, met laer kompleksiteit. Die gebruik van die iteratiewe Hopfield-SD en FFT-BP-dekodeerdersisteem maak ook daarvoor voorsiening dat werkverrigting opgeweeg kan word teen kompleksiteit deur die aantal dekodering-iterasies te varieer. Die volledige sisteem maak gebruik van ’n QC-NB-LDPC-kode wat met ’n ruimte-tyd-frekwensiekode by die sender aaneengeskakel is met ’n SISO-SD en FFT-BP-dekodeerder wat in ’n iteratiewe struktuur by die ontvanger gekoppel is. Die sisteem is onder ’n verskeidenheid kanaalkondisies ge-analiseer met inagneming van die effek van korrelasie en kwantisering. Die werkverrigting van verskillende ruimte-frekwensie- en ruimte-tyd-frekwensiekodes is vergelyk en in die sisteem ge-analiseer. ’n Analise om ’n wisselende aantal FFT-BP en buite-iterasies te vergelyk, is ook gedoen. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Electrical, Electronic and Computer Engineering / unrestricted

Aerospace structures comprising of metals and composites are exposed to extreme loading and environmental conditions which necessitates regular inspection and maintenance to verify and monitor overall structural integrity. The timely and accurate detection, characterization and monitoring of structural cracking, corrosion, delaminating, material degradation and other types of damage are of major concern in the operational environment. Along with these, stringent requirements of safety and operational reliability have lead to evolutionary methods for evaluation of structural integrity. As a result, conventional nondestructive evaluation methods have moved towards a new concept, Structural Health Monitoring (SHM). SHM provides in-situ information a bout the occurrence of damage if any, location and severity of damage and residual life of the structure and also helps in improving the safety, reliability and confidence levels of critical engineering structures. While the concepts underlying SHM are well understood, development of methods is still in a nascent stage which requires extensive research that is challenging and has been the main motivating factor for undertaking the work reported in the thesis. Under the scope of the investigations carried out in this thesis, an integrated approach using Ultrasonic (active) and Acoustic Emission (passive) methods has been explored for SHM of metallic and composite plate structures using a distributed array of surface bonded circular piezoelectric wafer active sensors(PWAS). In ultrasonic method, PWAS is used for actuation and reception of Lamb waves in plate structures. The damage detection is based on the interaction of waves with defects resulting in reflection, mode conversion and scattering. In acoustic emission (AE) technique, the same sensor is used to pick up the stress waves generated by initiation or growth of defects or damage. Thus, both the active and passive damage detection methods are used in this work for detection, location and characterization of defects and damage in metallic and composite plates with complex geometries and structural discontinuities. And, thus the strategy adopted is to use time-frequency analysis and time reversal technique to extract the information from Lamb wave signals for damage detection and a geodesic based Lamb wave approach for location of the damage in the structure. To start with experiments were conducted on aluminum plates to study the interaction of Lamb waves with cracks oriented at different angles and on a titanium turbine blade of complex geometry with a fine surface crack. Further, the interaction of Lamb wave modes with multiple layer delaminations in glass fiber epoxy composite laminates was studied. The data acquired from these experiments yielded complex sets of signals which were not easily discern able for obtaining the information required regarding the defects and damage. So, to obtain a basic understanding of the wave patterns, Spectral finite element method has been employed for simulation of wave propagation in composite beams with damages like delamination and material degradation. Following this, time-frequency analysis of a number of simulated and experimental signals due to elastic wave scattering from defects and damage were performed using wavelet transform (WT) and Hilbert-Huang transform(HHT).And, a comparison of their performances in the context of quantifying the damages has given detailed insight into the problem of identifying localized damages, dispersion of multi-frequency non-stationary signals after their interaction with different types of defects and damage, finally leading to quantification. Conventional Lamb wave based damage detection methods look for the presence of defects and damage in a structure by comparing the signal obtained with the baseline signal acquired under healthy conditions. The environmental conditions like change in temperature can alter the Lamb wave signals and when compared with baseline signals may lead to false damage prediction. So, in order to make Lamb wave based damage detection baseline free, in the present work, the time reversal technique has been utilized. And, experiments were conducted on metallic and composite plates to study the time reversal behavior ofA0 andS0Lamb wave modes. Damage in the form of a notch was introduced in an aluminum plate to study the changes in the characteristics of the time reversed Lamb wave modes experimentally. This experimental study showed that there is no change in the shape of the time reversed Lamb wave in the presence of defect implying no breakage of time reversibility. Time reversal experiments were further carried out on a carbon/epoxy composite T-pull specimen representing a typical structure. And, the specimen was subjected to a tensile loading in a Universal testing machine. PWAS sensor measurements were carried out at no load as also during different stages of delamination due to tensile loading. Application of time reversed A 0 and S0 modes for both healthy and delaminated specimens and studying the change in shape of the time reversed Lamb wave signals has resulted in successful detection of the presence of delamination. The aim of this study has been to show the effectiveness of Lamb wave time reversal technique for damage detection in health monitoring applications. The next step in SHM is to identify the damage location after the confirmation of presence of damage in the structure. Wave based acoustic damage detection methods (UT and AE) employing triangulation technique are not suitable for locating damage in a structure which has complicated geometry and contains structural discontinuities. And, the problem further gets compounded if the material of the structure is anisotropic warranting complex analytical velocity models. In this work, a novel geodesic approach using Lamb waves is proposed to locate the AE source/damage in plate like structures. The approach is based on the fact that the wave takes minimum energy path to travel from the source to any other point in the connected domain. The geodesics are computed numerically on the meshed surface of the structure using Dijkstra’s algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first inter section point of these waves, one can get the AE source/damage location. Experiments have been conducted on metallic and composite plate specimens of simple and complex geometry to validate this approach. And, the results obtained using this approach has demonstrated the advantages for a practicable source location solution with arbitrary surfaces containing finite discontinuities. The drawback of Dijkstra’s algorithm is that the geodesics are allowed to travel along the edges of the triangular mesh and not inside them. To overcome this limitation, the simpler Dijkstra’s algorithm has been replaced by a Fast Marching Method (FMM) which allows geodesic path to travel inside the triangular domain. The results obtained using FMM showed that one can accurately compute the geodesic path taken by the elastic waves in composite plates from the AE source/damage to the sensor array, thus obtaining a more accurate damage location. Finally, a new triangulation technique based on geodesic concept is proposed to locate damage in metallic and composite plates. The performances of triangulaton technique are then compared with the geodesic approach in terms of damage location results and their suitability to health monitoring applications is studied.

La syncope est une perte brusque de conscience. Bien qu'elle ne soit pas généralement mortelle, elle présente un impact économique sur le système de soins et sur la vie personnelle de personnes en souffrant. L'objet de la présente étude est de réduire la durée du test clinique (environ 1 heure) et d'éviter aux patients de développer une syncope en la prédisant. L'ensemble de travail s'inscrit dans une démarche de datamining associant l'extraction de paramètres, la sélection des variables et la classification. Trois approches complémentaires sont proposées, la première exploite des méthodes d'analyse non-linéaires de séries temporelles extraites de signaux acquises pendant le test, la seconde s'intéresse aux relations cardiovasculaires en proposant des indices dans le plan temps-fréquence et la troisième, plus originale, prendre en compte leurs dynamiques temporelles. / Syncope is a sudden loss of consciousness. Although it is not usually fatal, it has an economic impact on the health care system and the personal lives of people suffering. The purpose of this study is to reduce the duration of the clinical test (approximately 1 hour) and to avoid patients to develop syncope by early predicting the occurrence of syncope. The entire work fits into a data mining approach involving the feature extraction, feature selection and classification. 3 complementary approaches are proposed, the first one exploits nonlinear analysis methods of time series extracted from signals acquired during the test, the second one focuses on time- frequency (TF) relation between signals and suggests new indexes and the third one, the most original, takes into account their temporal dynamics.

Ce manuscrit porte sur la modélisation et l'estimation de certaines non-stationnarités dans les signaux audio. Nous nous intéressons particulièrement à une classe de modèles de sons que nous nommons timbre*dynamique dans lesquels un signal stationnaire, associé au phénomène physique à l'origine du son, est déformé au cours du temps par un opérateur linéaire unitaire, appelé opérateur de déformation, associé à l'évolution temporelle des caractéristiques de ce phénomène physique. Les signaux audio sont modélisés comme des processus gaussiens généralisés et nous donnons dans un premier temps un ensemble d'outils mathématiques qui étendent certaines notions utilisées en traitement du signal au cas des processus stochastiques généralisés.Nous introduisons ensuite les opérateurs de déformations étudiés dans ce manuscrit. L'opérateur de modulation fréquentielle qui est l'opérateur de multiplication par une fonction à valeurs complexes de module unité, et l'opérateur de changement d'horloge qui est la version unitaire de l'opérateur de composition.Lorsque ces opérateurs agissent sur des processus stationnaires les processus déformés possèdent localement des propriétés de stationnarité et les opérateurs de déformation peuvent être approximés par des opérateurs de translation dans les plans temps-fréquence et temps-échelle. Nous donnons alors des bornes pour les erreurs d'approximation correspondantes. Nous développons ensuite un estimateur de maximum de vraisemblance approché des fonctions de dilatation et de modulation. L'algorithme proposé est testé et validé sur des signaux synthétiques et des sons naurels. / This manuscript deals with the modeling and estimation of certain non-stationarities in audio signals. We are particularly interested in a sound class models which we call dynamic*timbre in which a stationary signal, associated with the physical phenomenon causing the sound, is deformed over time by a linear unitary operator, called deformation operator, associated with the temporal evolution of the characteristics of this physical phenomenon.Audio signals are modeled as generalized Gaussian processes. We give first a set of mathematical tools that extend some classical notions used in signal processing in case of generalized stochastic processes.We then introduce the two deformations operators studied in this manuscript. The frequency modulation operator is the multiplication operator by a complex-valued function of unit module and the time-warping operator is the unit version of the composition operator by a bijective function.When these operators act on generalized stationary processes, deformed process are non-stationary generalized process which locally have stationarity properties and deformation operators can be approximated by translation operators in the time-frequency plans and time-scale.We give accurate versions of these approximations, as well as bounds for the corresponding approximation errors.Based on these approximations, we develop an approximated maximum likelihood estimator of the warping and modulation functions. The proposed algorithm is tested and validated on synthetic signals. Its application to natural sounds confirm the validity of the timbre*dynamic model in this context.

The thesis deals with EEG signals, their description, methods of quantitative analysis and the processes in time-frequency domains, or power spectrums. The relationsheep between brain electrical activity and acustic stimuli (Mozart´s “Sonata K448”) was studied using EEG analysis in relation to sound impulses from replayed extracts of. The proposed experiment protocol included recording of EEG of volunteers. In order to visualize and analyze the data, the software with the graphic user interface was created, which enables topological mapping of brain activity and its vizualization in the time-frequency domain.

The doctoral thesis focuses on signal representation in the time-frequency domain with constant resolution. In theoretical introduction the possibilities of displaying a signal in time and frequency are summarized. Attention is concentrated on comparison of short-time Fourier Transform (STFT) and Wigner-Ville Distribution (WVD). The latter achieves a significantly better resolution, especially for a linearly modulated signal. The disadvantage of WVD, which is the presence of interferences resulting from the calculation of the instantaneous autocorrelation function, is described in detail. These interferences are due to the presence of multiple components in the signal or its non-linear modulation. Subsequently, several methods are discussed, which can suppress these interferences, but at the cost of resolution loss. One of the interference suppression methods is smoothed pseudo Wigner-Ville distribution. It is further used in this thesis for the analysis of interference suppression when various filtrations in the time-frequency plane are applied. Several signals with multiple components or various non-linear modulations are used. Based on the analysis, a method using a set of variously smoothed pseudo Wigner-Ville distributions is designed to estimate the time-frequency representation with high resolution and minimal interferences. To compare the results to other methods, the quantitative metrics used in the literature are compared. To select the appropriate one a new metric is suggested. It is applicable to simulated signals and uses mean square error. Based on the comparison, the Stankovi\' measure is selected as the most appropriate for comparing results. The selected metric is used to determine the appropriate minimal number of differently smoothed pseudo Wigner-Ville distributions. Using the selected metric, the proposed method is compared with other methods. These are STFT with optimized window length, S-method with optimized parameter and optimization method using radial Gaussian kernel (RGK). These methods are compared based on the set of signals previously used for interference suppression analysis. In addition, noises are added to the signals. Finally, the methods are also compared based on the real bat echo signal. In conclusion, the proposed method outperforms the compared methods in suppressing interference and resolution.

The master's thesis deals with the problem of restoring a block of missing samples in a digital audio signal. This problem is formulated as an optimization task, which seeks the sparsest time-frequency representation of a signal within the set of feasible reconstructed signals. Several particular formulations are discussed, namely the analyzing and the synthesizing model, both for convex and non-convex approaches. Suitable algorithms are proposed for solving these formulations, and in the convex case, the method is further enhanced by various procedures to compensate for the energy drop in the inpainted signal segment. The proposed algorithms are tested on real recordings, and their performance is shown to be competitive with the state-of-the-art.