La maladie de Parkinson (MP) est la deuxième affection neurodégénérative la plus fréquente après la maladie d’Alzheimer. Elle se caractérise par un dysfonctionnement du système des ganglions de la base, en rapport avec une dégénérescence des neurones dopaminergiques de la substance noire compacte. A côté des symptômes moteurs, la MP s’accompagne de troubles cognitifs, en particulier une altération des capacités de sélectivité attentionnelle. Ce déficit attentionnel se traduit par des difficultés à sélectionner les informations pertinentes pour la conduite en cours et peut entraîner des troubles cognitifs légers. L’origine des troubles attentionnels reste imprécise : on ignore s'ils résultent d’une défaillance des mécanismes volontaires d’orientation de l’attention ou d'une perturbation des processus automatiques de capture attentionnelle. Le filtrage sensoriel permet de focaliser notre attention grâce à une sélection des informations pertinentes pour l’action en cours et une inhibition des informations non pertinentes. Il peut être exploré en neurophysiologie par le paradigme d’inhibition par le prepulse (PPI). Ce dernier correspond à l’atténuation de la réponse motrice et corticale suite à la présentation d’un stimulus sursautant (pulse) lorsque celui-ci est précédé de quelques millisecondes d’un stimulus non sursautant (prepulse). Le PPI est influencé par l’attention, son amplitude étant majorée lorsque l’attention est portée volontairement sur le prepulse. L’objectif général était donc de mieux identifier la nature des troubles de la sélectivité attentionnelle dans la MP par un paradigme actif de PPI au cours duquel la réponse corticale au pulse est enregistrée. Nous faisions l’hypothèse que les parkinsoniens présenteraient une inhibition plus faible que les témoins sains. En cas de défaillance de mobilisation volontaire des ressources attentionnelles, l'inhibition de la réponse corticale au pulse devrait être moins importante lorsque les ressources attentionnelles allouées au traitement du prepulse mettent en jeu la mobilisation volontaire de l’attention. A l’inverse, en cas de défaut de capture attentionnelle, l’inhibition de la réponse serait moins importante lorsque le traitement du prepulse implique les processus automatiques de capture.Pour répondre à cet objectif, nous avons dans un premier temps développé et validé un paradigme actif de PPI au cours duquel l’effet de la mobilisation volontaire de l’attention et de la capture attentionnelle sur le processus de filtrage sensoriel a été évalué. Pour ce faire, 26 témoins sains jeunes ont bénéficié d’un électroencéphalogramme à haute résolution tout en réalisant une tâche attentionnelle sur laquelle a été greffé un paradigme actif de PPI. Nous avons recueilli la réponse corticale évoquée et induite par la présentation du pulse. 16 témoins sains âgés, 16 patients parkinsoniens sans trouble cognitif et 16 patients avec troubles cognitifs légers ont bénéficié du même enregistrement au cours de la même tâche attentionnelle. Chez les témoins sains jeunes, nous avons montré que les processus de mobilisation volontaire de l’attention et de capture attentionnelle modulaient de façon différentielle la réponse évoquée et induite par la présentation du pulse. Au cours du vieillissement, nous avons observé une meilleure sensibilité de la réponse corticale induite, ce qui nous a conduit à choisir ce marqueur cortical pour évaluer le filtrage sensoriel dans la MP. Nos résultats montrent une réduction de l’inhibition de la réponse induite chez les parkinsoniens avec troubles cognitifs légers, confirmant la distractibilité. La MP s’accompagne aussi d’une altération dans la génération des oscillations corticales dans la bande de fréquence thêta quand la focalisation de l’attention est engagée. / Parkinson’s disease (PD) is the most frequent neurodegenerative disorder after Alzheimer’s disease. It is characterized by degeneration of dopaminergic neurons in the substantia nigra pars compacta, causing a progressive loss of dopamine neurotransmission within the basal ganglia. Apart from motor symptoms, PD patients have cognitive disorders. Namely, focused attention is impaired and PD patients fail to select task-relevant information, leading sometimes to mild cognitive impairment (MCI). The origin of this impairment is still debated: PD-related selective attention deficit may be due either to a failure of goal-directed or stimulus-driven attention. Sensory gating helps the individuals to selectively allocate their attentional resources to salient stimuli and to inhibit irrelevant information. One of the physiological marker of this process is referred to as prepulse inhibition (PPI). It corresponds to the attenuation of the motor and cortical responses to a startling stimulus (pulse) when a non-startling stimulus (the prepulse) precedes the pulse by few milliseconds. PPI can be modulated by attention, its magnitude being greater after a to-be attended prepulse. Moreover, PPI is mediated by basal ganglia.The main aim of this work was to better identify the mechanisms involved in selective attention deficits in PD. We used an active PPI paradigm and recorded the cortical response to the pulse. We assumed that PD patients would exhibit a lower inhibition of the cortical response than healthy controls. If attention deficits in PD are related to an impairment of goal-directed attention, PD patients would exhibit lower inhibition after a to-be attended prepulse than in the other conditions. At the opposite, if it is due to a failure of stimulus-driven attention, inhibition would be lower after a prepulse which involuntarily captures attention than in the other conditions.In order to reach this objective, we have first developed and validated a new active PPI paradigm in order to investigate the role of goal-directed and stimulus-driven attention on sensory-cognitive gating. To this end, high resolution electroencephalogram was recorded in 26 young healthy subjects. They performed a selective attention task combined with an active PPI paradigm and the auditory-evoked and induced cortical response to the pulse was recorded. Then, the same procedure was administered in 16 elderly healthy subjects, 16 PD patients without MCI and 16 PD patients with MCI. In young healthy subjects, we found that stimulus-driven and goal-directed attention each had specific effects on the inhibition of the evoked and induced response to the pulse. The investigation of age-related changes on sensory gating revealed that the induced cortical response was more sensitive for assessing age-related changes than the evoked response. Then, we chose this cortical marker to investigate sensory gating in PD. Our results showed that PD patients with MCI exhibit lower inhibition of induced cortical response to the pulse than healthy controls. This finding confirms previous results showing a high distractibility in these patients. Moreover, PD patients exhibit impaired theta synchronization when focused attention was engaged.

En décembre 2015, les détecteurs LIGO ont pour la première fois détecté une onde gravitationnelle émise lors de la coalescence d'une paire de trous noirs il y a de cela 1.3 milliards d'années. Une telle première dans la toute nouvelle astronomie gravitationnelle a été suivie par plusieurs autres observations. La dernière en date est la fusion de deux étoiles à neutron dont la contrepartie électromagnétique a pu être observée par plusieurs observatoires à travers le monde. A cette occasion, les ondes gravitationnelles se sont inscrites dans l'astronomie multi-messager. Ces observations ont été rendues possibles par des techniques avancées d'analyse de données. Grâce à elles, la faible empreinte laissée par une onde gravitationnelle dans les données de détecteurs peut être isolée. Le travail de cette thèse est dédié au développement d'une technique de détection d'ondes gravitationnelles ne reposant que sur une connaissance minimale du signal à isoler. Le développement de cette méthode consiste plus précisément à introduire une information sur la phase du signal d'onde gravitationnelle selon un contexte astrophysique déterminé. La première partie de cette thèse est consacrée à la présentation de la méthode. Dans une seconde partie cette méthode est appliquée à la recherche de signaux d'ondes gravitationnelles en provenance de systèmes binaires de trous noirs de masse stellaire dans du bruit Gaussien. Puis l'étude est répétée dans du bruit de détecteurs collecté pendant la première période de prise de données. Enfin la troisième partie est dédiée à la recherche de binaires de trous noirs dont l'orbite montre un écart à la géométrie circulaire, ce qui complexifie la morphologie du signal. De telles orbites sont qualifiées d'excentriques. Cette troisième analyse permet d'établir de premiers résultats quant à la méthode proposée lorsque le signal d'intérêt est peu connu / In december 2015 the LIGO detectors have first detected a gravitational wave emitted by a pair of coalescing black holes 1.3 billion years ago. Many more observations have been realised since then and heralded gravitational waves as a new messenger in astronomy. The latest detection is the merge of two neutron stars whose electromagnetic counterpart has been followed up by many observatories around the globe. These direct observations have been made possible by the developpement of advanced data analysis techniques. With them the weak gravitational wave inprint in detectors may be recovered. The realised work during this thesis aims at developping an existing gravitational wave detection method which relies on minimal assumptions of the targeted signal. It more precisely consists in introducing an information on the signal phase depending on the astrophysical context. The first part is dedicated to a presentation of the method. The second one presents the results obtained when applying the method to the search of stellar mass binary black holes in simulated Gaussian noise data. The study is repeated in real instrumental data collected during the first run of LIGO. Finally, the third part presents the method applied in the search for eccentric binary black holes. Their orbit exhibits a deviation from the quasi-circular orbit case considered so far and thus complicates the signal morphology. This third analysis establishes first results with the proposed method in the case of a poorly modeled signal

Many of the existing ambient modal identification methods based on vibration data process information centrally to calculate the modal properties. Such methods demand relatively large memory and processing capabilities to interrogate the data. With the recent advances in wireless sensor technology, it is now possible to process information on the sensor itself. The decentralized information so obtained from individual sensors can be combined to estimate the global modal information of the structure. The main objective of this thesis is to present a new class of decentralized algorithms that can address the limitations stated above. The completed work in this regard involves casting the identification problem within the framework of underdetermined blind source separation (BSS). Time-frequency transformations of measurements are carried out, resulting in a sparse representation of the signals. Stationary wavelet packet transform (SWPT) is used as the primary means to obtain a sparse representation in the time-frequency domain. Several partial setups are used to obtain the partial modal information, which are then combined to obtain the global structural mode information. Most BSS methods in the context of modal identification assume that the excitation is white and do not contain narrow band excitation frequencies. However, this assumption is not satisfied in many situations (e.g., pedestrian bridges) when the excitation is a superposition of narrow-band harmonic(s) and broad-band disturbance. Under such conditions, traditional BSS methods yield sources (modes) without any indication as to whether the identified source(s) is a system or an excitation harmonic. In this research, a novel under-determined BSS algorithm is developed involving statistical characterization of the sources which are used to delineate the sources corresponding to external disturbances versus intrinsic modes of the system. Moreover, the issue of computational burden involving an over-complete dictionary of sparse bases is alleviated through a new underdetermined BSS method based on a tensor algebra tool called PARAllel FACtor (PARAFAC) decomposition. At the core of this method, the wavelet packet decomposition coefficients are used to form a covariance tensor, followed by PARAFAC tensor decomposition to separate the modal responses. Finally, the proposed methods are validated using measurements obtained from both wired and wireless sensors on laboratory scale and full scale buildings and bridges.

Visualization, processing and editing of audio, directly on a time-frequency surface, is the scope of this thesis. More precisely the scalogram produced by a Gabor Wavelet transform is used, which is a powerful alternative to traditional techinques where the wave form is the main visual aid and editting is performed by parametric filters. Reconstruction properties, scalogram design and enhancements as well audio manipulation algorithms are investigated for this audio representation.The scalogram is designed to allow a flexible choice of time-frequency ratio, while maintaining high quality reconstruction. For this mean, the Loglet is used, which is observed to be the most suitable filter choice.  Re-assignmentare tested, and a novel weighting function using partial derivatives of phase is proposed.  An audio interpolation procedure is developed and shown to perform well in listening tests.The feasibility to use the transform coefficients directly for various purposes is investigated. It is concluded that Pitch shifts are hard to describe in the framework while noise thresh holding works well. A downsampling scheme is suggested that saves on operations and memory consumption as well as it speeds up real world implementations significantly. Finally, a Scalogram 'compression' procedure is developed, allowing the caching of an approximate scalogram.

The aim of this thesis is to define a perceptual scale for the ‘Time-Frequency’ analysis of music signals. The equal tempered ‘Bach ’ scale is a suitable scale, since it covers most of the genres of music and the error is equally distributed for each semi-tone. However, it may be necessary to allow a tolerance of around 50 cents or half the interval of the Bach scale, so that the interval can accommodate other common intonation schemes. The thesis covers the formulation of the Bach scale filter-bank as a time-varying model. It makes a comparative study with other commonly used perceptual scales. Two applications for the Bach scale filter-bank are also proposed, namely automated segmentation of speech signals and transcription of singing voice for query-by-humming applications. Even though this filter-bank is suggested with a motivation from music, it could also be applied to speech. A method for automatically segmenting continuous speech into phonetic units is proposed. The results, obtained from the proposed method, show around 82% accuracy for the English and 85% accuracy for the Hindi databases. This is an improvement of around 2 -3% when the performance is compared with other popular methods in the literature. Interestingly, the Bach scale filters perform better than the filters designed for other common perceptual scales, such as Mel and Bark scales. ‘Musical transcription’ refers to the process of converting a musical rendering or performance into a set of symbols or notations. A query in a ‘query-by-humming system’ can be made in several ways, some of which are singing with words, or with arbitrary syllables, or whistling. Two algorithms are suggested to annotate a query. The algorithms are designed to be fairly robust for these various forms of queries. The first algorithm is a frequency selection based method. It works on the basis of selecting the most likely frequency components at any given time instant. The second algorithm works on the basis of finding time-connected contours of high energy in the ‘Time-Frequency’ plane of the input signal. The time domain algorithm works better in terms of instantaneous pitch estimates. It results in an error of around 10 -15%, while the frequency domain method results in an error of around 12 -20%. A song rendered by two different people will have quite a few different properties. Their absolute pitches, rates of rendering, timbres based on voice quality and inaccuracies, may be different. The thesis discusses a method to quantify the distance between two different renderings of musical pieces. The distance function has been evaluated by attempting a search for a particular song from a database of a size of 315, made up of songs sung by both male and female singers and whistled queries. Around 90 % of the time, the correct song is found among the top five best choices picked. Thus, the Bach scale has been proposed as a suitable scale for representing the perception of music. It has been explored in two applications, namely automated segmentation of speech and transcription of singing voices. Using the transcription obtained, a measure of the distance between renderings of musical pieces has also been suggested.

Diese Dissertation ist dem Studium temperierter Distributionen mittels mikrolokaler Methoden gewidmet. Die fundamentale Größe der mikrolokalen Analysis, die Wellenfrontmenge, wird durch zwei analoge Konzepte ersetzt, die den pseudo-differentiellen SG- und Shubin-Kalkülen zugeordnet sind. Die Eigenschaften dieser globalen Wellenfrontmengen werden studiert und ferner werden unterschiedliche Möglichkeiten, diese globalen Singularitäten zu charakterisieren, untersucht, insbesondere mittels der FBI-Transformation. Zahlreiche Konstruktionen, die den klassischen Wellenfrontmengenbegriff beinhalten, werden in den globalen Kontext übersetzt, insbesondere Rechenoperationen mit temperierten Distributionen wie etwa (getwistete) Produkte, Pull-backs und Paarungen, für die mikrolokale Existenzkriterien angegeben werden. Als eine Anwendung wird eine Klasse von temperierten Oszillatorintegralen eingeführt, welche durch inhomogene Phasenfunktionen und Amplituden aus SG-Symbolklassen parametrisiert werden. Die SG-Wellenfrontmengen dieser Distributionen werden untersucht und es stellt sich heraus, dass diese durch eine Verallgemeinerung der Menge stationärer Punkte der Phasenfunktionen beschränkt werden. In diesem Kontext wird eine Verallgemeinerung des klassischen Begriffs einer konischen Lagrange-Untermannifaltigkeit des T*R^d vorgenommen und diese Objekte werden auf ihre Parametrisierungseigenschaften untersucht. Es stellt sich heraus, dass jedes solche Objekt lokal als die Menge der stationären Punkte einer SG-Phasenfunktion realisiert werden kann. Als weitere Anwendung werden einige Konstruktionen der axiomatischen Quantenfeldtheorie, die Distributionen beinhalten, im temperierten Kontext realisiert.

Many of the existing ambient modal identification methods based on vibration data process information centrally to calculate the modal properties. Such methods demand relatively large memory and processing capabilities to interrogate the data. With the recent advances in wireless sensor technology, it is now possible to process information on the sensor itself. The decentralized information so obtained from individual sensors can be combined to estimate the global modal information of the structure. The main objective of this thesis is to present a new class of decentralized algorithms that can address the limitations stated above. The completed work in this regard involves casting the identification problem within the framework of underdetermined blind source separation (BSS). Time-frequency transformations of measurements are carried out, resulting in a sparse representation of the signals. Stationary wavelet packet transform (SWPT) is used as the primary means to obtain a sparse representation in the time-frequency domain. Several partial setups are used to obtain the partial modal information, which are then combined to obtain the global structural mode information. Most BSS methods in the context of modal identification assume that the excitation is white and do not contain narrow band excitation frequencies. However, this assumption is not satisfied in many situations (e.g., pedestrian bridges) when the excitation is a superposition of narrow-band harmonic(s) and broad-band disturbance. Under such conditions, traditional BSS methods yield sources (modes) without any indication as to whether the identified source(s) is a system or an excitation harmonic. In this research, a novel under-determined BSS algorithm is developed involving statistical characterization of the sources which are used to delineate the sources corresponding to external disturbances versus intrinsic modes of the system. Moreover, the issue of computational burden involving an over-complete dictionary of sparse bases is alleviated through a new underdetermined BSS method based on a tensor algebra tool called PARAllel FACtor (PARAFAC) decomposition. At the core of this method, the wavelet packet decomposition coefficients are used to form a covariance tensor, followed by PARAFAC tensor decomposition to separate the modal responses. Finally, the proposed methods are validated using measurements obtained from both wired and wireless sensors on laboratory scale and full scale buildings and bridges.

This thesis deals with the problem of estimating the velocity of a mobile station (MS)in a mobile communication system using the instantaneous frequency (IF) of the received signal at the MS antenna. This estimate is essential for satisfactory handover performance, effective dynamic channel assignment, and optimisation of adaptive multiple access wireless receivers. Conventional methods for estimating the MS velocity are based either on the statistics of the envelope or quadrature components of the received signal. In chapter 4 of the thesis, we show that their performance deteriorates in the presence of shadowing. Other velocity estimators have also been proposed which require prior estimation of the channel or the average received power. These are generally difficult to obtain due to the non-stationary nature of the received signal. An appropriate window which depends on the unknown MS velocity must first be applied in order to accurately estimate the required quantities. Using the statistics of the IF of the received signal at the MS antenna given in chapter 3, new velocity estimators are proposed in chapter 4 of this thesis. The proposed estimators are based on the moments, zero-crossing rate, and covariance of the received IF. Since the IF of the received signal is not affected by any amplitude distortion, the proposed IF-based estimators are robust to shadowing and propagation path-loss. The estimators for the MS velocity in a macro- and micro-cellular system are presented separately. A macro-cell system can be considered as a special case of a micro-cell in which there is no line-of-sight component at the receiver antenna. It follows that those estimators which are derived for micro-cells can be used in a macro-cell as well. In chapter 4, we analyse the performance of the proposed velocity estimators in the presence of additive noise, non-isotropic scattering, and shadowing. We also prove analytically that the proposed velocity estimators outperform the existing methods in the presence of shadowing and additive noise. The proposed IF-based estimators need prior estimation of both the IF of the received signal and Ricean K-factor. The IF estimation in a typical wireless environment, can be considered as a special case of a general problem of IF estimation in the presence of multiplicative and additive noise. In chapter 5, we show that current time-frequency approaches to this problem which are based on the peak of a time-frequency distribution (TFD) of the signal, fail because of the special shape of the power spectral density of the multiplicative noise in a wireless environment. To overcome this drawback, the use of the first-order moment of a TFD is studied in chapter 5. Theoretical analysis and simulations show that the IF estimator based on the first-order moment of a TFD exhibits negligible bias when the signal-to-additive noise ratio is more than 10 dB. The Ricean K-factor is not only necessary for velocity estimation in micro-cells, but also is a measure of the severity of fading and a good indicator of the channel quality. Two new methods for estimating the Ricean K-factor based on the first two moments of the envelope of the received signal, are proposed in chapter 6. Performance analysis presented in chapter 6, prove that the proposed K estimators are robust to non-isotropic scattering. Theoretical analysis and simulations which are presented in chapters 4 and 7 of this thesis, prove that the proposed velocity and K estimators outperform existing estimators in the presence of shadowing and additive noise.

This project attempts to quantify the integrity of the fixation of total hip arthro- T plasties (THAs) by observing vibration signal features. The aim of this thesis is, therefore, to find the signal differences between firm and loose prosthesis. These difference will be expressed in different transformed domains with the expectation that a certain domain will provide superior results. Once the signal differences have been determined they will be examined for their ability to quantify the looseness. Initially, a new definition of progressive, femoral component loosening was created, based on the application of mechanical fit, involving four general conditions. In order of increasing looseness the conditions (with their equivalent engineering associations) are listed as, firm (adherence), firm (interference), micro-loose (transition) and macro-loose (clearance). These conditions were then used to aid in the development and evaluation of a simple mathematical model based on an ordinary differential equation. Several possible parameters well suited to quantification such as gap displacement, cement/interface stiffness and apparent mass were the identified from the model. In addition, the development of this model provided a solution to the problem of unifying early and late loosening mentioned in the literature by Li et al. in 1995 and 1996. This unification permitted early (micro loose) and late (macro loose) loosening to be quantified, if necessary, with the same parameter. The quantification problem was posed as a detection problem by utilising a varying amplitude input. A set of detection techniques were developed to detect the quantity of a critical value, in this case a force. The detection techniques include deviation measures of the instantaneous frequency of the impulse response of the system (accuracy of 100%), linearity of the systems response to Gaussian input (total accuracy of 97.9% over all realisations) and observed resonant frequency linearity with respect to displacement magnitude (accuracy of 100%). Note, that as these techniques were developed with the model in mind their simulated performance was, therefore, considerably high. This critical value found by the detector was then fed into the model and a quantified output was calculated. The quantification techniques using the critical value approach include, ramped amplitude input resonant analysis (experimental accuracy of 94%) and ramped amplitude input stochastic analysis (experimental accuracy of 90%). These techniques were based on analysing the response of the system in the time-frequency domain and with respect to its short-time statistical moments to a ramping amplitude input force, respectively. In addition, other mechanically sound forms of analysis, were then applied to the output of the nonlinear model with the aim of quantifying the looseness or the integrity of fixation of the THA. The cement/interface stiffness and apparent mass techniques, inspired by the work of Chung et.al. in 1979, attempt to assess the integrity of fixation of the THA by tracking the mechanical behaviour of the components of the THA, using the frequency and magnitude of the raw transducer data. This technique has been developed fron the theory of Chung etal but with a differing perspective and provides accuracies of 82% in experimentation and 71% in simulation for the apparent mass and interface stiffness techniques, respectively. Theses techniques do not quantify all forms of clinical loosening, as clinical loosening can exist in many different forms, but they do quantify mechanical loosening or the mechanical functionality of the femoral component through related parameters that observe reduction in mechanical mass, stiffness and the amount of rattle generated by a select ghap betweent he bone/cement or prosthesis/cement interface. This form of mechanical loosening in currently extremely difficult to detect using radiographs. It is envisaged that a vibration test be used in conjunction with radiographs to provide a more complete picture of the integrity of fixation of the THA.

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.