Time-Frequency Analysis as Probabilistic Inference

This is the final published version. It was originally published by IEEE at http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6918491.This paper proposes a new view of time-frequency analysis framed in terms of probabilistic inference. Natural signals are assumed to be formed by the superposition of distinct time-frequency components, with the analytic goal being to infer these components by application of Bayes' rule. The framework serves to unify various existing models for natural time-series; it relates to both the Wiener and Kalman filters, and with suitable assumptions yields inferential interpretations of the short-time Fourier transform, spectrogram, filter bank, and wavelet representations. Value is gained by placing time-frequency analysis on the same probabilistic basis as is often employed in applications such as denoising, source separation, or recognition. Uncertainty in the time-frequency representation can be propagated correctly to application-specific stages, improving the handing of noise and missing data. Probabilistic learning allows modules to be co-adapted; thus, the time-frequency representation can be adapted to both the demands of the application and the time-varying statistics of the signal at hand. Similarly, the application module can be adapted to fine properties of the signal propagated by the initial time-frequency processing. We demonstrate these benefits by combining probabilistic time-frequency representations with non-negative matrix factorization, finding benefits in audio denoising and inpainting tasks, albeit with higher computational cost than incurred by the standard approach.Funding was provided by EPSRC (grant numbers EP/G050821/1 and EP/L000776/1) and Google (R.E.T.) and by the Gatsby Charitable Foundation (M.S.)

Characterizing the transition from balanced to unbalanced motions in the Southern California Current

Author Posting. © American Geophysical Union, 2019. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research-Oceans 124(3), (2019): 2088-2109, doi:10.1029/2018JC014583.As observations and models improve their resolution of oceanic motions at ever finer horizontal scales, interest has grown in characterizing the transition from the geostrophically balanced flows that dominate at large‐scale to submesoscale turbulence and waves that dominate at small scales. In this study we examine the mesoscale‐to‐submesoscale (100 to 10 km) transition in an eastern boundary current, the southern California Current System (CCS), using repeated acoustic Doppler current profiler transects, sea surface height from high‐resolution nadir altimetry and output from a (1/48)° global model simulation. In the CCS, the submesoscale is as energetic as in western boundary current regions, but the mesoscale is much weaker, and as a result the transition lacks the change in kinetic energy (KE) spectral slope observed for western boundary currents. Helmholtz and vortex‐wave decompositions of the KE spectra are used to identify balanced and unbalanced contributions. At horizontal scales greater than 70 km, we find that observed KE is dominated by balanced geostrophic motions. At scales from 40 to 10 km, unbalanced contributions such as inertia‐gravity waves contribute as much as balanced motions. The model KE transition occurs at longer scales, around 125 km. The altimeter spectra are consistent with acoustic Doppler current profiler/model spectra at scales longer than 70/125 km, respectively. Observed seasonality is weak. Taken together, our results suggest that geostrophic velocities can be diagnosed from sea surface height on scales larger than about 70 km in the southern CCS.This research was funded by NASA (NNX13AE44G, NNX13AE85G, NNX16AH67G, NNX16AO5OH, and NNX17AH53G). We thank Sung Yong Kim for providing the high‐frequency radar spectral estimates and the two anonymous reviewers for providing useful comments and suggestions that greatly improved the manuscript. High‐frequency ALES data for Jason‐1 and Jason‐2 altimeters are available upon request (https://openadb.dgfi.tum.de/en/contact/ALES). Both AltiKa and Sentinel‐3 altimeter products were produced and distributed by the Copernicus Marine and Environment Monitoring Service (CMEMS; http://www.marine.copernicus.eu). D. M. worked on the modeling component of this study at the Jet Propulsion Laboratory (JPL), California Institute of Technology, under a contract with the National Aeronautics and Space Administration (NASA). High‐end computing resources were provided by the NASA Advanced Supercomputing (NAS) Division of the Ames Research Center. The LLC output can be obtained from the ECCO project (ftp://ecco.jpl.nasa.gov/ECCO2/LLC4320/). The ADCP data are available at the Joint Archive for Shipboard ADCP data (JASADCP; http://ilikai.soest.hawaii.edu/sadcp).2019-08-2

Laterally constrained low-rank seismic data completion via cyclic-shear transform

A crucial step in seismic data processing consists in reconstructing the wavefields at spatial locations where faulty or absent sources and/or receivers result in missing data. Several developments in seismic acquisition and interpolation strive to restore signals fragmented by sampling limitations; still, seismic data frequently remain poorly sampled in the source, receiver, or both coordinates. An intrinsic limitation of real-life dense acquisition systems, which are often exceedingly expensive, is that they remain unable to circumvent various physical and environmental obstacles, ultimately hindering a proper recording scheme. In many situations, when the preferred reconstruction method fails to render the actual continuous signals, subsequent imaging studies are negatively affected by sampling artefacts. A recent alternative builds on low-rank completion techniques to deliver superior restoration results on seismic data, paving the way for data kernel compression that can potentially unlock multiple modern processing methods so far prohibited in 3D field scenarios. In this work, we propose a novel transform domain revealing the low-rank character of seismic data that prevents the inherent matrix enlargement introduced when the data are sorted in the midpoint-offset domain and develop a robust extension of the current matrix completion framework to account for lateral physical constraints that ensure a degree of proximity similarity among neighbouring points. Our strategy successfully interpolates missing sources and receivers simultaneously in synthetic and field data

Determination and evaluation of clinically efficient stopping criteria for the multiple auditory steady-state response technique

Background: Although the auditory steady-state response (ASSR) technique utilizes objective statistical detection algorithms to estimate behavioural hearing thresholds, the audiologist still has to decide when to terminate ASSR recordings introducing once more a certain degree of subjectivity. Aims: The present study aimed at establishing clinically efficient stopping criteria for a multiple 80-Hz ASSR system. Methods: In Experiment 1, data of 31 normal hearing subjects were analyzed off-line to propose stopping rules. Consequently, ASSR recordings will be stopped when (1) all 8 responses reach significance and significance can be maintained for 8 consecutive sweeps; (2) the mean noise levels were ≤ 4 nV (if at this “≤ 4-nV” criterion, p-values were between 0.05 and 0.1, measurements were extended only once by 8 sweeps); and (3) a maximum amount of 48 sweeps was attained. In Experiment 2, these stopping criteria were applied on 10 normal hearing and 10 hearing-impaired adults to asses the efficiency. Results: The application of these stopping rules resulted in ASSR threshold values that were comparable to other multiple-ASSR research with normal hearing and hearing-impaired adults. Furthermore, in 80% of the cases, ASSR thresholds could be obtained within a time-frame of 1 hour. Investigating the significant response-amplitudes of the hearing-impaired adults through cumulative curves indicated that probably a higher noise-stop criterion than “≤ 4 nV” can be used. Conclusions: The proposed stopping rules can be used in adults to determine accurate ASSR thresholds within an acceptable time-frame of about 1 hour. However, additional research with infants and adults with varying degrees and configurations of hearing loss is needed to optimize these criteria

Self-Mixing Diode Laser Interferometry

Self-mixing interferometry in a laser diode is a very powerful tool in measurement science. The Self-mixing interferometer is a very robust and low cost interferometer with extreme simplicity in alignment and setup. In this thesis, a self-mixing interferometer is analysed and developed. The measurements of the self-mixing interferometer are verified using a Michelson interferometer. It is then followed by the signal processing of the detected signal. Three different methods are developed to retrieve the movement of the target. Results obtained by applying these methods to different experimental data sets are presented. In the later part of the thesis, a phase locked self-mixing interferometer is developed. This slightly modified interferometer follows the target movement. As a result no additional circuitry or signal processing is necessary for the recovery of the target movement. Phase locked interferometer developed in this thesis was able to measure down to 1 nm of vibration. It is then followed by a novel method to detect cracks in eggshells using the phase locked vibrometer. The proposed method is tested and proved to be capable of differentiating between the intact and cracked eggs

Separation of musical sources and structure from single-channel polyphonic recordings

EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Impact of a heterogeneous stator on the rotor-stator interaction-noise: an analytical, experimental and numerical investigation

La présente étude vise à quantifier par une modélisation analytique, des essais et des simulations numériques, l’impact d’un stator hétérogène sur le bruit d’interaction rotor-stator dans les turbomachines axiales. Le travail développé s’appuie sur des premières observations sur un ventilateur axial à basse vitesse à l’École Centrale de Lyon, l’étage LP3. Il a été observé que les deux premières fréquences de passage des pales (FPP) rayonnaient à des niveaux élevés alors qu’elles devaient être coupées par le conduit selon le critère de Tyler & Sofrin. Une campagne expérimentale est alors réalisée sur la configuration de ventilateur hétérogène qui permet la caractérisation des contenus spectral et modal. Afin de s’assurer qu’aucune distorsion d’entrée d’air n’est présente, un écran pour le contrôle de la turbulence est utilisé. Des techniques de décomposition modale sont utilisées sur des antennes pseudo-aléatoires afin d’obtenir les modes acoustiques prédominants. Les résultats montrent un fort rayonnement acoustique des deux premières fréquences de passage des pales et mettent en évidence des modes dominants. La même expérience est ensuite simulée numériquement en utilisant la méthode de Boltzmann sur réseau. Les simulations montrent un bon comportement de la turbomachine mais prédisent une augmentation de pression inférieure à celle de l’expérience. La comparaison entre un stator homogène et hétérogène permet de quantifier directement l’impact de l’hétérogénéité. L’hétérogénéité est alors responsable d’une augmentation du niveau tonal de plus de 10 dB aux deux premières FPP. Le contenu modal mesuré sur la configuration hétérogène est bien retrouvé par les simulations numériques. En outre, l’analyse de l’écoulement dans l’espacement inter-rotor-stator a permis de mettre en évidence l’impact de l’hétérogénéité sur le champ potentiel. Finalement, la modélisation analytique est axée sur deux sources dominantes : le bruit d’interaction de sillages et le bruit d’interaction potentielle. Les résultats montrent une contribution mineure de ce dernier. Les mêmes modes dominants sont retrouvés dans certaines directions de propagation en accord avec ce qui est observé expérimentalement. En dernier lieu, une étude d’optimisation de la position des bras support est présentée. Une des configurations optimales montrant une forte atténuation du niveau de bruit tonal est validée numériquement par des simulations numériques. Les résultats montrent que l’optimisation du positionnement angulaire des aubes structurelles permet d’obtenir une réduction significative des niveaux aux deux premières FPP. L’étude des différentes composantes (analytique, expérimentale et numérique) fournit ainsi une meilleure compréhension des mécanismes de bruit modifiés par l’hétérogénéité du stator.Abstract: The present study aims to quantify by means of analytical modelling, experiments and numerical simulations, the impact of a heterogeneous stator on the rotor-stator noise in axial turbomachines. This study starts with the first observations on an axial low-speed fan at École Centrale de Lyon, the LP3 stage. It has been observed that the first two blade passing frequencies (BPF) were radiating at high levels while they were expected to be cut-off by the duct according to Tyler & Sofrin’s criterion. An experiment is then carried out with the heterogeneous stator configuration which makes it possible to characterize the spectral and modal contents. To ensure that no inflow distortion is present at the inlet, a Turbulence Control Screen is used. Modal decomposition techniques are used with pseudo-random antennas to obtain the predominant acoustic modes. Results show a strong acoustic radiation of the first two BPFs and evidence some dominant modes. The same experiment is then simulated numerically using the lattice Boltzmann method. The simulations show a good physical behaviour of the turbomachine but predict a lower pressure-rise compared with the experiment. The comparison between homogeneous and heterogeneous stators allows quantifying directly the impact of the heterogeneity. The heterogeneity is responsible for a level increase of more than 10 dB at the first two BPFs. The modal content from the numerical simulations on the heterogeneous configuration is also in good agreement with the experiment. In addition, the analysis of the flow in the inter-stage made it possible to highlight the impact of the heterogeneity on the potential field. Finally, the analytical modelling is focused on two dominant sources: wake-interaction noise and potential-interaction noise. Results put in evidence a minor contribution of the latter despite the short rotor-stator spacing. The same dominant modes are found in certain propagation directions in accordance with what is measured in the experiment. Finally, an optimisation of the modified vanes angular position is carried out. One of the optimal configurations showing a great noise attenuation is numerically validated by the LBM. The numerical results show that the optimisation of the azimuthal positioning of the modified vanes makes it possible to obtain a significant reduction of the levels at the first two BPFs. Thereby, the comparison of the analytical, experimental and numerical investigations allows achieving a better understanding of the modification of noise mechanisms caused by the heterogeneity of the stator