A Novel Algorithm for the Identification of Dirac Impulses from Filtered Noisy Measurements

International audienceIn this paper we address the recovery of a finite stream of Dirac pulses from noisy lowpass-filtered samples in the discrete-time setting. While this problem has been successfully addressed for the noise-free case using the concept of signals with finite rate of innovation, such techniques are not efficient in the presence of noise. In the FRI framework, the determination of the location of Dirac pulses is based on the singular value decomposition of a matrix whose rank in the noise-free case equals the number of Dirac pulses and the signal can be related to the non zero singular values. However, in noisy situations this matrix becomes full rank and the singular value decomposition is subject to subspace swap, meaning some singular values associated with noise become larger than some values related to the signal. This phenomenon has been recognized as the reason for performance breakdown in the method. The goal of this paper is to propose a novel algorithm that limits the alteration of these singular values in the presence of noise, thus significantly improving the estimation of Dirac pulses

Neuromorphic Sampling of Sparse Signals

Neuromorphic sampling is a bioinspired and opportunistic analog-to-digital conversion technique, where the measurements are recorded only when there is a significant change in the signal amplitude. Neuromorphic sampling has paved the way for a new class of vision sensors called event cameras or dynamic vision sensors (DVS), which consume low power, accommodate a high-dynamic range, and provide sparse measurements with high temporal resolution making it convenient for downstream inference tasks. In this paper, we consider neuromorphic sensing of signals with a finite rate of innovation (FRI), including a stream of Dirac impulses, sum of weighted and time-shifted pulses, and piecewise-polynomial functions. We consider a sampling-theoretic approach and leverage the close connection between neuromorphic sensing and time-based sampling, where the measurements are encoded temporally. Using Fourier-domain analysis, we show that perfect signal reconstruction is possible via parameter estimation using high-resolution spectral estimation methods. We develop a kernel-based sampling approach, which allows for perfect reconstruction with a sample complexity equal to the rate of innovation of the signal. We provide sufficient conditions on the parameters of the neuromorphic encoder for perfect reconstruction. Furthermore, we extend the analysis to multichannel neuromorphic sampling of FRI signals, in the single-input multi-output (SIMO) and multi-input multi-output (MIMO) configurations. We show that the signal parameters can be jointly estimated using multichannel measurements. Experimental results are provided to substantiate the theoretical claims

Fault Detection in Rotating Machinery: Vibration analysis and numerical modeling

This thesis investigates vibration based machine condition monitoring and consists of two parts: bearing fault diagnosis and planetary gearbox modeling. In the first part, a new rolling element bearing diagnosis technique is introduced. Envelope analysis is one of the most advantageous methods for rolling element bearing diagnostics but finding the suitable frequency band for demodulation has been a substantial challenge for a long time. Introduction of the Spectral Kurtosis (SK) and Kurtogram mostly solved this problem but in situations where signal to noise ratio is very low or in presence of non-Gaussian noise these methods will fail. This major drawback may noticeably decrease their effectiveness and goal of this thesis is to overcome this problem. Vibration signals from rolling element bearings exhibit high levels of 2nd order cyclostationarity, especially in the presence of localized faults. A second-order cyclostationary signal is one whose autocovariance function is a periodic function of time: the proposed method, named Autogram by the authors, takes advantage of this property to enhance the conventional Kurtogram. The method computes the kurtosis of the unbiased autocorrelation (AC) of the squared envelope of the demodulated and undecimated signal, rather than the kurtosis of the filtered time signal. Moreover, to take advantage of unique features of the lower and upper portions of the AC, two modified forms of kurtosis are introduced and the resulting colormaps are called Upper and Lower Autogram. In addition, a new thresholding method is also proposed to enhance the quality of the frequency spectrum analysis. Finally, the proposed method is tested on experimental data and compared with literature results so to assess its performances in rolling element bearing diagnostics. Moreover, a second novel method for diagnosis of rolling element bearings is developed. This approach is a generalized version of the cepstrum pre-whitening (CPW) which is a simple and effective technique for bearing diagnosis. The superior performance of the proposed method has been shown on two real case data. For the first case, the method successfully extracts bearing characteristic frequencies related to two defected bearings from the acquired signal. Moreover, the defect frequency was highlighted in case two, even in presence of strong electromagnetic interference (EMI). The second part presents a newly developed lumped parameter model (LPM) of a planetary gear. Planets bearings of planetary gear sets exhibit high rate of failure; detection of these faults which may result in catastrophic breakdowns have always been challenging. Another objective of this thesis is to investigate the planetary gears vibration properties in healthy and faulty conditions. To seek this goal a previously proposed lumped parameter model (LPM) of planetary gear trains is integrated with a more comprehensive bearing model. This modified LPM includes time varying gear mesh and bearing stiffness and also nonlinear bearing stiffness due to the assumption of Hertzian contact between the rollers/balls and races. The proposed model is completely general and accepts any inner/outer race bearing defect location and profile in addition to its original capacity of modelling cracks and spalls of gears; therefore, various combinations of gears and bearing defects are also applicable. The model is exploited to attain the dynamic response of the system in order to identify and analyze localized faults signatures for inner and outer races as well as rolling elements of planets bearings. Moreover, bearing defect frequencies of inner/outer race and ball/roller and also their sidebands are discussed thoroughly. Finally, frequency response of the system for different sizes of planets bearing faults are compared and statistical diagnostic algorithms are tested to investigate faults presence and growth

Opportunistic Angle of Arrival Estimation in Impaired Scenarios

This work if focused on the analysis and the development of Angle of Arrival (AoA) radio localization methods. The radio positioning system considered is constituted by a radio source and by a receiving array of antennas. The positioning algorithms treated in this work are designed to have a passive and opportunistic approach. The opportunistic attribute implies that the radio localization algorithms are designed to provide the AoA estimation with nearly-zero information on the transmitted signals. No training sequences or waveforms custom designed for localization are taken into account. The localization is termed passive since there is no collaboration between the transmitter and the receiver during the localization process. Then, the algorithms treated in this work are designed to eavesdrop already existing communication signals and to locate their radio source with nearly-zero knowledge of the signal and without the collaboration of the transmitting node. First of all, AoA radio localization algorithms can be classified in terms of involved signals (narrowband or broadband), antenna array pattern (L-shaped, circular, etc.), signal structure (sinusoidal, training sequences, etc.), Differential Time of Arrival (D-ToA) / Differential Phase of Arrival (D-PoA) and collaborative/non collaborative. Than, the most detrimental effects for radio communications are treated: the multipath (MP) channels and the impaired hardware. A geometric model for the MP is analysed and implemented to test the robustness of the proposed methods. The effects of MP on the received signals statistics from the AoA estimation point-of-view are discussed. The hardware impairments for the most common components are introduced and their effects in the AoA estimation process are analysed. Two novel algorithms that exploits the AoA from signal snapshots acquired sequentially with a time division approach are presented. The acquired signals are QAM waveforms eavesdropped from a pre-existing communication. The proposed methods, namely Constellation Statistical Pattern IDentification and Overlap (CSP-IDO) and Bidimensional CSP-IDO (BCID), exploit the probability density function (pdf) of the received signals to obtain the D-PoA. Both CSP-IDO and BCID use the statistical pattern of received signals exploiting the transmitter statistical signature. Since the presence of hardware impairments modify the statistical pattern of the received signals, CSP-IDO and BCID are able to exploit it to improve the performance with respect to (w.r.t.) the ideal case. Since the proposed methods can be used with a switched antenna architecture they are implementable with a reduced hardware contrariwise to synchronous methods like MUltiple SIgnal Classification (MUSIC) that are not applicable. Then, two iterative AoA estimation algorithms for the dynamic tracking of moving radio sources are implemented. Statistical methods, namely PF, are used to implement the iterative tracking of the AoA from D-PoA measures in two different scenarios: automotive and Unmanned Aerial Vehicle (UAV). The AoA tracking of an electric car signalling with a IEEE 802.11p-like standard is implemented using a test-bed and real measures elaborated with a the proposed Particle Swarm Adaptive Scattering (PSAS) algorithm. The tracking of a UAV moving in the 3D space is investigated emulating the UAV trajectory using the proposed Confined Area Random Aerial Trajectory Emulator (CARATE) algorithm

Exact and approximate Strang-Fix conditions to reconstruct signals with finite rate of innovation from samples taken with arbitrary kernels

In the last few years, several new methods have been developed for the sampling and exact reconstruction of specific classes of non-bandlimited signals known as signals with finite rate of innovation (FRI). This is achieved by using adequate sampling kernels and reconstruction schemes. An example of valid kernels, which we use throughout the thesis, is given by the family of exponential reproducing functions. These satisfy the generalised Strang-Fix conditions, which ensure that proper linear combinations of the kernel with its shifted versions reproduce polynomials or exponentials exactly. The first contribution of the thesis is to analyse the behaviour of these kernels in the case of noisy measurements in order to provide clear guidelines on how to choose the exponential reproducing kernel that leads to the most stable reconstruction when estimating FRI signals from noisy samples. We then depart from the situation in which we can choose the sampling kernel and develop a new strategy that is universal in that it works with any kernel. We do so by noting that meeting the exact exponential reproduction condition is too stringent a constraint. We thus allow for a controlled error in the reproduction formula in order to use the exponential reproduction idea with arbitrary kernels and develop a universal reconstruction method which is stable and robust to noise. Numerical results validate the various contributions of the thesis and in particular show that the approximate exponential reproduction strategy leads to more stable and accurate reconstruction results than those obtained when using the exact recovery methods.Open Acces

Statistical Analysis of 100 Gbps per Wavelength SWDM VCSEL-MMF Data Center Links on a Large Set of OM3 and OM4 Fibers

We present a detailed statistical study on achievable reach of 100 Gbps data center optical links based on vertical cavity surface emitting lasers (VCSEL) and multimode fibers (MMF). Based on the characterization of the spectral and spatial properties of eight lasers and of the modal and dispersion behavior of a large set of 20233 OM3 and OM4 modeled fibers (obtained by properly extending an initial set of 500 measured fibers), we compute the resulting frequency responses of all of the VCSEL-MMF combinations. Then, we feed them to a numerical tool modeling PAM-4 transmission at 100 Gbps net bit rate per wavelength. Our model analyzes performance at distances up to 400 meters, using three different adaptive equalizers at the receiver and considering two forward error correction overheads. We show that 100 Gbps operation is feasible for 99% of the simulated links reaching up to 120 m over OM4 at 850 nm and using a decision feedback equalizer (DFE). Aggregated data rates of 200 Gbps and 400 Gbps per fiber using Shortwave Wavelength Division Multiplexing (SWDM) are achievable for 99% of the links reaching 80 m over OM4 using two wavelengths and feed-forward equalizer (FFE) and four wavelengths and maximum likelihood sequence estimation (MLSE)-based equalizer, respectively

Development of Advanced Mathematical Morphology Algorithms and their Application to the Detection of Disturbances in Power Systems

This thesis is concerned with the development of Mathematical morphology (MM)-based algorithms and their applications to signal processing in power systems, including typical power quality disturbances such as low frequency oscillations (LFO) and harmonics. Traditional morphological operators are extended to advanced ones in the thesis, including multi-resolution morphological gradient (MMG) algorithms, envelope extraction morphological filters (MF), LFO extraction MF and convolved morphological filters (CMF). These advanced morphological operators are applied to the detection and classification of power disturbances, detection of continuous and damped LFO, and the detection and removal of harmonics in power systems

Coding Strategies for Cochlear Implants Under Adverse Environments

Cochlear implants are electronic prosthetic devices that restores partial hearing in patients with severe to profound hearing loss. Although most coding strategies have significantly improved the perception of speech in quite listening conditions, there remains limitations on speech perception under adverse environments such as in background noise, reverberation and band-limited channels, and we propose strategies that improve the intelligibility of speech transmitted over the telephone networks, reverberated speech and speech in the presence of background noise. For telephone processed speech, we propose to examine the effects of adding low-frequency and high- frequency information to the band-limited telephone speech. Four listening conditions were designed to simulate the receiving frequency characteristics of telephone handsets. Results indicated improvement in cochlear implant and bimodal listening when telephone speech was augmented with high frequency information and therefore this study provides support for design of algorithms to extend the bandwidth towards higher frequencies. The results also indicated added benefit from hearing aids for bimodal listeners in all four types of listening conditions. Speech understanding in acoustically reverberant environments is always a difficult task for hearing impaired listeners. Reverberated sounds consists of direct sound, early reflections and late reflections. Late reflections are known to be detrimental to speech intelligibility. In this study, we propose a reverberation suppression strategy based on spectral subtraction to suppress the reverberant energies from late reflections. Results from listening tests for two reverberant conditions (RT60 = 0.3s and 1.0s) indicated significant improvement when stimuli was processed with SS strategy. The proposed strategy operates with little to no prior information on the signal and the room characteristics and therefore, can potentially be implemented in real-time CI speech processors. For speech in background noise, we propose a mechanism underlying the contribution of harmonics to the benefit of electroacoustic stimulations in cochlear implants. The proposed strategy is based on harmonic modeling and uses synthesis driven approach to synthesize the harmonics in voiced segments of speech. Based on objective measures, results indicated improvement in speech quality. This study warrants further work into development of algorithms to regenerate harmonics of voiced segments in the presence of noise