ML Estimation and Detection of Multiple Frequencies Through Periodogram Estimate Refinement

This letter presents a method to detect and estimate multiple frequencies based on the maximum-likelihood principle. The method addresses the three main difficulties in this kind of computation, which are the detection of the number of frequencies, the coarse localization of the cost function's global maximum, and the iterative refinement of an initial estimate. Fundamentally, it consists of first detecting and estimating single frequencies or frequency clusters using the periodogram, and then refining this last estimate through a Newton-type method. This second step is fast because its complexity is independent of the number of samples, once a single fast Fourier transform (FFT) has been computed. These two steps are iteratively repeated until no mode frequency is above a fixed detection threshold. The main advantage of the proposed method is its low complexity, given that its computational burden is just that of a few FFTs in typical scenarios. The method is assessed in a numerical example.This work was supported by the Spanish Ministry of Economy and Competitiveness and EU FEDER under project TIN2014-55413-C2-2-P

Modelling, Analysis, and Simulation of Underwater Acoustic Channels : Doctoral Dissertation for the Degree Philosophiae Doctor (PhD) at the Faculty of Engineering and Science, Specialization in Information and Communication Technology

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Efficient Schemes for Adaptive Frequency Tracking and their Relevance for EEG and ECG

Amplitude and frequency are the two primary features of one-dimensional signals, and thus both are widely utilized to analysis data in numerous fields. While amplitude can be examined directly, frequency requires more elaborate approaches, except in the simplest cases. Consequently, a large number of techniques have been proposed over the years to retrieve information about frequency. The most famous method is probably power spectral density estimation. However, this approach is limited to stationary signals since the temporal information is lost. Time-frequency approaches were developed to tackle the problem of frequency estimation in non-stationary data. Although they can estimate the power of a signal in a given time interval and in a given frequency band, these tools have two drawbacks that make them less valuable in certain situations. First, due to their interdependent time and frequency resolutions, improving the accuracy in one domain means decreasing it in the other one. Second, it is difficult to use this kind of approach to estimate the instantaneous frequency of a specific oscillatory component. A solution to these two limitations is provided by adaptive frequency tracking algorithms. Typically, these algorithms use a time-varying filter (a band-pass or notch filter in most cases) to extract an oscillation, and an adaptive mechanism to estimate its instantaneous frequency. The main objective of the first part of the present thesis is to develop such a scheme for adaptive frequency tracking, the single frequency tracker. This algorithm compares favorably with existing methods for frequency tracking in terms of bias, variance and convergence speed. The most distinguishing feature of this adaptive algorithm is that it maximizes the oscillatory behavior at its output. Furthermore, due to its specific time-varying band-pass filter, it does not introduce any distortion in the extracted component. This scheme is also extended to tackle certain situations, namely the presence of several oscillations in a single signal, the related issue of harmonic components, and the availability of more than one signal with the oscillation of interest. The first extension is aimed at tracking several components simultaneously. The basic idea is to use one tracker to estimate the instantaneous frequency of each oscillation. The second extension uses the additional information contained in several signals to achieve better overall performance. Specifically, it computes separately instantaneous frequency estimates for all available signals which are then combined with weights minimizing the estimation variance. The third extension, which is based on an idea similar to the first one and uses the same weighting procedure as the second one, takes into account the harmonic structure of a signal to improve the estimation performance. A non-causal iterative method for offline processing is also developed in order to enhance an initial frequency trajectory by using future information in addition to past information. Like the single frequency tracker, this method aims at maximizing the oscillatory behavior at the output. Any approach can be used to obtain the initial trajectory. In the second part of this dissertation, the schemes for adaptive frequency tracking developed in the first part are applied to electroencephalographic and electrcardiographic data. In a first study, the single frequency tracker is used to analyze interactions between neuronal oscillations in different frequency bands, known as cross-frequency couplings, during a visual evoked potential experiment with illusory contour stimuli. With this adaptive approach ensuring that meaningful phase information is extracted, the differences in coupling strength between stimuli with and without illusory contours are more clearly highlighted than with traditional methods based on predefined filter-banks. In addition, the adaptive scheme leads to the detection of differences in instantaneous frequency. In a second study, two organization measures are derived from the harmonic extension. They are based on the power repartition in the frequency domain for the first one and on the phase relation between harmonic components for the second one. These measures, computed from the surface electrocardiogram, are shown to help predicting the outcome of catheter ablation of persistent atrial fibrillation. The proposed adaptive frequency tracking schemes are also applied to signals recorded in the field of sport sciences in order to illustrate their potential uses. To summarize, the present thesis introduces several algorithms for adaptive frequency tracking. These algorithms are presented in full detail and they are then applied to practical situations. In particular, they are shown to improve the detection of coupling mechanisms in brain activity and to provide relevant organization measures for atrial fibrillation

Mobile and Wireless Communications

Mobile and Wireless Communications have been one of the major revolutions of the late twentieth century. We are witnessing a very fast growth in these technologies where mobile and wireless communications have become so ubiquitous in our society and indispensable for our daily lives. The relentless demand for higher data rates with better quality of services to comply with state-of-the art applications has revolutionized the wireless communication field and led to the emergence of new technologies such as Bluetooth, WiFi, Wimax, Ultra wideband, OFDMA. Moreover, the market tendency confirms that this revolution is not ready to stop in the foreseen future. Mobile and wireless communications applications cover diverse areas including entertainment, industrialist, biomedical, medicine, safety and security, and others, which definitely are improving our daily life. Wireless communication network is a multidisciplinary field addressing different aspects raging from theoretical analysis, system architecture design, and hardware and software implementations. While different new applications are requiring higher data rates and better quality of service and prolonging the mobile battery life, new development and advanced research studies and systems and circuits designs are necessary to keep pace with the market requirements. This book covers the most advanced research and development topics in mobile and wireless communication networks. It is divided into two parts with a total of thirty-four stand-alone chapters covering various areas of wireless communications of special topics including: physical layer and network layer, access methods and scheduling, techniques and technologies, antenna and amplifier design, integrated circuit design, applications and systems. These chapters present advanced novel and cutting-edge results and development related to wireless communication offering the readers the opportunity to enrich their knowledge in specific topics as well as to explore the whole field of rapidly emerging mobile and wireless networks. We hope that this book will be useful for students, researchers and practitioners in their research studies

The bilinear-exponential closed-orbit model and its application to storage ring beam diagnostics

Im periodischen Fokussiersystem eines Speicherrings wird der Teilchenstrahl auf einen geschlossenen Orbit, d.h. eine sich wiederholende Teilchenbahn durch den Beschleuniger, abgebildet. Störungen dieses geschlossenen Orbits werden durch fehlerhafte Beschleunigerelemente erzeugt und durch spezielle Magnetstrukturen (Korrektoren) kompensiert. Die zur Kompensation erforderliche Diagnose über Strahlpositionsmonitore (BPMs) sowie die ebenfalls notwendige Charakterisierung der Korrektoren über Messung der sog. Responsematrix wird routinemäßig an vielen Speicherringen weltweit durchgeführt. Weiterhin ist die Bewegung der Einzelteilchen um den geschlossenen Orbit (Strahloptik) aus Stabilitätsgründen interessant, konnte jedoch bisher nur mittels zusätzlicher Spezialhardware beobachtet oder näherungsweise durch Simulation mithilfe eines vollständigen magnetischen Modells des Beschleunigers abgeschätzt werden. Es ist bekannt, dass in Responsematrizen ebenfalls aufschlussreiche Informationen über die Einzelteilchenbewegung um die Sollbahn (Strahloptik), wenn auch in verschlüsselter Form, enthalten sind. Da Responsematrizen routinemäßig an vielen Speicherringen aufgenommen werden und keine zusätzliche Hardware erfordern, ist ihre "Entschlüsselung" von besonderem Interesse. In der vorliegenden Arbeit wird ein Algorithmus mit dem Namen COBEA (Closed-Orbit Bilinear-Exponential Analysis) entwickelt, mit dessen Hilfe Responsematrizen in strahloptische Informationen zerlegt werden können. Grundlage dafür ist eine reduzierte und zugleich verallgemeinerte Darstellung der Störungen des geschlossenen Orbits (Bilinear-Exponentielles Modell) in Abhängigkeit von Strahlparametern an Monitor- und Korrektorpositionen. Abschliessend wird COBEA an drei Speicherringen (DELTA, MLS, BESSY II) mit existierenden Methoden, welche alle entweder zusätzliche Hardware oder zusätzliche Annahmen erfordern, verglichen und erfolgreich validiert. COBEA kann somit an vielen Speicherringen weltweit eingesetzt werden.In periodic focusing systems of accelerators, the particle beam is mapped onto its own closed trajectory (respectively closed orbit). Perturbations of this closed orbit are induced by imperfect accelerator parts and can be compensated by special magnetic devices (correctors). The beam diagnostics using beam position monitors (BPMs), as well as the characterization of corrector magnets by measurement of a so-called response matrix, which are both needed for orbit correction, are routinely performed at many storage rings around the world. Furthermore, the single-particle motion (beam optics) around the closed orbit is of interest due to its implication on beam stability and performance, but could hitherto only be observed by use of additional special hardware or, in approximation, by simulations using the complete magnetic setup of the respective storage ring. It is known that response matrices hold significant information about beam optics, although in an encrypted form. As response matrices are routinely measured at many storage rings without additional hardware, their decomposition is of particular interest. In the present work, an algorithm called Closed-Orbit Bilinear-Exponential Analysis (COBEA) is being developed, with which it is possible to decompose response matrices into beam-optical information with a minimal set of assumptions. The analysis is based on a reduced and simulataneously generalized description of closed-orbit perturbations in dependence of beam parameters at monitor and corrector positions. In closing, COBEA is compared against existing measurement methods, which either need more hardware or more assumptions, and is succesfully validated against them. COBEA can therefore be used at many storage rings around the world

A modal-based approach to the nonlinear vibration of strings against a unilateral obstacle:Simulations and experiments in the pointwise case

International audienceThis article is concerned with the vibration of a stiff linear string in the presence of a rigid obstacle. A numerical method for unilateral and arbitrary-shaped obstacles is developed, based on a modal approach in order to take into account the frequency dependence of losses in strings. The contact force of the barrier interaction is treated using a penalty approach, while a conservative scheme is derived for time integration, in order to ensure long-term numerical stability. In this way, the linear behaviour of the string when not in contact with the barrier can be controlled via a mode by mode fitting, so that the model is particularly well suited for comparisons with experiments. An experimental configuration is used with a point obstacle either centered or near an extremity of the string. In this latter case, such a pointwise obstruction approximates the end condition found in the tanpura, an Indian stringed instrument. The second polarisation of the string is also analysed and included in the model. Numerical results are compared against experiments, showing good accuracy over a long time scale

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target in Identification Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood ML estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar SAR data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations exponentials frequencies are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as 1 stationary noise, 2 autoregressive AR noise and 3 autoregressive moving-average ARMA noise and in two dimensions as 1 stationary noise, and 2 white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood IQML methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation MODE techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise

Maximum Likelihood Estimation of Exponentials in Unknown Colored Noise for Target Identification in Synthetic Aperture Radar Images

This dissertation develops techniques for estimating exponential signals in unknown colored noise. The Maximum Likelihood (ML) estimators of the exponential parameters are developed. Techniques are developed for one and two dimensional exponentials, for both the deterministic and stochastic ML model. The techniques are applied to Synthetic Aperture Radar (SAR) data whose point scatterers are modeled as damped exponentials. These estimated scatterer locations (exponentials frequencies) are potential features for model-based target recognition. The estimators developed in this dissertation may be applied with any parametrically modeled noise having a zero mean and a consistent estimator of the noise covariance matrix. ML techniques are developed for a single instance of data in colored noise which is modeled in one dimension as (1) stationary noise, (2) autoregressive (AR) noise and (3) autoregressive moving-average (ARMA) noise and in two dimensions as (1) stationary noise, and (2) white noise driving an exponential filter. The classical ML approach is used to solve for parameters which can be decoupled from the estimation problem. The remaining nonlinear optimization to find the exponential frequencies is then solved by extending white noise ML techniques to colored noise. In the case of deterministic ML, the computationally efficient, one and two-dimensional Iterative Quadratic Maximum Likelihood (IQML) methods are extended to colored noise. In the case of stochastic ML, the one and two-dimensional Method of Direction Estimation (MODE) techniques are extended to colored noise. Simulations show that the techniques perform close to the Cramer-Rao bound when the model matches the observed noise