Instantaneous Frequency (IF) estimation based on time-varying autoregressive (TVAR) modeling has been shown to perform well in practical scenarios when the IF variation is rapid and/or non-linear and only short data records are available for modeling. A challenging aspect of implementing IF estimation based on TVAR modeling is the efficient computation of the time-varying coefficients by solving a set of linear equations referred to as the generalized covariance equations. Conventional approaches such as Gaussian elimination or direct matrix inversion are computationally inefficient for solving such a system of equations especially when the covariance matrix has a high order. We implement two recursive algorithms for efficiently inverting the covariance matrix. First, we implement the Akaike algorithm which exploits the block-Toeplitz structure of the covariance matrix for its recursive inversion. In the second approach, we implement the Wax-Kailath algorithm that achieves a factor of 2 reduction over the Akaike algorithm in the number of recursions involved and the computational effort required to form the inverse matrix. Although a TVAR model works well for IF estimation of frequency modulated (FM) components in white noise, when the model is applied to a signal containing a finitely correlated signal in addition to the white noise, estimation performance degrades; especially when the correlated signal is not weak relative to the FM components. We propose a decorrelating TVAR (DTVAR) model based IF estimation and a DTVAR model based linear prediction error filter for FM interference rejection in a finitely correlated environment. Simulations show notable performance gains for a DTVAR model over the TVAR model for moderate to high SIRs. / Master of Science

Avec le paradigme du réseau intelligent, les ingénieurs de protection ont maintenant à leur disposition une large gamme de nouvelles technologies de communication. Parmi elles, la norme CEI 61850-9-2 a introduit le concept de bus de procédé qui permet l'envoi de valeurs échantillonnées horodatées à un temps absolu depuis les transformateurs de mesure du terrain jusqu’aux relais de protection numériques. Ces derniers peuvent intégrer la fonction d'unité de mesure de phaseur qui peut être utilisé pour échanger des synchrophaseurs entre les fonctions de protection et pour une nouvelle protection anti-îlotage. Les relais de fréquence et de dérivée de fréquence sont, de nos jours, les méthodes anti-îlotage les plus couramment employées, mais leurs performances ne sont pas satisfaisantes. Dans ce contexte, une nouvelle génération de techniques de traitement du signal pour les relais de protection ayant des échantillons horodatées comme signal d'entrée et intégrant la mesure de synchrophaseurs est nécessaire. Cette thèse étudie d'abord l'impact des valeurs échantillonnées sur le traitement du signal. Trois solutions sont ensuite proposées pour calculer les phaseurs, les fréquences et les dérivées de fréquence dans diverses conditions statiques et dynamiques, puis testées par simulation. Enfin, un algorithme de mesure de synchrophaseurs incorporé dans le traitement de signal initial est proposé. Cet algorithme a été testé selon la dernière version de la norme d'unité de mesure de phaseur et les résultats obtenus sont conformes aux exigences de mesure. / With the Smart Grid paradigm, protection engineers now have available to them a large range of new communication technologies. Among them, IEC Standard 61850-9-2 has introduced the process bus concept which permits sending of absolute time-stamped digitized analogue values from the instrument transformers of the field to numerical relays. The latter can incorporate the phasor measurement unit function which can be used for exchanging synchrophasors between protection functions and for new anti-islanding protection. Frequency and rate-of-change-of-frequency relays are, nowadays, the most commonly employed anti-islanding methods but their performance is not satisfactory. In this context, a new generation of signal processing techniques for protection relays having time-stamped digitized analogue values as input signal with synchrophasors measurement capability is required. This thesis first studies the impact of sampled measured values on the signal processing. Three solutions are then proposed to compute phasor, frequency and rate-of-change-of-frequency estimates under various static and dynamic conditions, and tested via simulation. Finally, a synchronized phasor measurement algorithm incorporated into the initial signal processing is proposed. This algorithm has been tested following the latest version of the phasor measurement unit standard and the results obtained comply with the measurement requirements.

The estimation of the frequency and phase of a complex exponential in additive white Gaussian noise (AWGN) is a fundamental and well-studied problem in signal processing and communications. A variety of approaches to this problem, distinguished primarily by estimation accuracy, computational complexity, and processing latency, have been developed. One class of approaches is based on the Fast Fourier Transform (FFT) due to its connections with the maximum likelihood estimator (MLE) of frequency. This thesis compares several FFT-based approaches to the MLE in terms of their estimation accuracy and computational complexity. While FFT-based frequency estimation tends to be very accurate, the computational complexity of the FFT and the latency associated with performing these computations after the entire signal has been received can be prohibitive in some scenarios. Another class of approaches that addresses some of these shortcomings is based on linear regression of samples of the instantaneous phase of the observation. Linear- regression-based techniques have been shown to be very accurate at moderate to high signal to noise ratios and have the additional benefit of low computational complexity and low latency due to the fact that the processing can be performed as the samples arrive. These techniques, however, typically require the computation of four-quadrant arctangents, which must be approximated to retain low computational complexity. This thesis proposes a new frequency and phase estimator based on simple estimates of the zero-crossing times of the observation. An advantage of this approach is that it does not require arctangent calculations. Simulation results show that the zero-crossing frequency and phase estimator can provide high estimation accuracy, low computational complexity, and low processing latency, making it suitable for real-time applications. Accordingly, this thesis also presents a real-time implementation of the zero-crossing frequency and phase estimator in the context of a time-slotted round-trip carrier synchronization system for distributed beamforming. The experimental results show this approach can outperform a Phase Locked Loop (PLL) implementation of the same distributed beamforming system.

Este trabajo propone una serie de métodos eficientes para convertir una señal de audio musical polifónica (WAV, MP3) en una partitura (MIDI).

<p>Periodic signal modeling plays an important role in different fields. The unifying theme of this thesis is using nonlinear techniques to model periodic signals. The suggested techniques utilize the user pre-knowledge about the signal waveform. This gives these techniques an advantage as compared to others that do not consider such priors.</p><p>The technique of Part I relies on the fact that a sine wave that is passed through a static nonlinear function produces a harmonic spectrum of overtones. Consequently, the estimated signal model can be parameterized as a known periodic function (with unknown frequency) in cascade with an unknown static nonlinearity. The unknown frequency and the parameters of the static nonlinearity are estimated simultaneously using the recursive prediction error method (RPEM). A treatment of the local convergence properties of the RPEM is provided. Also, an adaptive grid point algorithm is introduced to estimate the unknown frequency and the parameters of the static nonlinearity in a number of adaptively estimated grid points. This gives the RPEM more freedom to select the grid points and hence reduces modeling errors.</p><p>Limit cycle oscillations problem are encountered in many applications. Therefore, mathematical modeling of limit cycles becomes an essential topic that helps to better understand and/or to avoid limit cycle oscillations in different fields. In Part II, a second-order nonlinear ODE is used to model the periodic signal as a limit cycle oscillation. The right hand side of the ODE model is parameterized using a polynomial function in the states, and then discretized to allow for the implementation of different identification algorithms. Hence, it is possible to obtain highly accurate models by only estimating a few parameters.</p><p>In Part III, different user aspects for the two nonlinear approaches of the thesis are discussed. Finally, topics for future research are presented. </p>

Periodic signal modeling plays an important role in different fields. The unifying theme of this thesis is using nonlinear techniques to model periodic signals. The suggested techniques utilize the user pre-knowledge about the signal waveform. This gives these techniques an advantage as compared to others that do not consider such priors. The technique of Part I relies on the fact that a sine wave that is passed through a static nonlinear function produces a harmonic spectrum of overtones. Consequently, the estimated signal model can be parameterized as a known periodic function (with unknown frequency) in cascade with an unknown static nonlinearity. The unknown frequency and the parameters of the static nonlinearity are estimated simultaneously using the recursive prediction error method (RPEM). A treatment of the local convergence properties of the RPEM is provided. Also, an adaptive grid point algorithm is introduced to estimate the unknown frequency and the parameters of the static nonlinearity in a number of adaptively estimated grid points. This gives the RPEM more freedom to select the grid points and hence reduces modeling errors. Limit cycle oscillations problem are encountered in many applications. Therefore, mathematical modeling of limit cycles becomes an essential topic that helps to better understand and/or to avoid limit cycle oscillations in different fields. In Part II, a second-order nonlinear ODE is used to model the periodic signal as a limit cycle oscillation. The right hand side of the ODE model is parameterized using a polynomial function in the states, and then discretized to allow for the implementation of different identification algorithms. Hence, it is possible to obtain highly accurate models by only estimating a few parameters. In Part III, different user aspects for the two nonlinear approaches of the thesis are discussed. Finally, topics for future research are presented.

We have devised a processor for pulsed Doppler radars for multi-target detection in same folded range under land and moving clutter. To this end, we have investigated the estimation of parameters, i.e., frequencies, amplitudes, and phases, of complex exponentials that model target echoes under radar clutter characterized by antenna scanning modulation with observation limited to single snapshot, i.e., one burst. The Maximum Likelihood method of estimation is presented together with the bounds on estimates, i.e., Cram&eacute / r-Rao bounds. We have analyzed linear prediction, together with its efficient implementation invented by Tufts &amp / Kumaresan, and compared its performance to other high resolution frequency estimation algorithms all modified to run under clutter. The essential part of the work is that line spectra estimation techniques model the clutter process also as a complex exponential. In addition, linear prediction combined with linear time&ndash / invariant maximum Signal to Interference Ratio (SIR) processor is analyzed. A technique to determine the model order, which is required by the frequency estimation algorithms, is presented that does not distinguish between targets and clutter. Clutter region concept is introduced to identify targets from clutter. The possibility to use these algorithms for target classification is briefly explained after providing a literature survey on helicopter echoes.

Bei der Überführung eines wissenschaftlichen Laborsystems zur automatischen Spracherkennung in eine reale Anwendung ergeben sich verschiedene praktische Problemstellungen, von denen eine der Verlust an Erkennungsleistung durch umgebende akustische Störungen ist. Im Gegensatz zu additiven Störungen wie Lüfterrauschen o. ä. hat die Wissenschaft bislang die Störung des Raumhalls bei der Spracherkennung nahezu ignoriert. Dabei besitzen, wie in der vorliegenden Dissertation deutlich gezeigt wird, bereits geringfügig hallende Räume einen stark störenden Einfluss auf die Leistungsfähigkeit von Spracherkennern. Mit dem Ziel, die Erkennungsleistung wieder in einen praktisch benutzbaren Bereich zu bringen, nimmt sich die Arbeit dieser Problemstellung an und schlägt Lösungen vor. Der Hintergrund der wissenschaftlichen Aktivitäten ist die Erstellung von funktionsfähigen Sprachbenutzerinterfaces für Gerätesteuerungen im Wohn- und Büroumfeld, wie z.~B. bei der Hausautomation. Aus diesem Grund werden praktische Randbedingungen wie die Restriktionen von embedded Computerplattformen in die Lösungsfindung einbezogen. Die Argumentation beginnt bei der Beschreibung der raumakustischen Umgebung und der Ausbreitung von Schallfeldern in Räumen. Es wird theoretisch gezeigt, dass die Störung eines Sprachsignals durch Hall von zwei Parametern abhängig ist: der Sprecher-Mikrofon-Distanz (SMD) und der Nachhallzeit T60. Um die Abhängigkeit der Erkennungsleistung vom Grad der Hallstörung zu ermitteln, wird eine Anzahl von Erkennungsexperimenten durchgeführt, die den Einfluss von T60 und SMD nachweisen. Weitere Experimente zeigen, dass die Spracherkennung kaum durch hochfrequente Hallanteile beeinträchtigt wird, wohl aber durch tieffrequente. In einer Literaturrecherche wird ein Überblick über den Stand der Technik zu Maßnahmen gegeben, die den störenden Einfluss des Halls unterdrücken bzw. kompensieren können. Jedoch wird auch gezeigt, dass, obwohl bei einigen Maßnahmen von Verbesserungen berichtet wird, keiner der gefundenen Ansätze den o. a. praktischen Einsatzbedingungen genügt. In dieser Arbeit wird die Methode Harmonicity-based Feature Analysis (HFA) vorgeschlagen. Sie basiert auf drei Ideen, die aus den Betrachtungen der vorangehenden Kapitel abgeleitet werden. Experimentelle Ergebnisse weisen die Verbesserung der Erkennungsleistung in halligen Umgebungen nach. Es werden sogar praktisch relevante Erkennungsraten erzielt, wenn die Methode mit verhalltem Training kombiniert wird. Die HFA wird gegen Ansätze aus der Literatur evaluiert, die ebenfalls praktischen Implementierungskriterien genügen. Auch Kombinationen der HFA und einigen dieser Ansätze werden getestet. Im letzten Kapitel werden die beiden Basistechnologien Stimm\-haft-Stimmlos-Entscheidung und Grundfrequenzdetektion umfangreich unter Hallbedingungen getestet, da sie Voraussetzung für die Funktionsfähigkeit der HFA sind. Als Ergebnis wird dargestellt, dass derzeit für beide Technologien kein Verfahren existiert, das unter Hallbedingungen robust arbeitet. Es kann allerdings gezeigt werden, dass die HFA trotz der Unsicherheiten der Verfahren arbeitet und signifikante Steigerungen der Erkennungsleistung erreicht. / Automatic speech recognition (ASR) systems used in real-world indoor scenarios suffer from performance degradation if noise and reverberation conditions differ from the training conditions of the recognizer. This thesis deals with the problem of room reverberation as a cause of distortion in ASR systems. The background of this research is the design of practical command and control applications, such as a voice controlled light switch in rooms or similar applications. Therefore, the design aims to incorporate several restricting working conditions for the recognizer and still achieve a high level of robustness. One of those design restrictions is the minimisation of computational complexity to allow the practical implementation on an embedded processor. One chapter comprehensively describes the room acoustic environment, including the behavior of the sound field in rooms. It addresses the speaker room microphone (SRM) system which is expressed in the time domain as the room impulse response (RIR). The convolution of the RIR with the clean speech signal yields the reverberant signal at the microphone. A thorough analysis proposes that the degree of the distortion caused by reverberation is dependent on two parameters, the reverberation time T60 and the speaker-to-microphone distance (SMD). To evaluate the dependency of the recognition rate on the degree of distortion, a number of experiments has been successfully conducted, confirming the above mentioned dependency of the two parameters, T60 and SMD. Further experiments have shown that ASR is barely affected by high-frequency reverberation, whereas low frequency reverberation has a detrimental effect on the recognition rate. A literature survey concludes that, although several approaches exist which claim significant improvements, none of them fulfils the above mentioned practical implementation criteria. Within this thesis, a new approach entitled 'harmonicity-based feature analysis' (HFA) is proposed. It is based on three ideas that are derived in former chapters. Experimental results prove that HFA is able to enhance the recognition rate in reverberant environments. Even practical applicable results are achieved when HFA is combined with reverberant training. The method is further evaluated against three other approaches from the literature. Also combinations of methods are tested. In a last chapter the two base technologies fundamental frequency (F0) estimation and voiced unvoiced decision (VUD) are evaluated in reverberant environments, since they are necessary to run HFA. This evaluation aims to find one optimal method for each of these technologies. The results show that all F0 estimation methods and also the VUD methods have a strong decreasing performance in reverberant environments. Nevertheless it is shown that HFA is able to deal with uncertainties of these base technologies as such that the recognition performance still improves.

Orthogonal frequency-division multiplexing (OFDM) has been adopted by many broadband wireless communication systems for the simplicity of the receiver technique to support high data rates and user mobility. However, studies also show that the advantage of OFDM over the single-carrier modulation schemes could be substantially compromised by timing or frequency estimation errors at the receiver. In this thesis we investigate the synchronization problem for practical OFDM systems using a system model generalized from the IEEE 802.11 and IEEE 802.16 standards. For preamble based synchronization schemes, which are most common in the downlink of wireless communication systems, we propose a novel timing acquisition algorithm which minimizes false alarm probability and indirectly improves correct detection probability. We then introduce a universal fractional carrier frequency offset (CFO) estimator that outperforms conventional methods at low signal to noise ratio with lower complexity. More accurate timing and frequency estimates can be obtained by our proposed frequency-domain algorithms incorporating channel knowledge. We derive four joint frequency, timing, and channel estimators with different approximations, and then propose a hybrid integer CFO estimation scheme to provide flexible performance and complexity tradeoffs. When the exact channel delay profile is unknown at the receiver, we present a successive timing estimation algorithm to solve the timing ambiguity. Both analytical and simulation results are presented to confirm the performance of the proposed methods in various realistic channel conditions. The ranging based synchronization scheme is most commonly used in the uplink of wireless communication systems. Here we propose a successive multiuser detection algorithm to mitigate multiple access interference and achieve better performance than that of conventional single-user based methods. A reduced-complexity version of the successive algorithm feasible for hardware real-time implementation is also presented in the thesis. To better understand the performance of a ranging detector from a system point of view, we develop a technique that can directly translate a detector�s missed detection probability into the maximum number of users that the method can support in one cell with a given number of ranging opportunities. The analytical results match the simulations reasonably well and show that the proposed successive algorithms allow a base station to serve more than double the number of users supported by the conventional methods. Finally, we investigate inter-carrier interference which is caused by the timevarying communication channels. We derive the bounds on the power of residual inter-carrier interference that cannot be mitigated by a frequency-domain equalizer with a given number of taps. We also propose a Turbo equalization scheme using the novel grouped Particle filter, which approaches the performance of the Maximum A Posterior algorithm with much lower complexity.

Στην εργασία αυτή, μελετάται το πρόβλημα της ανίχνευσης κινούμενων στόχων και της εκτίμησης της θέσης και της ταχύτητάς τους από ένα σύστημα ραντάρ. Η κίνηση των στόχων ως προς το ραντάρ έχει σαν αποτέλεσμα τη μετατόπιση Doppler της συχνότητας της επιστρεφόμενης ακτινοβολίας ως προς τη συχνότητα εκπομπής του ραντάρ. Εκτιμώντας αυτή τη μετατόπιση στη συχνότητα μπορούμε να ανιχνεύσουμε το στόχο καθώς και να εκτιμήσουμε τη θέση και την ταχύτητά του. Διερευνάται η δυνατότητα βελτίωσης της πιθανότητας ανίχνευσης των στόχων καθώς και του μέσου τετραγωνικού σφάλματος των εκτιμήσεων θέσης και ταχύτητας, με χρήση μοντέρνων εκτιμητών συχνοτήτων, αντί των κλασσικών εκτιμητών που βασίζονται στο Μετασχηματισμό Fourrier. Αναλύονται θεωρητικά και μέσω προσομοιώσεων οι δυνατότητες των μοντέρνων εκτιμητών συχνοτήτων, δίνοντας ιδιαίτερη έμφαση στους εκτιμητές Υποχώρου (MUSIC, ESPRIT). Ακολουθεί, η παρουσίαση μιας γενίκευσης της χρήσης των εκτιμητών συχνοτήτων στην περίπτωση διανυσματικών σημάτων. Ο αλγόριθμος που προτείνεται για την ανίχνευση στόχων από ένα σύστημα ραντάρ, επεξεργάζεται τα δείγματα της ληφθείσας ακτινοβολίας κατά μπλοκ οπότε προκύπτει η ανάγκη χρήσης αυτής της διανυσματικής μορφής των εκτιμητών συχνοτήτων. Παρουσιάζονται, τέλος, αποτελέσματα προσομοιώσεων, για διάφορα σενάρια, που επιβεβαιώνουν την αποτελεσματικότητα του αλγορίθμου και φανερώνουν τα πλεονεκτήματα της χρήσης των μοντέρνων τεχνικών εκτίμησης συχνοτήτων. / This report focuses on the problem of detection of moving targets and estimation of their positions and velocities using a radar system. By estimating the targets' Doppler frequencies it is possible to detect the targets and estimate both their position and velocity. It is shown how the use of modern frequency estimators results in higher values of the probability of detection compared to the Fourrier-based methods. Modern estimators are analyzed, with emphasis shown on the subspace-based estimators (MUSIC, ESPRIT) and their use is generalized for the case of estimating frequencies in vector signals. This generalized form of frequency estimators is used by our proposed algorithm for target detection. Simulation results are presented that prove the superiority of modern techniques.