Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts. Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems. Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy. Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.

<p>Designing estimators based on low rank signal models is a common practice in signal processing. Some of these estimators are designed to use a single low rank snapshot vector, while others employ multiple snapshots. This dissertation deals with both these cases in different contexts.</p><p>Separable nonlinear least squares is a popular tool to extract parameter estimates from a single snapshot vector. Asymptotic statistical properties of the separable non-linear least squares estimates are explored in the first part of the thesis. The assumptions imposed on the noise process and the data model are general. Therefore, the results are useful in a wide range of applications. Sufficient conditions are established for consistency, asymptotic normality and statistical efficiency of the estimates. An expression for the asymptotic covariance matrix is derived and it is shown that the estimates are circular. The analysis is extended also to the constrained separable nonlinear least squares problems.</p><p>Nonparametric estimation of the material functions from wave propagation experiments is the topic of the second part. This is a typical application where a single snapshot vector is employed. Numerical and statistical properties of the least squares algorithm are explored in this context. Boundary conditions in the experiments are used to achieve superior estimation performance. Subsequently, a subspace based estimation algorithm is proposed. The subspace algorithm is not only computationally efficient, but is also equivalent to the least squares method in accuracy.</p><p>Estimation of the frequencies of multiple real valued sine waves is the topic in the third part, where multiple snapshots are employed. A new low rank signal model is introduced. Subsequently, an ESPRIT like method named R-Esprit and a weighted subspace fitting approach are developed based on the proposed model. When compared to ESPRIT, R-Esprit is not only computationally more economical but is also equivalent in performance. The weighted subspace fitting approach shows significant improvement in the resolution threshold. It is also robust to additive noise.</p>

[pt] Identificação paramétrica de sistemas mecânicos é uma das principais aplicações das técnicas de identificação de sistemas na Engenharia Mecânica, especificamente para a identificação de parâmetros modais de estruturas flexíveis. Um dos principais problemas na identificação é a presença de ruido nas medições. Este trabalho apresenta uma análise na presença de ruído de alguns dos métodos no domínio do tempo aplicáveis na identificação de parâmetros modais de sistemas mecânicos lineares invariantes no tempo com múltiplas entradas e múltiplas saídas (MIMO), usando como base o modelo em espaço de estados tipicamente usado em Dinâmica e Vibrações. Os algoritmos de subespaço envolvidos neste estudo destacam-se pela utilização da decomposição em valores singulares (SVD) dos dados, obtendo subespaços ortogonais dos modos associados ao sistema e dos modos associados ao ruído. Outros complicadores no processo de identificação que serão explorados neste trabalho são: flexibilidde e baixo amortecimento. Comparam-se as técnicas usando o modelo no espaço de estado da estrutura Mini- mast desenvolvida pela NASA Langley Research Center e simulações são feitas variando o nível de ruído nos dados, o amortecimento e a flexibilidade da estrutura. O problema de identificação de parâmetros estruturais (matrizes de massa, rigidez e amortecimento) também é estudado, as características e limitações dos algoritmos utilizados são analisados. Como exemplo de aplicação prática, um experimento foi realizado para identificar os parâmetros modais e estruturais de um rotor flexível e os resultados são discutidos. / [en] Parametric identification of mechanical systems is one of the main applications of the system identification techniques in Mechanical Engineering, specifically for the identification of modal parameters of flexible structures. One of the main problems in the identification is the presence of noise in the measurements. This work presents an analysis in the presence of noise of some of the time domain methods applicable in modal parameters identification of linear time-invariant mechanical systems with multiple inputs and multiple outputs (MIMO), using as base the state-space model typically used in Dynamics and Vibrations. The subspace algorithms involved in this study are distinguished for the use of the singular values decomposition (SVD) of the data, obtaining ortogonal subspaces of the modes associates to the system and of the modes associates to the noise. Other complicators in the identification process that will be explored in this work are: flexibility and low damping. The techniques are compared using the state-space model of the Mini-mast structure developed for NASA Langley Research Center and simulations are made varying the level of noise in the data, the damping and the flexibility of the structure. The problem of identification of structural parameters (mass, stiffness and damping matrices) also is studied, the characteristics and limitations of the used algorithm is analyzed. As example of practical application, an experiment was made to identify the modal parameters of a flexible rotor and the results are discussed.

Στην παρούσα εργασία επιχειρείται η εφαρμογή αλγορίθμων αποθορυβοποίησης σε σήματα μουσικής και η εξαγωγή συμπερασμάτων σχετικά με την απόδοση αυτών ανά μουσικό είδος. Η κύρια επιδίωξη είναι να αποσαφηνιστούν τα βασικά προβλήματα της ενίσχυσης ήχων και να παρουσιαστούν οι διάφοροι αλγόριθμοι που έχουν αναπτυχθεί για την επίλυση των προβλημάτων αυτών. Αρχικά γίνεται μία σύντομη εισαγωγή στις βασικές έννοιες πάνω στις οποίες δομείται η τεχνολογία ενίσχυσης ομιλίας. Στην συνέχεια εξετάζονται και αναλύονται αντιπροσωπευτικοί αλγόριθμοι από κάθε κατηγορία τεχνικών αποθορυβοποίησης, την κατηγορία φασματικής αφαίρεσης, την κατηγορία στατιστικών μοντέλων και αυτήν του υποχώρου. Για να μπορέσουμε να αξιολογήσουμε την απόδοση των παραπάνω αλγορίθμων χρησιμοποιούμε αντικειμενικές μετρήσεις ποιότητας, τα αποτελέσματα των οποίων μας δίνουν την δυνατότητα να συγκρίνουμε την απόδοση του κάθε αλγορίθμου. Με την χρήση τεσσάρων διαφορετικών μεθόδων αντικειμενικών μετρήσεων διεξάγουμε τα πειράματα εξάγοντας μια σειρά ενδεικτικών τιμών που μας δίνουν την ευχέρεια να συγκρίνουμε είτε τυχόν διαφοροποιήσεις στην απόδοση των αλγορίθμων της ίδιας κατηγορίας είτε διαφοροποιήσεις στο σύνολο των αλγορίθμων. Από την σύγκριση αυτή γίνεται εξαγωγή χρήσιμων συμπερασμάτων σχετικά με τον προσδιορισμό των παραμέτρων κάθε αλγορίθμου αλλά και με την καταλληλότητα του κάθε αλγορίθμου για συγκεκριμένες συνθήκες θορύβου και για συγκεκριμένο μουσικό είδος. / This thesis attempts to apply Noise Reduction algorithms to signals of music and draw conclusions concerning the performance of each algorithm for every musical genre. The main aims are to clarify the basic problems of sound enhancement and present the various algorithms developed for solving these problems. After a brief introduction to basic concepts on sound enhancement we examine and analyze various algorithms that have been proposed at times in the literature for speech enhancement. These algorithms can be divided into three main classes: spectral subtractive algorithms, statistical-model-based algorithms and subspace algorithms. In order to evaluate the performance of the above algorithms we use objective measures of quality, the results of which give us the opportunity to compare the performance of each algorithm. By using four different methods of objective measures to conduct the experiments we draw a set of values that facilitate us to make within-class algorithm comparisons and across-class algorithm comparisons. From these comparisons we can draw conclusions on the determination of parameters for each algorithm and the appropriateness of algorithms for specific noise conditions and music genre.