Con la crescente disponibilità di potenza di calcolo, gli algoritmi di analisi del segnale digitale hanno il potenziale di evolversi dal metodo operativo framewise comune alle operazioni campionarie che offrono una maggiore precisione nel tempo. Questa tesi discute un insieme di metodi con operazioni campionarie: approssimazione del segnale locale tramite Recursive Least Squares (RLS) in cui un modello matematico è adatto al segnale all'interno di una finestra scorrevole in ogni campione. Pertanto, sia i modelli di segnale che le finestre di costo sono generati da Autonomous Linear State Space Models (ALSSM). La capacità di modellazione degli ALSSM è vasta, in quanto possono modellare esponenziali, polinomi e funzioni sinusoidali, nonché qualsiasi combinazione lineare e moltiplicativa degli stessi. Il metodo di adattamento offre ricorsioni efficienti, precisione del sottocampione tramite il modello di segnale e bontà aggiuntiva delle misure di adattamento basate sul costo di adattamento calcolato ricorsivamente. I metodi classici come i filtri di livellamento Savitzky-Golay (SG) standard e la Trasformazione di Fourier Short Time (STFT) sono uniti in un quadro comune. Innanzitutto, completiamo il quadro esistente. La parametrizzazione ALSSM e le ricorsioni RLS sono fornite per una funzione generale. Vengono esaminate la soluzione dei parametri di adattamento per diversi problemi di vincolo. Inoltre, l'estrazione delle funzionalità sia dai parametri di adattamento che dal costo è dettagliata, nonché esempi del loro utilizzo. In particolare, introduciamo la terminologia per analizzare il problema di adattamento dal punto di vista della proiezione a uno spazio locale di Hilbert e come filtro lineare. Vengono fornite regole analitiche per il calcolo della risposta del filtro equivalente e della matrice di precisione dello stato stazionario del costo. Dopo aver stabilito il quadro di approssimazione locale, discutiamo ulteriormente due classi di modelli di segnale in particolare, vale a dire le funzioni polinomiali e sinusoidali. I modelli di segnale sono complementari, poiché per natura, i polinomi sono adatti per la descrizione del dominio temporale dei segnali mentre i sinusoidi sono adatti per il dominio della frequenza. Fo
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -With increasing availability of computation power, digital signal analysis algorithms have the potential of evolving from the common framewise operational method to samplewise operations which offer more precision in time. This thesis discusses a set of methods with samplewise operations: local signal approximation via Recursive Least Squares (RLS) where a mathematical model is fit to the signal within a sliding window at each sample. Thereby both the signal models and cost windows are generated by Autonomous Linear State Space Models (ALSSMs). The modeling capability of ALSSMs is vast, as they can model exponentials, polynomials and sinusoidal functions as well as any linear and multiplicative combination thereof. The fitting method offers efficient recursions, subsample precision by way of the signal model and additional goodness of fit measures based on the recursively computed fitting cost. Classical methods such as standard Savitzky-Golay (SG) smoothing filters and the Short-Time Fourier Transform (STFT) are united under a common framework.First, we complete the existing framework. The ALSSM parameterization and RLS recursions are provided for a general function. The solution of the fit parameters for different constraint problems are reviewed. Moreover, feature extraction from both the fit parameters and the cost is detailed as well as examples of their use. In particular, we introduce terminology to analyze the fitting problem from the perspective of projection to a local Hilbert space and as a linear filter. Analytical rules are given for computation of the equivalent filter response and the steady-state precision matrix of the cost.After establishing the local approximation framework, we further discuss two classes of signal models in particular, namely polynomial and sinusoidal functions. The signal models are complementary, as by nature, polynomials are suited for time-domain description of signals while sinusoids are suited for the frequency-domain.For local approximation of polynomials, we derive analytical expressions for the steady-state covariance matrix and the linear filter of the coefficients based on the theory of orthogonal polynomial bases. We then discuss the fundamental application of smoothing filters based on local polynomial approximation. We generalize standard SG filters to any ALSSM window and introduce a novel class of smoothing filters based on polynomial fitting to running sums. 286 pp. Englisch. Codice articolo 9783866287921
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Taschenbuch. Condizione: Neu. This item is printed on demand - Print on Demand Titel. Neuware -With increasing availability of computation power, digital signal analysis algorithms have the potential of evolving from the common framewise operational method to samplewise operations which offer more precision in time. This thesis discusses a set of methods with samplewise operations: local signal approximation via Recursive Least Squares (RLS) where a mathematical model is fit to the signal within a sliding window at each sample. Thereby both the signal models and cost windows are generated by Autonomous Linear State Space Models (ALSSMs). The modeling capability of ALSSMs is vast, as they can model exponentials, polynomials and sinusoidal functions as well as any linear and multiplicative combination thereof. The fitting method offers efficient recursions, subsample precision by way of the signal model and additional goodness of fit measures based on the recursively computed fitting cost. Classical methods such as standard Savitzky-Golay (SG) smoothing filters and the Short-Time Fourier Transform (STFT) are united under a common framework.First, we complete the existing framework. The ALSSM parameterization and RLS recursions are provided for a general function. The solution of the fit parameters for different constraint problems are reviewed. Moreover, feature extraction from both the fit parameters and the cost is detailed as well as examples of their use. In particular, we introduce terminology to analyze the fitting problem from the perspective of projection to a local Hilbert space and as a linear filter. Analytical rules are given for computation of the equivalent filter response and the steady-state precision matrix of the cost.After establishing the local approximation framework, we further discuss two classes of signal models in particular, namely polynomial and sinusoidal functions. The signal models are complementary, as by nature, polynomials are suited for time-domain description of signals while sinusoids are suited for the frequency-domain.For local approximation of polynomials, we derive analytical expressions for the steady-state covariance matrix and the linear filter of the coefficients based on the theory of orthogonal polynomial bases. We then discuss the fundamental application of smoothing filters based on local polynomial approximation. We generalize standard SG filters to any ALSSM window and introduce a novel class of smoothing filters based on polynomial fitting to running sums.Books on Demand GmbH, Überseering 33, 22297 Hamburg 286 pp. Englisch. Codice articolo 9783866287921
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Taschenbuch. Condizione: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - With increasing availability of computation power, digital signal analysis algorithms have the potential of evolving from the common framewise operational method to samplewise operations which offer more precision in time. This thesis discusses a set of methods with samplewise operations: local signal approximation via Recursive Least Squares (RLS) where a mathematical model is fit to the signal within a sliding window at each sample. Thereby both the signal models and cost windows are generated by Autonomous Linear State Space Models (ALSSMs). The modeling capability of ALSSMs is vast, as they can model exponentials, polynomials and sinusoidal functions as well as any linear and multiplicative combination thereof. The fitting method offers efficient recursions, subsample precision by way of the signal model and additional goodness of fit measures based on the recursively computed fitting cost. Classical methods such as standard Savitzky-Golay (SG) smoothing filters and the Short-Time Fourier Transform (STFT) are united under a common framework.First, we complete the existing framework. The ALSSM parameterization and RLS recursions are provided for a general function. The solution of the fit parameters for different constraint problems are reviewed. Moreover, feature extraction from both the fit parameters and the cost is detailed as well as examples of their use. In particular, we introduce terminology to analyze the fitting problem from the perspective of projection to a local Hilbert space and as a linear filter. Analytical rules are given for computation of the equivalent filter response and the steady-state precision matrix of the cost.After establishing the local approximation framework, we further discuss two classes of signal models in particular, namely polynomial and sinusoidal functions. The signal models are complementary, as by nature, polynomials are suited for time-domain description of signals while sinusoids are suited for the frequency-domain.For local approximation of polynomials, we derive analytical expressions for the steady-state covariance matrix and the linear filter of the coefficients based on the theory of orthogonal polynomial bases. We then discuss the fundamental application of smoothing filters based on local polynomial approximation. We generalize standard SG filters to any ALSSM window and introduce a novel class of smoothing filters based on polynomial fitting to running sums. Codice articolo 9783866287921
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