One and two dimensional maximum entropy spectral estimation

Originally published as thesis (Dept. of Electrical Engineering and Computer Science, Sc.D., 1981).Bibliography: p. 115-117.Naveed Akhtar Malik

Bayesian methods in music modelling

This thesis presents several hierarchical generative Bayesian models of musical signals designed to improve the accuracy of existing multiple pitch detection systems and other musical signal processing applications whilst remaining feasible for real-time computation. At the lowest level the signal is modelled as a set of overlapping sinusoidal basis functions. The parameters of these basis functions are built into a prior framework based on principles known from musical theory and the physics of musical instruments. The model of a musical note optionally includes phenomena such as frequency and amplitude modulations, damping, volume, timbre and inharmonicity. The occurrence of note onsets in a performance of a piece of music is controlled by an underlying tempo process and the alignment of the timings to the underlying score of the music. A variety of applications are presented for these models under differing inference constraints. Where full Bayesian inference is possible, reversible-jump Markov Chain Monte Carlo is employed to estimate the number of notes and partial frequency components in each frame of music. We also use approximate techniques such as model selection criteria and variational Bayes methods for inference in situations where computation time is limited or the amount of data to be processed is large. For the higher level score parameters, greedy search and conditional modes algorithms are found to be sufficiently accurate. We emphasize the links between the models and inference algorithms developed in this thesis with that in existing and parallel work, and demonstrate the effects of making modifications to these models both theoretically and by means of experimental results

Discovering Regularity in Point Clouds of Urban Scenes

Despite the apparent chaos of the urban environment, cities are actually replete with regularity. From the grid of streets laid out over the earth, to the lattice of windows thrown up into the sky, periodic regularity abounds in the urban scene. Just as salient, though less uniform, are the self-similar branching patterns of trees and vegetation that line streets and fill parks. We propose novel methods for discovering these regularities in 3D range scans acquired by a time-of-flight laser sensor. The applications of this regularity information are broad, and we present two original algorithms. The first exploits the efficiency of the Fourier transform for the real-time detection of periodicity in building facades. Periodic regularity is discovered online by doing a plane sweep across the scene and analyzing the frequency space of each column in the sweep. The simplicity and online nature of this algorithm allow it to be embedded in scanner hardware, making periodicity detection a built-in feature of future 3D cameras. We demonstrate the usefulness of periodicity in view registration, compression, segmentation, and facade reconstruction. The second algorithm leverages the hierarchical decomposition and locality in space of the wavelet transform to find stochastic parameters for procedural models that succinctly describe vegetation. These procedural models facilitate the generation of virtual worlds for architecture, gaming, and augmented reality. The self-similarity of vegetation can be inferred using multi-resolution analysis to discover the underlying branching patterns. We present a unified framework of these tools, enabling the modeling, transmission, and compression of high-resolution, accurate, and immersive 3D images

A method of voltage tracking for power system applications

An algorithm that is capable of estimating the parameters of non-stationary sinusoids in real-time lends application to various branches of engineering. Non-stationary sinusoids are sinusoidal signals with time-varying parameters. In this dissertation, a nonlinear filter is applied to power system applications to test its performance. The filter has a structure which renders it fully adaptive to tracking time variations in the parameters of the targeted sinusoid, including its phase and frequency. Mathematical properties of the differential equations which govern the proposed filter are presented. The performance of the proposed filter in the field of power systems is demonstrated with the aid of computer simulations and practical experimentations. The filter is applied to synchronous generator excitation control, voltage dip mitigation as well as the real-time estimation of symmetrical components. The parameter settings of the filter are tested and optimized for each of the applications. This dissertation demonstrates the simulation and experimental results of the filter when applied to the various power system applications. AFRIKAANS : 'n Filter wat bevoeglik is met die beraming van die parameters van beweeglike sinusoïdale in ware-tyd, kan bruikbaar aangewend word in verskeie takke van ingenieurswese. Beweeglike sinuskrommes is sinusoïdale seine met tyd-wisselende parameters. In hierdie verhandeling word `n nie-liniêre filter aangewend in verskeie kragstelseltoepassings om die werksverrigting van die filter te toets. Die filter het 'n struktuur wat dit toelaat om wisselende tydvariasies in die parameters van die teikensinusoïdaal op te spoor, insluitende die fase en frekwensie. Wiskundige eienskappe van die differensiaalvergelykings wat die voorgestelde filter beheer is ondersoek. Die werksverrigting van die voorgestelde filter in die veld van kragstelsels is gedemonstreer met die hulp van rekenaarsimulasies asook praktiese eksperimente. Die filter is toegepas tot opgewekte, sinkrone eksitasie-beheer, spanningsverlaging versagting, asook die ware tyd estimasie van simmetriese komponente. Die parameter verstellings van die filter is getoets en geoptimeer vir elk van die toepassings. Hierdie verhandeling demonstreer die simulering en eksperimentele resultate van die filter wat aangewend is vir verskeie kragstelseltoepassings. CopyrightDissertation (MSc)--University of Pretoria, 2010.Electrical, Electronic and Computer Engineeringunrestricte

Novel Deterministic Detection and Estimation Algorithms for Colocated Multiple-Input Multiple-Output Radars

In this manuscript, the problem of detecting multiple targets and estimating their spatial coordinates (namely, their range and the direction of arrival of their electromagnetic echoes) in a colocated multiple-input multiple-output radar system operating in a static or slowly changing two-dimensional or three-dimensional propagation scenario is investigated. Various solutions, collectively called range & angle serial cancellation algorithms, are developed for both frequency modulated continuous wave radars and stepped frequency continuous wave radars. Moreover, specific technical problems experienced in their implementation are discussed. Finally, the accuracy achieved by these algorithms in the presence of multiple targets is assessed on the basis of both synthetically generated data and of the measurements acquired through three different multiple-input multiple-output radars and is compared with that provided by other methods based on multidimensional Fourier analysis and multiple signal classification

Statistical signal processing using a class of iterative estimation algorithms

Bibliography: p. 12-13.Supported in part by the M.I.T.--W.H.O.I. Joint Program. Supported in part by the Advanced Research Projects Agency monitored by ONR under contract no. N00014-81-K-0742 Supported in part by the National Science Foundation under grant ECS-8407285Meir Feder

Nonlinear adaptive estimation with application to sinusoidal identification

Parameter estimation of a sinusoidal signal in real-time is encountered in applications in numerous areas of engineering. Parameters of interest are usually amplitude, frequency and phase wherein frequency tracking is the fundamental task in sinusoidal estimation. This thesis deals with the problem of identifying a signal that comprises n (n ≥ 1) harmonics from a measurement possibly affected by structured and unstructured disturbances. The structured perturbations are modeled as a time-polynomial so as to represent, for example, bias and drift phenomena typically present in applications, whereas the unstructured disturbances are characterized as bounded perturbation. Several approaches upon different theoretical tools are presented in this thesis, and classified into two main categories: asymptotic and non-asymptotic methodologies, depending on the qualitative characteristics of the convergence behavior over time. The first part of the thesis is devoted to the asymptotic estimators, which typically consist in a pre-filtering module for generating a number of auxiliary signals, independent of the structured perturbations. These auxiliary signals can be used either directly or indirectly to estimate—in an adaptive way—the frequency, the amplitude and the phase of the sinusoidal signals. More specifically, the direct approach is based on a simple gradient method, which ensures Input-to-State Stability of the estimation error with respect to the bounded-unstructured disturbances. The indirect method exploits a specific adaptive observer scheme equipped with a switching criterion allowing to properly address in a stable way the poor excitation scenarios. It is shown that the adaptive observer method can be applied for estimating multi-frequencies through an augmented but unified framework, which is a crucial advantage with respect to direct approaches. The estimators’ stability properties are also analyzed by Input-to-State-Stability (ISS) arguments. In the second part we present a non-asymptotic estimation methodology characterized by a distinctive feature that permits finite-time convergence of the estimates. Resorting to the Volterra integral operators with suitably designed kernels, the measured signal is processed, yielding a set of auxiliary signals, in which the influence of the unknown initial conditions is annihilated. A sliding mode-based adaptation law, fed by the aforementioned auxiliary signals, is proposed for deadbeat estimation of the frequency and amplitude, which are dealt with in a step-by-step manner. The worst case behavior of the proposed algorithm in the presence of bounded perturbation is studied by ISS tools. The practical characteristics of all estimation techniques are evaluated and compared with other existing techniques by extensive simulations and experimental trials.Open Acces

Real-time spectral modelling of audio for creative sound transformation

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