Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github

Sound Source Separation

This is the author's accepted pre-print of the article, first published as G. Evangelista, S. Marchand, M. D. Plumbley and E. Vincent. Sound source separation. In U. Zölzer (ed.), DAFX: Digital Audio Effects, 2nd edition, Chapter 14, pp. 551-588. John Wiley & Sons, March 2011. ISBN 9781119991298. DOI: 10.1002/9781119991298.ch14file: Proof:e\EvangelistaMarchandPlumbleyV11-sound.pdf:PDF owner: markp timestamp: 2011.04.26file: Proof:e\EvangelistaMarchandPlumbleyV11-sound.pdf:PDF owner: markp timestamp: 2011.04.2

New Particles Working Group Report of the Snowmass 2013 Community Summer Study

This report summarizes the work of the Energy Frontier New Physics working group of the 2013 Community Summer Study (Snowmass)

Discrete Breathers

Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattices - quantum breathers. Finally we will formulate a new conceptual aproach capable of predicting whether discrete breather exist for a given system or not, without actually solving for the breather. We discuss potential applications in lattice dynamics of solids (especially molecular crystals), selective bond excitations in large molecules, dynamical properties of coupled arrays of Josephson junctions, and localization of electromagnetic waves in photonic crystals with nonlinear response.Comment: 62 pages, LaTeX, 14 ps figures. Physics Reports, to be published; see also at http://www.mpipks-dresden.mpg.de/~flach/html/preprints.htm

Topology by dissipation

Topological states of fermionic matter can be induced by means of a suitably engineered dissipative dynamics. Dissipation then does not occur as a perturbation, but rather as the main resource for many-body dynamics, providing a targeted cooling into a topological phase starting from an arbitrary initial state. We explore the concept of topological order in this setting, developing and applying a general theoretical framework based on the system density matrix which replaces the wave function appropriate for the discussion of Hamiltonian ground-state physics. We identify key analogies and differences to the more conventional Hamiltonian scenario. Differences mainly arise from the fact that the properties of the spectrum and of the state of the system are not as tightly related as in a Hamiltonian context. We provide a symmetry-based topological classification of bulk steady states and identify the classes that are achievable by means of quasi-local dissipative processes driving into superfluid paired states. We also explore the fate of the bulk-edge correspondence in the dissipative setting, and demonstrate the emergence of Majorana edge modes. We illustrate our findings in one- and two-dimensional models that are experimentally realistic in the context of cold atoms.Comment: 61 pages, 8 figure

Pre-Trained Driving in Localized Surroundings with Semantic Radar Information and Machine Learning

Entlang der Signalverarbeitungskette von Radar Detektionen bis zur Fahrzeugansteuerung, diskutiert diese Arbeit eine semantischen Radar Segmentierung, einen darauf aufbauenden Radar SLAM, sowie eine im Verbund realisierte autonome Parkfunktion. Die Radarsegmentierung der (statischen) Umgebung wird durch ein Radar-spezifisches neuronales Netzwerk RadarNet erreicht. Diese Segmentierung ermöglicht die Entwicklung des semantischen Radar Graph-SLAM SERALOC. Auf der Grundlage der semantischen Radar SLAM Karte wird eine beispielhafte autonome Parkfunktionalität in einem realen Versuchsträger umgesetzt. Entlang eines aufgezeichneten Referenzfades parkt die Funktion ausschließlich auf Basis der Radar Wahrnehmung mit bisher unerreichter Positioniergenauigkeit. Im ersten Schritt wird ein Datensatz von 8.2 · 10^6 punktweise semantisch gelabelten Radarpunktwolken über eine Strecke von 2507.35m generiert. Es sind keine vergleichbaren Datensätze dieser Annotationsebene und Radarspezifikation öffentlich verfügbar. Das überwachte Training der semantischen Segmentierung RadarNet erreicht 28.97% mIoU auf sechs Klassen. Außerdem wird ein automatisiertes Radar-Labeling-Framework SeRaLF vorgestellt, welches das Radarlabeling multimodal mittels Referenzkameras und LiDAR unterstützt. Für die kohärente Kartierung wird ein Radarsignal-Vorfilter auf der Grundlage einer Aktivierungskarte entworfen, welcher Rauschen und andere dynamische Mehrwegreflektionen unterdrückt. Ein speziell für Radar angepasstes Graph-SLAM-Frontend mit Radar-Odometrie Kanten zwischen Teil-Karten und semantisch separater NDT Registrierung setzt die vorgefilterten semantischen Radarscans zu einer konsistenten metrischen Karte zusammen. Die Kartierungsgenauigkeit und die Datenassoziation werden somit erhöht und der erste semantische Radar Graph-SLAM für beliebige statische Umgebungen realisiert. Integriert in ein reales Testfahrzeug, wird das Zusammenspiel der live RadarNet Segmentierung und des semantischen Radar Graph-SLAM anhand einer rein Radar-basierten autonomen Parkfunktionalität evaluiert. Im Durchschnitt über 42 autonome Parkmanöver (∅3.73 km/h) bei durchschnittlicher Manöverlänge von ∅172.75m wird ein Median absoluter Posenfehler von 0.235m und End-Posenfehler von 0.2443m erreicht, der vergleichbare Radar-Lokalisierungsergebnisse um ≈ 50% übertrifft. Die Kartengenauigkeit von veränderlichen, neukartierten Orten über eine Kartierungsdistanz von ∅165m ergibt eine ≈ 56%-ige Kartenkonsistenz bei einer Abweichung von ∅0.163m. Für das autonome Parken wurde ein gegebener Trajektorienplaner und Regleransatz verwendet

Doctor of Philosophy

dissertationIn wireless sensor networks, knowing the location of the wireless sensors is critical in many remote sensing and location-based applications, from asset tracking, and structural monitoring to geographical routing. For a majority of these applications, received signal strength (RSS)-based localization algorithms are a cost effective and viable solution. However, RSS measurements vary unpredictably because of fading, the shadowing caused by presence of walls and obstacles in the path, and non-isotropic antenna gain patterns, which affect the performance of the RSS-based localization algorithms. This dissertation aims to provide efficient models for the measured RSS and use the lessons learned from these models to develop and evaluate efficient localization algorithms. The first contribution of this dissertation is to model the correlation in shadowing across link pairs. We propose a non-site specific statistical joint path loss model between a set of static nodes. Radio links that are geographically proximate often experience similar environmental shadowing effects and thus have correlated shadowing. Using a large number of multi-hop network measurements in an ensemble of indoor and outdoor environments, we show statistically significant correlations among shadowing experienced on different links in the network. Finally, we analyze multihop paths in three and four node networks using both correlated and independent shadowing models and show that independent shadowing models can underestimate the probability of route failure by a factor of two or greater. Second, we study a special class of algorithms, called kernel-based localization algorithms, that use kernel methods as a tool for learning correlation between the RSS measurements. Kernel methods simplify RSS-based localization algorithms by providing a means to learn the complicated relationship between RSS measurements and position. We present a common mathematical framework for kernel-based localization algorithms to study and compare the performance of four different kernel-based localization algorithms from the literature. We show via simulations and an extensive measurement data set that kernel-based localization algorithms can perform better than model-based algorithms. Results show that kernel methods can achieve an RMSE up to 55% lower than a model-based algorithm. Finally, we propose a novel distance estimator for estimating the distance between two nodes a and b using indirect link measurements, which are the measurements made between a and k, for k ? b and b and k, for k ? a. Traditionally, distance estimators use only direct link measurement, which is the pairwise measurement between the nodes a and b. The results show that the estimator that uses indirect link measurements enables better distance estimation than the estimator that uses direct link measurements