Research Collection. Digital estimation of continuous-time signals using factor graphs. Doctoral Thesis. ETH Library. Author(s): Bolliger, Lukas
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1 Research Collection Doctoral Thesis Digital estimation of continuous-time signals using factor graphs Author(s): Bolliger, Lukas Publication Date: 2012 Permanent Link: Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library
2 ETH Series in Diss. ETH No Signal and Information Processing Volume 22 Digital Estimation of Continuous-Time Signals Using Factor Graphs A dissertation submitted to ETH Zurich for the degree of Doctor of Sciences presented by Lukas Bolliger Master of Science ETH in Electrical Engineering and Information Technology, ETH Zurich, Switzerland born on May 03, 1981 citizen of Luzern LU and Uerkheim AG Hartung Gorre Konstanz 2012 accepted on the recommendation of Prof. Dr. H.-A. Loeliger, examiner Prof. Dr. A. Singer, co-examiner Dr. Ch. Vogel, co-examiner
3 Abstract A digital signal may represent noisy, quantized, discrete-time observations of a continuous-time signal. If the continuous-time signal is bandlimited to half the sampling rate, and the samples are taken without noise and with infinite precision, the continuous-time signal can be fully reconstructed from its digital samples. In this thesis we introduce a model of a continuous-time signal that is not bandlimited in the traditional sense, but its spectrum is shaped by the transfer function of a known, finite-order linear system/ filter. Among other applications the continuous-time system/ filter may represent the analog parts of a receiver, or it may represent a sensor that delivers a filtered version of the actual force applied. We use Forney factor graphs to represent the continuous-time signal and its noisy, quantized, discrete-time observations. The factor graph approach, which is well developed for discrete-time systems, is extended in this thesis for continuous-time systems. We use message passing algorithms in the factor graph to estimate both, the input and output signal of the continuous-time system/ filter at arbitrary time instances. The estimation of the output signal is essentially a Kalman smoother. The estimate of the input signal (which appears to be new) can be viewed as a generalized bandlimited reconstruction of a continuous-time signal. Two applications are described in this thesis. We show how our model can be extended to increase the quality of a digital signal that was sampled with clock jitter. We also introduce a general view on the widely used sigma-delta converter: an A/D converter may consist of any unstable linear system with feedback. The feedback ensures that the internal vii
4 viii Abstract variables of the system stay in a predefined range. We use our proposed model to represent the components of such an Unstable Linear Filter ADC and we can then estimate its input signal given quantized, discrete-time observations of some internal variables of the system.
5 Kurzfassung Ein digitales Signal kann betrachtet werden als eine Liste von zeitdiskreten, verrauschten und quantisierten Beobachtungen eines zeitkontiuierlichen Signals. Falls das zeitkontinuierliche Signal bandbegrenzt ist, und die Beobachtungen mit einer höheren Rate als die doppelte Bandbreite abgetastet werden, kann das zeitkontinuierliche Signal wieder fehlerfrei rekonstuiert werden. In dieser Arbeit beschreiben wir ein Modell eines zeitkontinuierlichen Signals welches nicht bandbegrenzt ist, sondern ein Spektrum hat welches geformt ist durch die Übertragungsfuktion eines bekannten, linearen und zeitinvarianten Systems/ Filters endlicher Ordnung. Unter anderem könnte das System/ Filter den analogen Teil eines Empfängers oder einen Sensor welcher eine gefilterte Version der zu messenden Grösse liefert modellieren. Mit Hilfe von Forney Faktorgraphen modellieren wir das zeitkontinuierliche System/ Filter und dessen Ausganssignal, sowie die zeitdiskreten Beobachtungen. Das modellieren von zeitdiskreten Systemen mit Hilfe von Faktorgraphen ist weit verbreitet, wir zeigen wie dieser Ansatz auf zeitkontinuierliche Systeme/ Filter erweitert werden kann. Mit Message- Passing Algorithmen im Faktorgraphen berechnen wir eine Schätzung des Eingang- und Ausgangssignals des zeitkontinuierlichen Systems/ Filters zu beliebigen Zeitpunkten. Die Schätzung des Ausgangssignals ist im wesentlichen ein Kalman Smoother, wobei die Schätzung des Einganssignals neu zu sein scheint. Zum Modell und den Algorithmen beschreiben wir zwei Anwendungen. Wir zeigen, wie das Modell erweitert werden kann für zeitdiskreix
6 x Kurzfassung te Signale welche zusätzlich durch Clock-Jitter verfälscht wurden. Des Weiteren beschreiben wir eine allgemeine Sicht auf den weit verbreiteten Sigma-Delta Wandler: Ein Analog-Digital Wandler kann ein beliebiges instabiles, lineares System enthalten, welches mit Hilfe von Rückkopplungen in einem definierten Bereich gehalten wird. Wir zeigen wie unser Modell und die aufgezeigten Algorithmen in einem solchen Unstable Linear Filter ADC genutzt werden können um das Einganssignal eines solchen Wandlers anhand von zeitdiskreten Beobachtungen zu schätzen.
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Research Collection Doctoral Thesis The measurement of the oxygenation status of the newborn infant Author(s): Wolf, Martin Peter Publication Date: 1996 Permanent Link: https://doi.org/10.3929/ethz-a-001630372
Multiscale modeling and simulation of fullerenes in liquids
Research Collection Doctoral Thesis Multiscale modeling and simulation of fullerenes in liquids Author(s): Kotsalis, Evangelos M. Publication Date: 2008 Permanent Link: https://doi.org/10.3929/ethz-a-005772771
Research Collection. Security of quantum key distribution. Doctoral Thesis. ETH Library. Author(s): Renner, Renato. Publication Date: 2005
Research Collection Doctoral Thesis Security of quantum key distribution Author(s): Renner, Renato Publication Date: 2005 Permanent Link: https://doi.org/10.3929/ethz-a-005115027 Rights / License: In Copyright
Location fingerprinting for ultra-wideband systems The key to efficient and robust localization
Research Collection Doctoral Thesis Location fingerprinting for ultra-wideband systems The key to efficient and robust localization Author(s): Steiner, Christoph Publication Date: 2010 Permanent Link:
Quantum Teleportation and Efficient Process Verification with Superconducting Circuits
Research Collection Doctoral Thesis Quantum Teleportation and Efficient Process Verification with Superconducting Circuits Author(s): Steffen, Lars Publication Date: 2013 Permanent Link: https://doi.org/10.3929/ethz-a-010050047
Robust Indoor Positioning through Adaptive Collaborative Labeling of Location Fingerprints
Research Collection Doctoral Thesis Robust Indoor Positioning through Adaptive Collaborative Labeling of Location Fingerprints Author(s): Bolliger, Philipp L. Publication Date: 2011 Permanent Link: https://doi.org/10.3929/ethz-a-007052434
Restricted structural equation models for causal inference
Research Collection Doctoral Thesis Restricted structural equation models for causal inference Author(s): Peters, Jonas Martin Publication Date: 2012 Permanent Link: https://doi.org/10.3929/ethz-a-007597940
Immersive Environments: From Virtual Indoor Tours to Outdoor Modelling
Research Collection Doctoral Thesis Immersive Environments: From Virtual Indoor Tours to Outdoor Modelling Author(s): Saurer, Olivier Publication Date: 2016 Permanent Link: https://doi.org/10.3929/ethz-a-010710664
Sterilisation von stückigen Lebensmitteln mit Mikrowellen
Research Collection Doctoral Thesis Sterilisation von stückigen Lebensmitteln mit Mikrowellen Author(s): Spreng, Hans Publication Date: 1975 Permanent Link: https://doi.org/10.3929/ethza000119193 Rights
Model-Based Adaptive Air/Fuel Ratio Control for an Automotive Gasoline Engine
Diss. ETH No. 18302 Model-Based Adaptive Air/Fuel Ratio Control for an Automotive Gasoline Engine A dissertation submitted to ETH ZURICH for the degree of Doctor of Sciences presented by Daniel Rupp Dipl.
Resource management in a multicore operating system
Research Collection Doctoral Thesis Resource management in a multicore operating system Author(s): Peter, Simon Publication Date: 2012 Permanent Link: https://doi.org/10.3929/ethz-a-007579246 Rights /