125 research outputs found
ロバスト性解析と制御器設計のための離散時間非因果的周期時変スケーリング
京都大学0048新制・課程博士博士(工学)甲第17889号工博第3798号新制||工||1581(附属図書館)30709京都大学大学院工学研究科電気工学専攻(主査)教授 萩原 朋道, 教授 土居 伸二, 准教授 久門 尚史学位規則第4条第1項該当Doctor of Philosophy (Engineering)Kyoto UniversityDFA
Analysis, estimation and control for perturbed and singular systems and for systems subject to discrete events.
Annual technical report for grant AFOSR-88-0032.Investigators: Alan S. Willsky, George C. Verghese.Includes bibliographical references (p. [10]-[15]).Research supported by the AFOSR. AFOSR-88-003
Identification of linear periodically time-varying (LPTV) systems
A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results.
A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure
the noise-contaminated output. Using such periodic inputs, we show that we can formulate the
problem of identification of LPTV systems in the frequency domain. With the help of the discrete
Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification.
In the frequency domain, we show that the input and the output can be related by using the
discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias
components. A lower bound on the mean square error (MSE) of the estimated alias components
is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is
designed subsequently. The algorithm is extended to the identification of infinite impulse response
(IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the
efficiency of the optimal training signal design
Resource-aware motion control:feedforward, learning, and feedback
Controllers with new sampling schemes improve motion systems’ performanc
Analysis of Implicit Uncertain Systems. Part II: Constant Matrix Problems and Application to Robust H2 Analysis
This paper introduces an implicit framework for the analysis of uncertain systems, of which the general properties were described in Part I. In Part II, the theory is specialized to problems which admit a finite dimensional formulation. A constant matrix version of implicit analysis is presented, leading to a generalization of the structured singular value μ as the stability measure; upper bounds are developed and analyzed in detail. An application of this framework results in a practical method for robust H2 analysis: computing robust performance in the presence of norm-bounded perturbations and white-noise disturbances
Noncoherent Capacity of Underspread Fading Channels
We derive bounds on the noncoherent capacity of wide-sense stationary
uncorrelated scattering (WSSUS) channels that are selective both in time and
frequency, and are underspread, i.e., the product of the channel's delay spread
and Doppler spread is small. For input signals that are peak constrained in
time and frequency, we obtain upper and lower bounds on capacity that are
explicit in the channel's scattering function, are accurate for a large range
of bandwidth and allow to coarsely identify the capacity-optimal bandwidth as a
function of the peak power and the channel's scattering function. We also
obtain a closed-form expression for the first-order Taylor series expansion of
capacity in the limit of large bandwidth, and show that our bounds are tight in
the wideband regime. For input signals that are peak constrained in time only
(and, hence, allowed to be peaky in frequency), we provide upper and lower
bounds on the infinite-bandwidth capacity and find cases when the bounds
coincide and the infinite-bandwidth capacity is characterized exactly. Our
lower bound is closely related to a result by Viterbi (1967).
The analysis in this paper is based on a discrete-time discrete-frequency
approximation of WSSUS time- and frequency-selective channels. This
discretization explicitly takes into account the underspread property, which is
satisfied by virtually all wireless communication channels.Comment: Submitted to the IEEE Transactions on Information Theor
From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals
Conventional sub-Nyquist sampling methods for analog signals exploit prior
information about the spectral support. In this paper, we consider the
challenging problem of blind sub-Nyquist sampling of multiband signals, whose
unknown frequency support occupies only a small portion of a wide spectrum. Our
primary design goals are efficient hardware implementation and low
computational load on the supporting digital processing. We propose a system,
named the modulated wideband converter, which first multiplies the analog
signal by a bank of periodic waveforms. The product is then lowpass filtered
and sampled uniformly at a low rate, which is orders of magnitude smaller than
Nyquist. Perfect recovery from the proposed samples is achieved under certain
necessary and sufficient conditions. We also develop a digital architecture,
which allows either reconstruction of the analog input, or processing of any
band of interest at a low rate, that is, without interpolating to the high
Nyquist rate. Numerical simulations demonstrate many engineering aspects:
robustness to noise and mismodeling, potential hardware simplifications,
realtime performance for signals with time-varying support and stability to
quantization effects. We compare our system with two previous approaches:
periodic nonuniform sampling, which is bandwidth limited by existing hardware
devices, and the random demodulator, which is restricted to discrete multitone
signals and has a high computational load. In the broader context of Nyquist
sampling, our scheme has the potential to break through the bandwidth barrier
of state-of-the-art analog conversion technologies such as interleaved
converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in
Signal Processing, the special issue on Compressed Sensin
Efficient algorithms for arbitrary sample rate conversion with application to wave field synthesis
Arbitrary sample rate conversion (ASRC) is used in many fields of digital signal processing to alter the sampling rate of discrete-time signals by arbitrary, potentially time-varying ratios.
This thesis investigates efficient algorithms for ASRC and proposes several improvements. First, closed-form descriptions for the modified Farrow structure and Lagrange interpolators are derived that are directly applicable to algorithm design and analysis. Second, efficient implementation structures for ASRC algorithms are investigated. Third, this thesis considers coefficient design methods that are optimal for a selectable error norm and optional design constraints.
Finally, the performance of different algorithms is compared for several performance metrics. This enables the selection of ASRC algorithms that meet the requirements of an application with minimal complexity.
Wave field synthesis (WFS), a high-quality spatial sound reproduction technique, is the main application considered in this work. For WFS, sophisticated ASRC algorithms improve the quality of moving sound sources. However, the improvements proposed in this thesis are not limited to WFS, but applicable to general-purpose ASRC problems.Verfahren zur unbeschränkten Abtastratenwandlung (arbitrary sample rate
conversion,ASRC) ermöglichen die Änderung der Abtastrate zeitdiskreter
Signale um beliebige, zeitvarianteVerhältnisse. ASRC wird in vielen
Anwendungen digitaler Signalverarbeitung eingesetzt.In dieser Arbeit wird
die Verwendung von ASRC-Verfahren in der Wellenfeldsynthese(WFS), einem
Verfahren zur hochqualitativen, räumlich korrekten Audio-Wiedergabe,
untersucht.Durch ASRC-Algorithmen kann die Wiedergabequalität bewegter
Schallquellenin WFS deutlich verbessert werden. Durch die hohe Zahl der in
einem WFS-Wiedergabesystembenötigten simultanen ASRC-Operationen ist eine
direkte Anwendung hochwertigerAlgorithmen jedoch meist nicht möglich.Zur
Lösung dieses Problems werden verschiedene Beiträge vorgestellt. Die
Komplexitätder WFS-Signalverarbeitung wird durch eine geeignete
Partitionierung der ASRC-Algorithmensignifikant reduziert, welche eine
effiziente Wiederverwendung von Zwischenergebnissenermöglicht. Dies
erlaubt den Einsatz hochqualitativer Algorithmen zur Abtastratenwandlungmit
einer Komplexität, die mit der Anwendung einfacher konventioneller
ASRCAlgorithmenvergleichbar ist. Dieses Partitionierungsschema stellt
jedoch auch zusätzlicheAnforderungen an ASRC-Algorithmen und erfordert
Abwägungen zwischen Performance-Maßen wie der algorithmischen
Komplexität, Speicherbedarf oder -bandbreite.Zur Verbesserung von
Algorithmen und Implementierungsstrukturen für ASRC werdenverschiedene
Maßnahmen vorgeschlagen. Zum Einen werden geschlossene,
analytischeBeschreibungen für den kontinuierlichen Frequenzgang
verschiedener Klassen von ASRCStruktureneingeführt. Insbesondere für
Lagrange-Interpolatoren, die modifizierte Farrow-Struktur sowie
Kombinationen aus Überabtastung und zeitkontinuierlichen
Resampling-Funktionen werden kompakte Darstellungen hergeleitet, die sowohl
Aufschluss über dasVerhalten dieser Filter geben als auch eine direkte
Verwendung in Design-Methoden ermöglichen.Einen zweiten Schwerpunkt bildet
das Koeffizientendesign für diese Strukturen, insbesonderezum optimalen
Entwurf bezüglich einer gewählten Fehlernorm und optionaler
Entwurfsbedingungenund -restriktionen. Im Gegensatz zu bisherigen Ansätzen
werden solcheoptimalen Entwurfsmethoden auch für mehrstufige
ASRC-Strukturen, welche ganzzahligeÜberabtastung mit zeitkontinuierlichen
Resampling-Funktionen verbinden, vorgestellt.Für diese Klasse von
Strukturen wird eine Reihe angepasster Resampling-Funktionen
vorgeschlagen,welche in Verbindung mit den entwickelten optimalen
Entwurfsmethoden signifikanteQualitätssteigerungen ermöglichen.Die
Vielzahl von ASRC-Strukturen sowie deren Design-Parameter bildet eine
Hauptschwierigkeitbei der Auswahl eines für eine gegebene Anwendung
geeigneten Verfahrens.Evaluation und Performance-Vergleiche bilden daher
einen dritten Schwerpunkt. Dazu wirdzum Einen der Einfluss verschiedener
Entwurfsparameter auf die erzielbare Qualität vonASRC-Algorithmen
untersucht. Zum Anderen wird der benötigte Aufwand bezüglich
verschiedenerPerformance-Metriken in Abhängigkeit von Design-Qualität
dargestellt.Auf diese Weise sind die Ergebnisse dieser Arbeit nicht auf WFS
beschränkt, sondernsind in einer Vielzahl von Anwendungen unbeschränkter
Abtastratenwandlung nutzbar
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