Polyphase Implementation of Non-recursive Comb Decimators for Sigma-Delta A/D Converters

In a sigma-delta analog to digital (A/D) As most of the sigma-delta ADC applications require converter, the most computationally intensive block is decimation filters with linear phase characteristics, the decimation filter and its hardware implementation symmetric Finite Impulse Response (FIR) filters are may require millions of transistors. Since these widely used for implementation. But the number of FIR converters are now targeted for a portable application, filter coefficients will be quite large for implementing a a hardware efficient design is an implicit requirement. narrow band decimation filter. Implementing decimation In this effect, this paper presents a computationally filter in several stages reduces the total number of filter efficient polyphase implementation of non-recursive coefficients, and hence reduces the hardware complexity cascaded integrator comb (CIC) decimators for and power consumption [2]. Sigma-Delta Converters (SDCs). The SDCs are The first stage of decimation filter can be operating at high oversampling frequencies and hence implemented very efficiently using a cascade of integrators require large sampling rate conversions. The filtering and comb filters which do not require multiplication or and rate reduction are performed in several stages to coefficient storage. The remaining filtering is performed reduce hardware complexity and power dissipation. either in single stage or in two stages with more complex The CIC filters are widely adopted as the first stage of FIR or infinite impulse response (IIR) filters according to decimation due to its multiplier free structure. In this the requirements. The amount of passband aliasing or research, the performance of polyphase structure is imaging error can be brought within prescribed bounds by compared with the CICs using recursive and increasing the number of stages in the CIC filter. The non-recursive algorithms in terms of power, speed and width of the passband and the frequency characteristics area. This polyphase implementation offers high speed outside the passband are severely limited. So, CIC filters operation and low power consumption. The polyphase are used to make the transition between high and low implementation of 4th order CIC filter with a sampling rates. Conventional filters operating at low decimation factor of '64' and input word length of sampling rate are used to attain the required transition '4-bits' offers about 70% and 37% of power saving bandwidth and stopband attenuation. compared to the corresponding recursive and Several papers are available in literature that deals non-recursive implementations respectively. The same with different implementations of decimation filter polyphase CIC filter can operate about 7 times faster architecture for sigma-delta ADCs. Hogenauer has than the recursive and about 3.7 times faster than the described the design procedures for decimation and non-recursive CIC filters.

A Numerically efficient power optimization scheme for coded OFDM systems in achieving minimum frame error rate

Coded OFDM is a transmission technique that is used in many practical communication systems. In a coded OFDM system, source data are coded, interleaved and multiplexed for transmission over many frequency sub-channels. In a conventional coded OFDM system, the transmission power of each subcarrier is the same regardless of the channel condition. However, some subcarrier can suffer deep fading with multi-paths and the power allocated to the faded subcarrier is likely to be wasted. In this paper, we compute the FER and BER bounds of a coded OFDM system given as convex functions for a given channel coder, inter-leaver and channel response. The power optimization is shown to be a convex optimization problem that can be solved numerically with great efficiency. With the proposed power optimization scheme, near-optimum power allocation for a given coded OFDM system and channel response to minimize FER or BER under a constant transmission power constraint is obtained

Some Dynamic Generalized Information Measures In The Context Of Weighted Models

In this paper, we study some dynamic generalized information measures between a true distribution and an observed (weighted) distribution, useful in life length studies. Further, some bounds and inequalities related to these measures are also studied

Characterizations of bivariate models using dynamic Kullback–Leibler discrimination measures

In this paper, the residual Kullback–Leibler discrimination information measure is extended to conditionally specified models. The extension is used to characterize some bivariate distributions. These distributions are also characterized in terms of proportional hazard rate models and weighted distributions. Moreover, we also obtain some bounds for this dynamic discrimination function by using the likelihood ratio order and some preceding results.

Characterizations of Bivariate Models Using Some Dynamic Conditional Information Divergence Measures

In this article, we study some relevant information divergence measures viz. Renyi divergence and Kerridge’s inaccuracy measures. These measures are extended to conditionally specifiedmodels and they are used to characterize some bivariate distributions using the concepts of weighted and proportional hazard rate models. Moreover, some bounds are obtained for these measures using the likelihood ratio order

Raman and FTIR spectra of [Cu(H2O)6](BrO3)2 and [Al(H2O)6](BrO3)3 · 3H2O

Raman and FTIR spectra of [Cu(H2O)6](BrO3)2 and [Al(H2O)6](BrO3)3 · 3H2O are recorded and analyzed. The observed bands are assigned on the basis of BrO3 − and H2O vibrations. Additional bands obtained in the region of 3 and 1 modes in [Cu(H2O)6](BrO3)2 are due to the lifting of degeneracy of 3 modes, since the BrO3 − ion occupies a site of lower symmetry. The appearance 1 mode of BrO3 − anion at a lower wavenumber (771 cm−1) is attributed to the attachment of hydrogen to the BrO3 − anion. The presence of three inequivalent bromate groups in the [Al(H2O)6](BrO3)3 · 3H2O structure is confirmed. The lifting of degeneracy of 4 mode indicates that the symmetry of BrO3 − anion is lowered in the above crystal from C3v to C1. The appearance of additional bands in the stretching and bonding mode regions of water indicates the presence of hydrogen bonds of different strengths in both the crystals. Temperature dependent Raman spectra of single crystal [Cu(H2O)6](BrO3)2 are recorded in the range 77–523 K for various temperatures. A small structural rearrangement takes place in BrO3 − ion in the crystal at 391 K. Hydrogen bounds in the crystal are rearranging themselves leading to the loss of one water molecule at 485 K. This is preceded by the reorientation of BrO3 − ions causing a phase transition at 447 K. Changes in intensities and wavenumbers of the bands and the narrowing down of the bands at 77 K are attributed to the settling down of protons into ordered positions in the crystal

Restarting automata with restricted utilization of auxiliary symbols

The restarting automaton is a restricted model of computation that was introduced by Jancar et al. to model the so-called analysis by reduction, which is a technique used in linguistics to analyze sentences of natural languages. The most general models of restarting automata make use of auxiliary symbols in their rewrite operations, although this ability does not directly correspond to any aspect of the analysis by reduction. Here we put restrictions on the way in which restarting automata use auxiliary symbols, and we investigate the influence of these restrictions on their expressive power. In fact, we consider two types of restrictions. First, we consider the number of auxiliary symbols in the tape alphabet of a restarting automaton as a measure of its descriptional complexity. Secondly, we consider the number of occurrences of auxiliary symbols on the tape as a dynamic complexity measure. We establish some lower and upper bounds with respect to these complexity measures concerning the ability of restarting automata to recognize the (deterministic) context-free languages and some of their subclasses.

Asymptotics of number fields and the Cohen-Lenstra heuristics

We study the asymptotics conjecture of Malle for dihedral groups Dl of order 2l, where l is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen-Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

Root parametrized differential equations

The present thesis is about the inverse problem in differential Galois Theory. Given a differential field, the inverse  problem asks which linear algebraic groups can be realized as differential Galois groups of Picard-Vessiot extensions of this field.   In this thesis we will concentrate on the realization of the classical groups as differential Galois groups. We introduce a method for a very general realization of these groups. This means that we present for the classical groups of Lie rank $l$ explicit linear differential equations where the coefficients are differential polynomials in $l$ differential indeterminates over an algebraically closed field of constants $C$, i.e. our differential ground field is purely differential transcendental over the constants.   For the groups of type $A_l$, $B_l$, $C_l$, $D_l$ and $G_2$ we managed to do these realizations at the same time in terms of Abhyankar's program 'Nice Equations for Nice Groups'. Here the choice of the defining matrix is important. We found out that an educated choice of $l$ negative roots for the parametrization together with the positive simple roots leads to a nice differential equation and at the same time defines a sufficiently general element of the Lie algebra. Unfortunately for the groups of type $F_4$ and $E_6$ the linear differential equations for such elements are of enormous length. Therefore we keep in the case of $F_4$ and $E_6$ the defining matrix differential equation which has also an easy and nice shape.   The basic idea for the realization is the application of an upper and lower bound criterion for the differential Galois group to our parameter equations and to show that both bounds coincide. An upper and lower bound criterion can be found in literature. Here we will only use the upper bound, since for the application of the lower bound criterion an important condition has to be satisfied. If the differential ground field is $C_1$, e.g., $C(z)$ with standard derivation, this condition is automatically satisfied. Since our differential ground field is purely differential transcendental over $C$, we have no information whether this condition holds or not.   The main part of this thesis is the development of an alternative lower bound criterion and its application. We introduce the specialization bound. It states that the differential Galois group of a specialization of the parameter equation is contained in the differential Galois group of the parameter equation. Thus for its application we need a differential equation over $C(z)$ with given differential Galois group. A modification of a result from Mitschi and Singer yields such an equation over $C(z)$ up to differential conjugation, i.e. up to transformation to the required shape. The transformation of their equation to a specialization of our parameter equation is done for each of the above groups in the respective transformation lemma.

Die aeroelastische Stabilitätsanalyse – ein praxisnaher Ansatz zur intervalltheoretischen Betrachtung von Modellierungsunsicherheiten am Flugzeug

Die Untersuchung des dynamischen aeroelastischen Stabilitätsverhaltens von Flugzeugen erfordert sehr komplexe Rechenmodelle, welche die wesentlichen elastomechanischen und instationären aerodynamischen Eigenschaften der Konstruktion wiedergeben sollen. Bei der Modellbildung müssen einerseits Vereinfachungen und Idealisierungen im Rahmen der Anwendung der Finite Elemente Methode und der aerodynamischen Theorie vorgenommen werden, deren Auswirkungen auf das Simulationsergebnis zu bewerten sind. Andererseits können die strukturdynamischen Kenngrößen durch den Standschwingungsversuch identifiziert werden, wobei die Ergebnisse Messungenauigkeiten enthalten. Für eine robuste Flatteruntersuchung müssen die identifizierten Unwägbarkeiten in allen Prozessschritten über die Festlegung von unteren und oberen Schranken konservativ ermittelt werden, um für alle Flugzustände eine ausreichende Flatterstabilität sicherzustellen. Zu diesem Zweck wird in der vorliegenden Arbeit ein Rechenverfahren entwickelt, welches die klassische Flatteranalyse mit den Methoden der Fuzzy- und Intervallarithmetik verbindet. Dabei werden die Flatterbewegungsgleichungen als parameterabhängiges nichtlineares Eigenwertproblem formuliert. Die Änderung der komplexen Eigenlösung infolge eines veränderlichen Einflussparameters wird mit der Methode der numerischen Fortsetzung ausgehend von der nominalen Startlösung verfolgt. Ein modifizierter Newton-Iterations-Algorithmus kommt zur Anwendung. Als Ergebnis liegen die berechneten aeroelastischen Dämpfungs- und Frequenzverläufe in Abhängigkeit von der Fluggeschwindigkeit mit Unschärfebändern vor.

Systems of Parallel Communicating Restarting Automata

In der vorliegenden Dissertation werden Systeme von parallel arbeitenden und miteinander kommunizierenden Restart-Automaten (engl.: systems of parallel communicating restarting automata; abgekürzt PCRA-Systeme) vorgestellt und untersucht. Dabei werden zwei bekannte Konzepte aus den Bereichen Formale Sprachen und Automatentheorie miteinander vescrknüpft: das Modell der Restart-Automaten und die sogenannten PC-Systeme (systems of parallel communicating components). Ein PCRA-System besteht aus endlich vielen Restart-Automaten, welche einerseits parallel und unabhängig voneinander lokale Berechnungen durchführen und andererseits miteinander kommunizieren dürfen. Die Kommunikation erfolgt dabei durch ein festgelegtes Kommunikationsprotokoll, das mithilfe von speziellen Kommunikationszuständen realisiert wird. Ein wesentliches Merkmal hinsichtlich der Kommunikationsstruktur in Systemen von miteinander kooperierenden Komponenten ist, ob die Kommunikation zentralisiert oder nichtzentralisiert erfolgt. Während in einer nichtzentralisierten Kommunikationsstruktur jede Komponente mit jeder anderen Komponente kommunizieren darf, findet jegliche Kommunikation innerhalb einer zentralisierten Kommunikationsstruktur ausschließlich mit einer ausgewählten Master-Komponente statt. Eines der wichtigsten Resultate dieser Arbeit zeigt, dass zentralisierte Systeme und nichtzentralisierte Systeme die gleiche Berechnungsstärke besitzen (das ist im Allgemeinen bei PC-Systemen nicht so). Darüber hinaus bewirkt auch die Verwendung von Multicast- oder Broadcast-Kommunikationsansätzen neben Punkt-zu-Punkt-Kommunikationen keine Erhöhung der Berechnungsstärke. Desweiteren wird die Ausdrucksstärke von PCRA-Systemen untersucht und mit der von PC-Systemen von endlichen Automaten und mit der von Mehrkopfautomaten verglichen. PC-Systeme von endlichen Automaten besitzen bekanntermaßen die gleiche Ausdrucksstärke wie Einwegmehrkopfautomaten und bilden eine untere Schranke für die Ausdrucksstärke von PCRA-Systemen mit Einwegkomponenten. Tatsächlich sind PCRA-Systeme auch dann stärker als PC-Systeme von endlichen Automaten, wenn die Komponenten für sich genommen die gleiche Ausdrucksstärke besitzen, also die regulären Sprachen charakterisieren. Für PCRA-Systeme mit Zweiwegekomponenten werden als untere Schranke die Sprachklassen der Zweiwegemehrkopfautomaten im deterministischen und im nichtdeterministischen Fall gezeigt, welche wiederum den bekannten Komplexitätsklassen L (deterministisch logarithmischer Platz) und NL (nichtdeterministisch logarithmischer Platz) entsprechen. Als obere Schranke wird die Klasse der kontextsensitiven Sprachen gezeigt. Außerdem werden Erweiterungen von Restart-Automaten betrachtet (nonforgetting-Eigenschaft, shrinking-Eigenschaft), welche bei einzelnen Komponenten eine Erhöhung der Berechnungsstärke bewirken, in Systemen jedoch deren Stärke nicht erhöhen. Die von PCRA-Systemen charakterisierten Sprachklassen sind unter diversen Sprachoperationen abgeschlossen und einige Sprachklassen sind sogar abstrakte Sprachfamilien (sogenannte AFL's). Abschließend werden für PCRA-Systeme spezifische Probleme auf ihre Entscheidbarkeit hin untersucht. Es wird gezeigt, dass Leerheit, Universalität, Inklusion, Gleichheit und Endlichkeit bereits für Systeme mit zwei Restart-Automaten des schwächsten Typs nicht semientscheidbar sind. Für das Wortproblem wird gezeigt, dass es im deterministischen Fall in quadratischer Zeit und im nichtdeterministischen Fall in exponentieller Zeit entscheidbar ist.

Time Discretization of the SST-generalized Navier-Stokes Equations: Positive and Negative Results

In the theory of the Navier-Stokes equations, the proofs of some basic known results, like for example the uniqueness of solutions to the stationary Navier-Stokes equations under smallness assumptions on the data or the stability of certain time discretization schemes, actually only use a small range of properties and are therefore valid in a more general context. This observation leads us to introduce the concept of SST spaces, a generalization of the functional setting for the Navier-Stokes equations. It allows us to prove (by means of counterexamples) that several uniqueness and stability conjectures that are still open in the case of the Navier-Stokes equations have a negative answer in the larger class of SST spaces, thereby showing that proof strategies used for a number of classical results are not sufficient to affirmatively answer these open questions. More precisely, in the larger class of SST spaces, non-uniqueness phenomena can be observed for the implicit Euler scheme, for two nonlinear versions of the Crank-Nicolson scheme, for the fractional step theta scheme, and for the SST-generalized stationary Navier-Stokes equations. As far as stability is concerned, a linear version of the Euler scheme, a nonlinear version of the Crank-Nicolson scheme, and the fractional step theta scheme turn out to be non-stable in the class of SST spaces. The positive results established in this thesis include the generalization of classical uniqueness and stability results to SST spaces, the uniqueness of solutions (under smallness assumptions) to two nonlinear versions of the Euler scheme, two nonlinear versions of the Crank-Nicolson scheme, and the fractional step theta scheme for general SST spaces, the second order convergence of a version of the Crank-Nicolson scheme, and a new proof of the first order convergence of the implicit Euler scheme for the Navier-Stokes equations. For each convergence result, we provide conditions on the data that guarantee the existence of nonstationary solutions satisfying the regularity assumptions needed for the corresponding convergence theorem. In the case of the Crank-Nicolson scheme, this involves a compatibility condition at the corner of the space-time cylinder, which can be satisfied via a suitable prescription of the initial acceleration.

Schauder – Zur Dekonstruktion eines Spürens

Zusammenfassung: Ziel der Arbeit ist den Sinn von Schauder philosophisch zu erhellen. An einem Einzelphänomen, wie es so bisher nicht behandelt wurde, wird zugleich das Geflecht von Affekt/Emotion/Gefühl, gestützt auf Hegel, Heidegger, Husserl, Freud und Lacan, in immer neuen Ansätzen kritisch reflektiert und Zug um Zug mit Derrida dekonstruiert. In einem Textverfahren, das sich auch grafisch durch gegenübergestellte Kolumnen auszeichnet, werden heterogene Ansätze zum Sinn von Schauder mit dekonstruktivistischen Einsichten konfrontiert. Die Ansätze, Schauder über Datum, Begriff, Phänomen oder Strukturelement bestimmen zu wollen, durchdringen sich dabei mit denjenigen, die sich einer solchen Bestimmung entziehen (Hegels Negativität, Heideggers Seinsentzug oder Lacans Signifikantenmangel). Am Fokus Schauder, an dem sich das Fiktive einer mit sich selbst identischen Präsenz besonders eindringlich darstellt, werden so spezifische Aporien der Metaphysik der Präsenz entfaltet und die Geschlossenheit logozentristischer Systeme in die Bewegung einer anderen Öffnung und Schließung im Sinn der Schrift bzw. des allgemeinen Textes transformiert. Neben der différance, dem Entzug der Metapher, dem Supplement und dem Gespenstischen stützt sich die Arbeit auf die Iterabilität, bei der im selben Zug die Identität des Sinns gestiftet und zerstreut wird (Dissemination). Im Kapitel Piloerection werden Ambivalenzen und Paradoxien des Schauders am Beispiel von computergestützten empirisch-psychologischen Studien aufgezeigt. Im Kapitel Atopologie des Schauders prädikative, propositionale und topologische Bedingungen zum Sinn von Schauder analysiert und dekonstruiert. Ebenso, im Folgekapitel Etymon, etymologische und technisch-mediale Bedingungen. Im Schlußkapitel Maß, Anmaß, Unmaß der Empfindung des Schauders wird am Beispiel der konkreten Beiträge zum Schauder von Aristoteles, Kant, Fechner, Otto, Klages, Lorenz und Adorno aufgezeigt, dass (1) ein Schauder nicht von einem Außen aus an-gemessen werden kann, (2) sich im Schauder die metaphysische Opposition von Fiktion und Realität in einer Unentscheidbarkeit zerstreut, (3) dass trotz der Heterogenität der Ansätze in diesen Beiträgen eine Komplizenschaft zum Ausdruck kommt: ein Begehren nach Präsenz, das durch den Ausschluß des Anderen zugleich die Gewalt des Einen produziert, (4) dass der Signifikant Schauder, der selbst in Abwesenheit eines Referenten, eines bestimmten Signifikats, einer aktuellen Bedeutungs­intention, eines Sen­ders oder Empfängers funktioniert, als verändertes Zu­rückbleiben eines differenzieller Zeichens betrachtet werden muss, als Effekt von Spuren, die sich nur in ihrem eige­nen Auslöschen ereignen. Die Arbeit schließt mit dem Vorschlag, Spüren jenseits von Arché, Telos oder Eschaton, jenseits eines Phallogozentrismus in der derridaschen Spur zu denken. Nicht zuletzt über diese Pfropfung, wie sie im Französischen [trace] so nicht möglich ist, schließt sie als deutschsprachiger Beitrag an sein Werk an.

Modeling, Estimation, and Control of Robot-Soil Interactions

This thesis presents the development of hardware, theory, and experimental methods to enable a robotic manipulator arm to interact with soils and estimate soil properties from interaction forces. Unlike the majority of robotic systems interacting with soil, our objective is parameter estimation, not excavation. To this end, we design our manipulator with a flat plate for easy modeling of interactions. By using a flat plate, we take advantage of the wealth of research on the similar problem of earth pressure on retaining walls. There are a number of existing earth pressure models. These models typically provide estimates of force which are in uncertain relation to the true force. A recent technique, known as numerical limit analysis, provides upper and lower bounds on the true force. Predictions from the numerical limit analysis technique are shown to be in good agreement with other accepted models. Experimental methods for plate insertion, soil-tool interface friction estimation, and control of applied forces on the soil are presented. In addition, a novel graphical technique for inverting the soil models is developed, which is an improvement over standard nonlinear optimization. This graphical technique utilizes the uncertainties associated with each set of force measurements to obtain all possible parameters which could have produced the measured forces. The system is tested on three cohesionless soils, two in a loose state and one in a loose and dense state. The results are compared with friction angles obtained from direct shear tests. The results highlight a number of key points. Common assumptions are made in soil modeling. Most notably, the Mohr-Coulomb failure law and perfectly plastic behavior. In the direct shear tests, a marked dependence of friction angle on the normal stress at low stresses is found. This has ramifications for any study of friction done at low stresses. In addition, gradual failures are often observed for vertical tools and tools inclined away from the direction of motion. After accounting for the change in friction angle at low stresses, the results show good agreement with the direct shear values.

Reinforcement Learning by Policy Search

One objective of artificial intelligence is to model the behavior of an intelligent agent interacting with its environment. The environment's transformations can be modeled as a Markov chain, whose state is partially observable to the agent and affected by its actions; such processes are known as partially observable Markov decision processes (POMDPs). While the environment's dynamics are assumed to obey certain rules, the agent does not know them and must learn. In this dissertation we focus on the agent's adaptation as captured by the reinforcement learning framework. This means learning a policy---a mapping of observations into actions---based on feedback from the environment. The learning can be viewed as browsing a set of policies while evaluating them by trial through interaction with the environment. The set of policies is constrained by the architecture of the agent's controller. POMDPs require a controller to have a memory. We investigate controllers with memory, including controllers with external memory, finite state controllers and distributed controllers for multi-agent systems. For these various controllers we work out the details of the algorithms which learn by ascending the gradient of expected cumulative reinforcement. Building on statistical learning theory and experiment design theory, a policy evaluation algorithm is developed for the case of experience re-use. We address the question of sufficient experience for uniform convergence of policy evaluation and obtain sample complexity bounds for various estimators. Finally, we demonstrate the performance of the proposed algorithms on several domains, the most complex of which is simulated adaptive packet routing in a telecommunication network.