Interaction of additive and quantization noises in digital PLLs

Phase-locked loops (PLLs) are a crucial component in modern communications systems. Comprising of a phase-detector, linear filter, and controllable oscillator, they are widely used in radio receivers to retrieve the information content from remote signals. As such, they are capable of signal demodulation, phase and carrier recovery, frequency synthesis, and clock synchronization. Continuous-time PLLs are a mature area of study, and have been covered in the literature since the early classical work by Viterbi [1] in the 1950s. With the rise of computing in recent decades, discrete-time digital PLLs (DPLLs) are a more recent discipline; most of the literature published dates from the 1990s onwards. Gardner [2] is a pioneer in this area. It is our aim in this work to address the difficulties encountered by Gardner [3] in his investigation of the DPLL output phase-jitter where additive noise to the input signal is combined with frequency quantization in the local oscillator. The model we use in our novel analysis of the system is also applicable to another of the cases looked at by Gardner, that is the DPLL with a delay element integrated in the loop. This gives us the opportunity to look at this system in more detail, our analysis providing some unique insights into the variance `dip' seen by Gardner in [3]. We initially provide background on the probability theory and stochastic processes. These branches of mathematics are the basis for the study of noisy analogue and digital PLLs. We give an overview of the classical analogue PLL theory as well as the background on both the digital PLL and circle map, referencing the model proposed by Teplinsky et al. [4, 5]. For our novel work, the case of the combined frequency quantization and noisy input from [3] is investigated first numerically, and then analytically as a Markov chain via its Chapman-Kolmogorov equation. The resulting delay equation for the steady-state jitter distribution is treated using two separate asymptotic analyses to obtain approximate solutions. It is shown how the variance obtained in each case matches well to the numerical results. Other properties of the output jitter, such as the mean, are also investigated. In this way, we arrive at a more complete understanding of the interaction between quantization and input noise in the first order DPLL than is possible using simulation alone. We also do an asymptotic analysis of a particular case of the noisy first-order DPLL with delay, previously investigated by Gardner [3]. We show a unique feature of the simulation results, namely the variance `dip' seen for certain levels of input noise, is explained by this analysis. Finally, we look at the second-order DPLL with additive noise, using numerical simulations to see the effects of low levels of noise on the limit cycles. We show how these effects are similar to those seen in the noise-free loop with non-zero initial conditions.

State building as strategy: An interrogation of NATO's comprehensive approach in Afghanistan between 2006 and 2011

The core of this thesis is the study of NATO’s Comprehensive Approach strategy to state building in Afghanistan between 2006 and 2011. It argues that this strategy sustained operational and tactical practices which were ineffective in responding to the evolved nature of the security problem. The thesis interrogates the Comprehensive Approach along ontological, empirical and epistemological lines and concludes that the failure of the Comprehensive Approach in the specific Afghan case is, in fact, indicative of underlying theoretical and pragmatic flaws which, therefore, generalize the dilemma. The research is pragmatic in nature, employing mixed methods (quantitative and qualitative) concurrently. Qualitative methods include research into primary and secondary literature sources supplemented with the author’s personal experiences in Afghanistan in 2008 and various NATO HQ and Canadian settings. Quantitative research includes an empirical case study focussing on NATO’s Afghan experience and its attempt at state building between 2006 and 2011. This study incorporates a historical review of NATO’s evolutionary involvement in Afghanistan incorporating the subject timeframe; offers an analysis of human development and governance related data mapped to expected outcomes of the Afghan National Development Strategy and NATO’s comprehensive campaign design; and interrogates the Comprehensive Approach strategy by means of an analysis of conceptual, institutional and capability gaps in the context of an integrated investigational framework. The results of the case study leads to an investigation of a series of research questions related to the potential impact of the failure of the Comprehensive Approach for NATO in Afghanistan and the limits of state building as a means of attaining security for the Alliance.

The political philosophy of Miki Kiyoshi: A close reading of the philosophical foundations of cooperative communitarianism

The thesis is a historical and philological study of the mature political theory of Miki Kiyoshi (1897-1945) focused on Philosophical Foundations of Cooperative Communitarianism (1939), a full translation of which is included. As the name suggests, it was a methodological and normative communitarianism, which critically built on liberalism, Marxism and Confucianism to realise a regional political community. Some of Miki’s Western readers have wrongly considered him a fascist ideologue, while he has been considered a humanist Marxist in Japan. A closer reading cannot support either view. The thesis argues that the Anglophone study of Japanese philosophy is a degenerating research programme ripe for revolution in the sense of returning full circle to an original point. That means returning to the texts, reading them contextually and philologically, in principle as early modern European political theory is read by intellectual historians, such as the representatives of Cambridge School history of political thought. The resulting reading builds critically on the Japanese scholarship and relates it to contemporary Western and postcolonial political theory and the East Asian tradition, particularly neo-Confucianism. The thesis argues for a Cambridge School perspective radicalised by the critical addendum of geo-cultural context, supplemented by Geertzian intercultural hermeneutics and a Saidian ‘return to philology’. As against those who have seen radical reorientations in Miki’s political thought, the thesis finds gradual progression and continuity between his neo-Kantian, existentialist, Marxian anthropology, Hegelian and finally communitarian phases. The theoretical underpinnings are his philosophical anthropology, a structurationist social theory of praxis, and a critique of liberalism, Marxism, nationalism and idealism emphasising concrete as opposed to abstract theory and the need to build on existing cultural traditions to modernise rather than westernise East Asia. This post-Western fusion was imagined to be the beginning of a true and pluralistic universalism.

Action design research: a comparison with canonical action research and design science

This research in progress paper addresses the IS issue in relation to conducting relevant research while keeping academic rigor. In particular, it contributes to the ongoing academic conversation around the investigation on how to incor-porate action in design science research. In this document the philosophical underpinnings of the recently proposed methodology called Action Design Re-search [1] are derived, outlined and integrated into Burrel and Morgan’s Par-adigmatic Framework (1979)[6]. The results so far show how Action Design Research can be considered as a particular case of Design Science Research (rather than a methodology closely related to Action Research) although they can assume two different epistemological positions. From these philosophical perspectives, future works will involve the inclusion of actual research projects using the three different methodologies. The final goal is to outline and structure the divergences and similarities of Action Design Research with Design Science Research and Canonical Action Research.

Textual criticism and medieval Irish studies

Many textual scholars will be aware that the title of the present thesis has been composed in a conscious revisionary relation to Tim William Machan’s influential Textual Criticism and Middle English Texts. (Tim William Machan, Textual Criticism and Middle English Texts (Charlottesville, 1994)). The primary subjects of Machan’s study are works written in English between the fourteenth and sixteenth centuries, the latter part of the period conventionally labelled Middle English. In contrast, the works with which I am primarily concerned are those written by scholars of Old and Middle Irish in the nineteenth, twentieth and twenty-first centuries. Where Machan aims to articulate the textual and cultural factors that characterise Middle English works as Middle English, the purposes of this thesis are (a) to identify the underlying ideological and epistemological perspectives which have informed much of the way in which medieval Irish documents and texts are rendered into modern editions, and (b) to begin to place the editorial theory and methodology of medieval Irish studies within the broader context of Biblical, medieval and modern textual criticism. Hence, the title is Textual Criticism and Medieval Irish Studies, rather than Textual Criticism and Medieval Irish Texts