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.

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.

A cultural study on communication and technology with specific reference to media in China

This dissertation examines the role of communications technology in social change. It examines secondary data on contemporary China arguing that many interpretations of events in China are unsuitable at best and at worst conceptually damages our understanding of social change in China. This is especially the case in media studies under the ‘democratic framework’. It proposes that there is an alternative framework in studying the media and social change. This alternative conceptual framework is termed a zone of interpretative development offering a means by which to discuss events that take place in a mediated environment. Taking a theoretical foundation using the philosophy of Mikhail Bakhtin this dissertation develops a platform with which to understand communication technology from an anthropological perspective. Three media events from contemporary China are examined. The first examines the Democracy Wall event and the implications of using a public sphere framework. The second case examines the phenomenon of the Grass Mud Horse, a symbol that has gained popular purchase as a humorous expression of political dissatisfaction and develops the problems seen in the first case but with some solutions. Using a modification of Lev Vygotskiĭ’s zone of proximal development this symbol is understood as an expression of the collective recognition of a shared experience. In the second example from the popular TV talent show contests in China further expressions of collective experience are introduced. With the evidence from these media events in contemporary China this dissertation proposes that we can understand certain modes of communication as occurring in a zone of interpretative development. This proposed anthropological feature of social change via communication and technology can fruitfully describe meaning-formation in society via the expression and recognition of shared experiences.