Methods for the transfer function design of multiple narrow-band bandpass sigma-delta modulators

This paper presents the design analysis of novel tunable narrow-band bandpass sigma-delta modulators, which can achieve concurrent multiple noise-shaping for multi-tone input signals. Four different design methodologies based on the noise transfer functions of comb filters, slink filters, multi-notch filters and fractional delay comb filters are applied for the design of these multiple-band sigma-delta modulators. The latter approach utilises conventional comb filters in conjunction with FIR, or allpass IIR fractional delay filters, to deliver the desired nulls for the quantisation noise transfer function. Detailed simulation results show that FIR fractional delay comb filter-based sigma-delta modulators tune accurately to most centre frequencies, but suffer from degraded resolution at frequencies close to Nyquist. However, superior accuracies are obtained from their allpass IIR fractional delay counterpart at the expense of a slight shift in noise-shaping bands at very high frequencies. The merits and drawbacks of each technique for the various sigma-delta topologies are assessed in terms of in-band signal-to-noise ratios, accuracy of tunability and coefficient complexity for ease of implementation.

Supporting the learning and networking experiences of doctoral students

This study explores the impact of a Graduate Virtual Research Environment (GVRE) on the learning and networking experiences of research students. The GVRE was established to support and enhance research skills and employability training across a university. It provides an extensive range of resources including video reflections based on the experiences of students and staff; GVRE members are encouraged to comment and engage in discussions on these resources. Our work is framed using social theories of learning and the role of communities in the support and development of research students. In particular, we are interested in exploring the challenges involved in developing communities and networks for students whose main focus is their individual research. The GVRE was made available to over 600 students and in this research we explore its impact on the experiences of research students. In particular, we investigate four questions: (a) what impact does the students use of the GVRE have on the development of their research skills; (b) what impact does membership of the GVRE have on the networks and communities of research students; (c) how do research students view the relationships between their research skills training programme, their individual research and the GVRE; and (d) how do research students currently use social media. We use an interpretivist approach and our data sources include site statistics, responses to a questionnaire and also feedback from a focus group. Our findings indicate that networking remains an issue and students suggested approaches to facilitating this using the GVRE: (1) A clearer pathway from skills need identification to skills acquisition; (2) Rewards for activities around networking - possibly through credit on the training scheme; (3) Activities that would involve research directly. Feedback on the GVRE indicated that it is valued by research students as it facilitates the development of their research skills. In terms of marketing the GVRE to research students important factors identified were: the ease of access to the site, the overview it gives of the PhD process; and the value of the site to students around the defining moments of their studies when the students felt they needed additional advice and guidance.

Default Invariance: Naïve Category of Law and Finance

Default invariance is the idea that default does not change at any scale of law and finance. Default is a conserved quantity in a universe where fundamental principles of law and finance operate. It exists at the micro-level as part of the fundamental structure of every financial transaction, and at the macro- level, as a fixed critical point within the relatively stable phases of the law and finance cycle. A key point is that default is equivalent to maximizing uncertainty at the micro-level and at the macro-level, is equivalent to the phase transition where unbearable fluctuations occur in all forms of risk transformation, including maturity, liquidity and credit. As such, default invariance is the glue that links the micro and macro structures of law and finance. In this essay, we apply naïve category theory (NCT), a type of mapping logic, to these types of phenomena. The purpose of using NCT is to introduce a rigorous (but simple) mathematical methodology to law and finance discourse and to show that these types of structural considerations are of prime practical importance and significance to law and finance practitioners. These mappings imply a number of novel areas of investigation. From the micro- structure, three macro-approximations are implied. These approximations form the core analytical framework which we will use to examine the phenomena and hypothesize rules governing law and finance. Our observations from these approximations are grouped into five findings. While the entirety of the five findings can be encapsulated by the three approximations, since the intended audience of this paper is the non-specialist in law, finance and category theory, for ease of access we will illustrate the use of the mappings with relatively common concepts drawn from law and finance, focusing especially on financial contracts, derivatives, Shadow Banking, credit rating agencies and credit crises.