Rational Function Interpolation of Electromagnetic Transfer Functions of High-Speed Interconnect Systems from Discrete Time-Domain and Frequency-Domain Data

We present new methodologies to generate rational function approximations of broadband electromagnetic responses of linear and passive networks of high-speed interconnects, and to construct SPICE-compatible, equivalent circuit representations of the generated rational functions. These new methodologies are driven by the desire to improve the computational efficiency of the rational function fitting process, and to ensure enhanced accuracy of the generated rational function interpolation and its equivalent circuit representation. Toward this goal, we propose two new methodologies for rational function approximation of high-speed interconnect network responses. The first one relies on the use of both time-domain and frequency-domain data, obtained either through measurement or numerical simulation, to generate a rational function representation that extrapolates the input, early-time transient response data to late-time response while at the same time providing a means to both interpolate and extrapolate the used frequency-domain data. The aforementioned hybrid methodology can be considered as a generalization of the frequency-domain rational function fitting utilizing frequency-domain response data only, and the time-domain rational function fitting utilizing transient response data only. In this context, a guideline is proposed for estimating the order of the rational function approximation from transient data. The availability of such an estimate expedites the time-domain rational function fitting process. The second approach relies on the extraction of the delay associated with causal electromagnetic responses of interconnect systems to provide for a more stable rational function process utilizing a lower-order rational function interpolation. A distinctive feature of the proposed methodology is its utilization of scattering parameters. For both methodologies, the approach of fitting the electromagnetic network matrix one element at a time is applied. It is shown that, with regard to the computational cost of the rational function fitting process, such an element-by-element rational function fitting is more advantageous than full matrix fitting for systems with a large number of ports. Despite the disadvantage that different sets of poles are used in the rational function of different elements in the network matrix, such an approach provides for improved accuracy in the fitting of network matrices of systems characterized by both strongly coupled and weakly coupled ports. Finally, in order to provide a means for enforcing passivity in the adopted element-by-element rational function fitting approach, the methodology for passivity enforcement via quadratic programming is modified appropriately for this purpose and demonstrated in the context of element-by-element rational function fitting of the admittance matrix of an electromagnetic multiport.

Formal and philological inquiries into the nature of interrogatives, indefinites, disjunction, and focus in Sinhala and other languages

In this thesis I examine a variety of linguistic elements which involve ``alternative'' semantic values---a class arguably including focus, interrogatives, indefinites, and disjunctions---and the connections between these elements. This study focusses on the analysis of such elements in Sinhala, with comparison to Malayalam, Tlingit, and Japanese. The central part of the study concerns the proper syntactic and semantic analysis of Q[uestion]-particles (including Sinhala "da", Malayalam "-oo", Japanese "ka"), which, in many languages, appear not only in interrogatives, but also in the formation of indefinites, disjunctions, and relative clauses. This set of contexts is syntactically-heterogeneous, and so syntax does not offer an explanation for the appearance of Q-particles in this particular set of environments. I propose that these contexts can be united in terms of semantics, as all involving some element which denotes a set of ``alternatives''. Both wh-words and disjunctions can be analysed as creating Hamblin-type sets of ``alternatives''. Q-particles can be treated as uniformly denoting variables over choice functions which apply to the aforementioned Hamblin-type sets, thus ``restoring'' the derivation to normal Montagovian semantics. The treatment of Q-particles as uniformly denoting variables over choice functions provides an explanation for why these particles appear in just this set of contexts: they all include an element with Hamblin-type semantics. However, we also find variation in the use of Q-particles; including, in some languages, the appearance of multiple morphologically-distinct Q-particles in different syntactic contexts. Such variation can be handled largely by positing that Q-particles may vary in their formal syntactic feature specifications, determining which syntactic contexts they are licensed in. The unified analysis of Q-particles as denoting variables over choice functions also raises various questions about the proper analysis of interrogatives, indefinites, and disjunctions, including issues concerning the nature of the semantics of wh-words and the syntactic structure of disjunction. As well, I observe that indefinites involving Q-particles have a crosslinguistic tendency to be epistemic indefinites, i.e. indefinites which explicitly signal ignorance of details regarding who or what satisfies the existential claim. I provide an account of such indefinites which draws on the analysis of Q-particles as variables over choice functions. These pragmatic ``signals of ignorance'' (which I argue to be presuppositions) also have a further role to play in determining the distribution of Q-particles in disjunctions. The final section of this study investigates the historical development of focus constructions and Q-particles in Sinhala. This diachronic study allows us not only to observe the origin and development of such elements, but also serves to delimit the range of possible synchronic analyses, thus providing us with further insights into the formal syntactic and semantic properties of Q-particles. This study highlights both the importance of considering various components of the grammar (e.g. syntax, semantics, pragmatics, morphology) and the use of philology in developing plausible formal analyses of complex linguistic phenomena such as the crosslinguistic distribution of Q-particles.