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Thesis (M.S.)--Oregon State University, 2004. / Typescript (photocopy). Includes bibliographical references (leaves 77-79). Also available on the World Wide Web.

The shape of drift function in continuous time interest rate models has been investigated by many authors during the past decade. The main concerns have been whether the drift function is linear or nonlinear, but no convincing conclusions have been seen. In this dissertation, we investigate the reason for this problem and test several models of the drift function using a nonparametric test. Furthermore, we study some related problems, including the empirical properties of the nonparametric test. First, we propose regression models for the estimation of the drift function in some continuous time models. The limiting distribution of the parameter estimator in the proposed regression model is derived under certain conditions. Based on our analyses, we conclude that the effect of drift function for some U.S. Treasury Bill yields data is negligible. Therefore, neither linear nor nonlinear modeling has a significant effect. Second, parametric linear and nonlinear proposed regression models are applied and the correctness of those models is examined using the consistent nonparametric model specification test introduced by Li (1994) and Zheng (1996), henceforth the Jn test. The test results indicate that there is no strong statistical evidence against the assumed drift models. Furthermore, the constant drift model is not rejected either. Third, we compare the Jn and generalized likelihood ratio (GLR) tests through Monte Carlo simulation studies concerning whether the sizes of tests are stable over a range of bandwidth values, which is an important indicator to measure the usefulness of nonparametric tests. The GLR test was applied to testing the linear drift function in continuous time models by Fan and Zhang (2003). Our simulation study shows that the GLR test does not provide stable sizes over a grid of bandwidth values in testing the drift function of some continuous time models, whereas the Jn test usually does.

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Software radio architecture can support multiple standards by performing analogto- digital (A/D) conversion of the radio frequency (RF) signals and running reconfigurable software programs on the backend digital signal processor (DSP). A slight variation of this architecture is the software defined radio architecture in which the A/D conversion is performed on intermediate frequency (IF) signals after a single down conversion. The first part of this research deals with the design and implementation of a fourth order continuous time bandpass sigma-delta (CT BP) C based on LC filters for direct RF digitization at 950 MHz with a clock frequency of 3.8 GHz. A new ADC architecture is proposed which uses only non-return to zero feedback digital to analog converter pulses to mitigate problems associated with clock jitter. The architecture also has full control over tuning of the coefficients of the noise transfer function for obtaining the best signal to noise ratio (SNR) performance. The operation of the architecture is examined in detail and extra design parameters are introduced to ensure robust operation of the ADC. Measurement results of the ADC, implemented in IBM 0.25 µm SiGe BiCMOS technology, show SNR of 63 dB and 59 dB in signal bandwidths of 200 kHz and 1 MHz, respectively, around 950 MHz while consuming 75 mW of power from ± 1.25 V supply. The second part of this research deals with the design of a fourth order CT BP ADC based on gm-C integrators with an automatic digital tuning scheme for IF digitization at 125 MHz and a clock frequency of 500 MHz. A linearized CMOS OTA architecture combines both cross coupling and source degeneration in order to obtain good IM3 performance. A system level digital tuning scheme is proposed to tune the ADC performance over process, voltage and temperature variations. The output bit stream of the ADC is captured using an external DSP, where a software tuning algorithm tunes the ADC parameters for best SNR performance. The IF ADC was designed in TSMC 0.35 µm CMOS technology and it consumes 152 mW of power from ± 1.65 V supply.

In this thesis, a simple on-chip automatic frequency tuning circuit is presented. The tuning circuit is improved from voltage-controlled filter (VCF) frequency tuning circuit. We use a single time constant (STC) circuit to substitute the voltage-controlled filter. The STC circuit can produce a controllable delay time clock. The tuning circuit uses the constant delay time to tune the frequency of the filter. The design of a STC circuit is easy. Because the circuit is simple, the tuning circuit has less chip area and less power consumption. The circuit has been fabricated with 0.35£gm CMOS technology. It operates with supply voltages ¡Ó1.5 V. The filter operates at a 3-dB frequency of 10MHz. In simulation, the frequency tuning circuit has a 3-dB frequency tuning error of less than 12% and the power consumption less than 9.05mW over a range of supply voltages (¡Ó10%), operating temperatures (-20¢J to 70¢J) and five models of SPICE model.

A thorough review of the literature on the model reduction of linear, time-invariant, dynamical systems in both the frequency and time domains is presented. Particular attention is paid to the least-squares extension of the classical method of Padé approximation. An account is given of the development of apparently different approaches of least-squares parameter- matching Padé model reduction applied to continuous-time and discrete-time systems. These approaches are shown to be related via a unifying theory. From the formulation it is possible to show several interesting features of the least-squares approach which lead to a fuller understanding of exactly how the reduced model approximates the full system. An error index is derived in the general continuous-time case and it is shown that a range of system parameter preservation options are available. Using the theory developed in the continuous-time case a non-uniqueness property of the method is proven. An ‘optimal’ least-squares method based on the approach and the introduction of weighting for the system parameters are both investigated. The unifying theory is extended to the discrete-time case where an important new stability preservation property is proved and is shown to provide the basis for a new least- squares Padé method. This method uses transformations between the z- and 5-planes to guarantee stable reduced order models approximating stable high order continuous-time systems. The application of least-squares Padé approximation is further extended to the multivariable case with particular attention given to the factors affecting the levels of order reduction achieved. Appropriate numerical examples are used to illustrate the main points of the thesis and graphs of the impulse and step responses are used throughout to visually highlight the accuracy of approximation.

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Orientador: Edvaldo Assunção / Banca: Marcelo Carvalho Minhoto Teixeira / Banca: Alfredo Del Sole Lordelo / Resumo: Uma técnica de projeto de controladores robustos para sistemas não-lineares contínuos no tempo é proposta neste trabalho. É suposto que a planta não-linear está sujeita a falhas estruturais, que podem ser consideradas como incertezas politópicas. Os sistemas não-lineares são representados por modelos fuzzy propostos por Takagi-Sugeno e uma formulação para o tratamento das incertezas politópicas é apresentado para o projeto dos controladores. Este trabalho aborda projetos de controle usando a realimentação dos estados e a realimentação da derivada dos estados. O projeto do controlador é realizado através de condições baseadas em Desigualdades Matriciais Lineares (em inglês, Linear Matrix Inequalities (LMI)), que podem ser resolvidas facilmente utilizando técnicas de programação convexa. Essa metodologia permite a inclusão de restrições de desempenho no projeto, tais como: taxa de decaimento e restrição na entrada. Ao final, exemplos numéricos e suas simulações ilustram a eficiência da técnica proposta. / Abstract: A technique of robust controllers design for nonlinear continuous-time systems is proposed in this work. It is supposed that the nonlinear plant is subject to structural failures, which can be considered as polytope uncertainties. The nonlinear systems are represented through fuzzy models proposed by Takagi-Sugeno and a formulation for the treatment of polytope uncertain is presented for the controllers design. This work focuses control designs using state feedback and state-derivative feedback. The controllers design is made through conditions based in Linear Matrix Inequalities (LMIs), which can be easily solved using convex programming techniques. This methodology allows the inclusion of performance restrictions on design, such as: decay rate and input constraint. Finally, numeric examples and their simulations show the efficiency of the proposed method. / Mestre