Over the past two decades there has been substantial growth in speech communications and new speech related applications. Bandwidth constraints led researchers to investigate ways of compressing speech signals whilst maintaining speech quality and intelligibility so as to increase the possible number of customers for the given bandwidth. Because of this a variety of speech coding techniques have been proposed over this period. At the heart of any proposed speech coding method is quantisation of the speech production model parameters that need to be transmitted to the decoder. Quantisation is a controlling factor for the targeted bit rates and for meeting quality requirements. The objectives of the research presented in this thesis are twofold. The first enabling the development of a very low bit rate speech coder which maintains quality and intelligibility. This includes increasing the robustness to various operating conditions as well as enhancing the estimation and improving the quantisation of speech model parameters. The second objective is to provide a method for enhancing the performance of an existing speech related application. The first objective is tackled with the aid of three techniques. Firstly, various novel estimation techniques are proposed which are such that the resultant estimated speech production model parameters have less redundant information and are highly correlated. This leads to easier quantisation (due to higher correlation) and therefore to bit saving. The second approach is to make use of the joint effect of the quantisation of spectral parameters (i.e. LSF and spectral amplitudes) for their big impact on the overall bit allocation required. Work towards the first objective also includes a third technique which enhances the estimation of a speech model parameter (i.e. the pitch) through a robust statistics-based post-processing (or tracking) method which operates in noise contaminated environments. Work towards the second objective focuses on an application where speech plays an important role, namely echo-canceller and noise-suppressor systems. A novel echo-canceller method is proposed which resolves most of the weaknesses present in existing echo-canceller systems and improves the system performance.

The aim of this thesis is to investigate of bootstrap methods (Efron, 1979), in the the performance estimation of parameter estimates in non-linear time series models, in particular SETAR models (Tong, 1993). First and higher order SETAR models in known and unknown thresholds cases are considered. To assess the performance of bootstrap methods, we first give an extensive simulation study (by using simulated normal errors), in chapters 3 and 4, to investigate large and small sample behaviours of the true sampling distributions of parameter estimates of SETAR models and how they are affected by sample size. First and higher order SETAR models in the known and unknown threshold cases are considered. An introduction to the bootstrap methods (Efron, 1979 ) is given in chapter 5. The effect of sample size on the bootstrap distributions of parameter estimates of first and higher order SETAR models in the known and unknown threshold cases ( for given order, delay and number of thresholds ) are also investigated in this chapter, via simulation and by using the same models used in the simulated normal errors 'true distribution' case ( chapters 3 & 4). The results are compared with simulated normal case in order to assess the bootstrap results. Tong and Lim (1980) method is used for fitting SETAR models to bootstrap samples, which is also used in the initial fit. Moreover, applications of bootstrap to celebrated data sets, namely, the logarithmically transformed lynx data covering the period (182-1934); and the sunspot numbers covering the period (1700- 1920), are attempted. The cyclical behaviours of bootstrap models are also examined. Finally, in chapter 5, an attempt is also made to study the problem of non-linear properties of the skeleton of a non-linear autoregressive process (Jones, 1976) via simulation and we study in particular a limit cycle behaviour.

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The purpose of this thesis is to give a survey of the methods currently used to solve the numerical eigenvalue problem for real symmetric matrices. On the basis of the advantages and disadvantages inherent in the various methods, it is concluded that Householder's method is the best. Since the methods of Givens, Lanczos, and Householder use the Sturm sequence bisection algorithm as the final stage, a complete theoretical discussion of this process is included. Error bounds from a floating point error analysis (due to Ortega), for the Householder reduction are given. In addition, there is a complete error analysis for the bisection process. / Science, Faculty of / Mathematics, Department of / Graduate

The managements of integrated forest products firms in British Columbia and elsewhere must make many involved decisions in order to effectively plan the intermediate-range (one year) operations of their firms. The production systems of the forest industry involve complex allocations of many resources among competing activities. In addition, interdependencies between processes exist and frequently products are transferred between divisions. This thesis explains and illustrates how linear programming may be used to assist managements of integrated forest products firms in their planning activities. In particular, the linear programming technique is used to find suggested optimal operating plans for the total range of the firm's operations — from woodlands, through production plants to sales operations. The specific details of model construction, the mathematical programming, and the problems encountered are illustrated by a hypothetical forest products firm. A linear model has been developed for the hypothetical firm, computer solutions have been interpreted, and suggestions have been made for implementation of results. Although the author does not attempt to quantify the value of linear programming to a firm's profitability, the many explanations and illustrations serve to support the view that managerial effectiveness is enhanced through use of the technique. Decisions regarding intermediate-range planning can be made by managers with an increased understanding of the complex relationships within their firm's production and sales functions. In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and Study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. / Business, Sauder School of / Graduate

In this thesis we consider the group of fractional linear transformations of a variable x over an algebraically closed field k. The purpose of the thesis is to determine all finite subgroups of this group whose orders are not divisible by the characteristic of k. / Science, Faculty of / Mathematics, Department of / Graduate

Three graphical methods, similar to Popov's approach, are derived to test a stability criterion for a general class of multivariable nonlinear feedback systems. Various simplifications of these methods are then derived for four particular classes of system: the series system, the parallel system, the internal feedback system, and the symmetric system. These stability tests may be applied to active networks that consist of passive linear time-invariant elements and many nonlinear controlled sources. It is further shown that certain special network structures may be represented as one of the four particular classes of system. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Our subject matter consists of a survey of the major results concerning the topological space βN-N where N represents the space of natural numbers with the discrete topology, and βN the Stone-Čech compactification of N . We are mainly concerned with the results which were derived during the last ten years. When there is no advantage in restricting our work to the space N we work with an arbitrary discrete space X and finally formulate our results in terms of βN-N . In some cases, pre-1960 results concerning βN-N are obtained as special cases of the results we derive using an arbitrary discrete space X . The material presented is divided into four chapters. In Chapter I, we discuss certain subsets of βN-N which can be C*-embedded in other subsets of βN-N . This study leads to the conclusion that no proper dense subset of βN-N can be C*-embedded. In the second chapter we devise a general method of associating certain classes of points of βN-N with certain subalgebras of C(N) . The P-points of βN-N form one of these classes. The answer to R. S. Pierce's question, "Does there exist a point of βN-N which lies simultaneously in the closures of three pairwise disjoint open sets" is discussed in Chapter III. Finally in Chapter IV we present two proofs of the non-homogeneity of βN-N , without the use of the Continuum Hypothesis. / Science, Faculty of / Mathematics, Department of / Graduate

A combination of many grades of veneer may be jointly produced by peeling any one type of logs. This means that the plywood manufacturer can not really know the profit margins of the panels he produces. And for most of the manufacturers, the cost of the logs constitutes about 65% of the total cost of producing the plywood panels. Consequently, the manufacturer finds it very difficult to select his sales strategy and to price his panels. The plywood manufacturer also has opportunities to minimize his log cost and processing cost by selecting the right combination of logs to peel and using the right constructions in laying up the panels. Linear programming techniques are used in this study to provide an approach to the above mentioned problems for a selected plywood manufacturer. Through this, it is hoped as well to provide an examination of the way to use linear programming techniques and an evaluation of their usefulness as management tools in plywood manufacturing. A survey of the reported experience of some plywood manufacturers indicated that the use of L. P. had been instrumental in saving some hundreds of thousands of dollars per annum for some manufacturers. An L. P. model was constructed for the largest of the four mills of the Case Company, using the operating situations predicted for the year 1967. Such problems (and their solutions) as were encountered in defining, identifying and measuring the variable process costs and the need for making simplifying assumptions were examined. The L. P. model seeks to optimize the choice of panel output, the choice of log input and the choice of panel constructions simultaneously because these three decisions are interrelated and somewhat interdependent. The L. P. analysis suggests that about 30% of the dollar sales of the Case Mill in 1967 were made in unprofitable (thin) panels. Even after allowing for possible over estimation in measuring the variable processing cost, this may call for a thorough re-examination of the sales strategy and the panel pricing system. To produce the panel output selected for 1967, the best log combination apparently includes the use of a much higher proportion of Fir Peeler #2 and Sawlog #3, Interior Fir and Hemlock-Balsam Mix than was used by the Company in its mill. Also, the model suggests proportions of Fir Peeler #1, #4 and S. F.P. might be much lower than what the Company tended to use. These tentative findings may have significant implications for choosing log acquisition policies. The model suggests the choice in panel construction may be to peel Peeler logs for .104" high quality veneer, Interior Fir for .130" veneer and other low quality logs for .171" core veneer. It also suggests down-grading some veneer and using some subsidiary panel constructions so as to utilize fully the total supply of veneer from the logs peeled. The usefulness of the L.P. analysis is fully realized by making a comprehensive post-optimal analysis of the sensitivity of the optimality of the solution to various changes in the log supply and/or panel demand and/or processing cost situations. This analysis may enable the company to determine which of the operating factors seem crucial in determining the profitability of the panels and what may constitute the best log combination to use. From this, the manufacturer could possibly know when and how to adapt his program of operation in response to any future changes in (or any revision in the forecast of) the operating situation. This analysis is also helpful in gauging the importance of the assumptions made when constructing the model. No comprehensive sensitivity analysis was carried out in this study. However, recommendations regarding appropriate post-optimal analyses are presented. Lastly, the study concludes by presenting an L. P. model of possible use to analyze the four mills of the Company together, recognizing the possibilities of specialization and cooperation among the mills. / Business, Sauder School of / Graduate

A class of complete non-Archimedean pseudo-normed linear spaces for which the field of scalars has a trivial valuation is introduced; we call these spaces "V-spaces." V-spaces differ from the classical normed linear spaces in that the homogeneity of the norm is replaced by the requirement that llαxll = llxll for all x and all scalars α≠0; the usual triangle inequality is modified to [ Equation omitted ] and it is assumed that the norm of an element is either zero or is equal to ρⁿ for a fixed real ρ > 1 and some integer n. The concept of a "distinguished basis" in a V-space is defined. By use of a modified form of Riesz's Lemma, it is shown that every V-space admits a distinguished basis. Each element of a V-space then has a uniquely determined series expansion in terms of the elements of a given distinguished basis. An analogue of the Paley-Wiener Theorem is proved for distinguished bases. Properties of distinguished bases are exploited throughout this work. Linear and non-linear operators on V-spaces are also studied. In the usual way, a norm is defined under which the set of bounded operators is a V-space and the set of bounded linear operators is a "V-algebra." A characterization of bounded linear operators is given as well as theorems on spectral decompositions. Under certain assumptions on the expansions of x, y, A, the existence of solutions to equations of the form xz = y in V-algebras, and of the form Ax = y in arbitrary V-spaces is proved. Approximations of the solutions are obtained. A representation theorem for continuous linear functionals on a V-space is given. This representation uses an analogue of the classical inner product. Examples of V-spaces and V-algebras discussed include spaces of functions from a Hausdorff space to a normed linear space, on which the pseudo-norm characterizes the asymptotic behaviour of the functions. Some results of the theory of pure asymptotics are extended to arbitrary V-spaces. / Science, Faculty of / Mathematics, Department of / Graduate