Listing Unique Fractional Factorial Designs

Fractional factorial designs are a popular choice in designing experiments for studying the effects of multiple factors simultaneously. The first step in planning an experiment is the selection of an appropriate fractional factorial design. An appro- priate design is one that has the statistical properties of interest of the experimenter and has a small number of runs. This requires that a catalog of candidate designs be available (or be possible to generate) for searching for the "good" design. In the attempt to generate the catalog of candidate designs, the problem of design isomor- phism must be addressed. Two designs are isomorphic to each other if one can be obtained from the other by some relabeling of factor labels, level labels of each factor and reordering of runs. Clearly, two isomorphic designs are statistically equivalent. Design catalogs should therefore contain only designs unique up to isomorphism. There are two computational challenges in generating such catalogs. Firstly, testing two designs for isomorphism is computationally hard due to the large number of possible relabelings, and, secondly, the number of designs increases very rapidly with the number of factors and run-size, making it impractical to compare all designs for isomorphism. In this dissertation we present a new approach for tackling both these challenging problems. We propose graph models for representing designs and use this relationship to develop efficient algorithms. We provide a new efficient iso- morphism check by modeling the fractional factorial design isomorphism problem as graph isomorphism problem. For generating the design catalogs efficiently we extend a result in graph isomorphism literature to improve the existing sequential design catalog generation algorithm. The potential of the proposed methods is reflected in the results. For 2-level regular fractional factorial designs, we could generate complete design catalogs of run sizes up to 4096 runs, while the largest designs generated in literature are 512 run designs. Moreover, compared to the next best algorithms, the computation times for our algorithm are 98% lesser in most cases. Further, the generic nature of the algorithms makes them widely applicable to a large class of designs. We give details of graph models and prove the results for two classes of designs, namely, 2-level regular fractional factorial designs and 2-level regular fractional factorial split-plot designs, and provide discussions for extensions, with graph models, for more general classes of designs

A computer-aided design for digital filter implementation

Imperial Users onl

Perceptual models in speech quality assessment and coding

The ever-increasing demand for good communications/toll quality speech has created a renewed interest into the perceptual impact of rate compression. Two general areas are investigated in this work, namely speech quality assessment and speech coding. In the field of speech quality assessment, a model is developed which simulates the processing stages of the peripheral auditory system. At the output of the model a "running" auditory spectrum is obtained. This represents the auditory (spectral) equivalent of any acoustic sound such as speech. Auditory spectra from coded speech segments serve as inputs to a second model. This model simulates the information centre in the brain which performs the speech quality assessment. [Continues.

Digital Signal Processing (Second Edition)

This book provides an account of the mathematical background, computational methods and software engineering associated with digital signal processing. The aim has been to provide the reader with the mathematical methods required for signal analysis which are then used to develop models and algorithms for processing digital signals and finally to encourage the reader to design software solutions for Digital Signal Processing (DSP). In this way, the reader is invited to develop a small DSP library that can then be expanded further with a focus on his/her research interests and applications. There are of course many excellent books and software systems available on this subject area. However, in many of these publications, the relationship between the mathematical methods associated with signal analysis and the software available for processing data is not always clear. Either the publications concentrate on mathematical aspects that are not focused on practical programming solutions or elaborate on the software development of solutions in terms of working ‘black-boxes’ without covering the mathematical background and analysis associated with the design of these software solutions. Thus, this book has been written with the aim of giving the reader a technical overview of the mathematics and software associated with the ‘art’ of developing numerical algorithms and designing software solutions for DSP, all of which is built on firm mathematical foundations. For this reason, the work is, by necessity, rather lengthy and covers a wide range of subjects compounded in four principal parts. Part I provides the mathematical background for the analysis of signals, Part II considers the computational techniques (principally those associated with linear algebra and the linear eigenvalue problem) required for array processing and associated analysis (error analysis for example). Part III introduces the reader to the essential elements of software engineering using the C programming language, tailored to those features that are used for developing C functions or modules for building a DSP library. The material associated with parts I, II and III is then used to build up a DSP system by defining a number of ‘problems’ and then addressing the solutions in terms of presenting an appropriate mathematical model, undertaking the necessary analysis, developing an appropriate algorithm and then coding the solution in C. This material forms the basis for part IV of this work. In most chapters, a series of tutorial problems is given for the reader to attempt with answers provided in Appendix A. These problems include theoretical, computational and programming exercises. Part II of this work is relatively long and arguably contains too much material on the computational methods for linear algebra. However, this material and the complementary material on vector and matrix norms forms the computational basis for many methods of digital signal processing. Moreover, this important and widely researched subject area forms the foundations, not only of digital signal processing and control engineering for example, but also of numerical analysis in general. The material presented in this book is based on the lecture notes and supplementary material developed by the author for an advanced Masters course ‘Digital Signal Processing’ which was first established at Cranfield University, Bedford in 1990 and modified when the author moved to De Montfort University, Leicester in 1994. The programmes are still operating at these universities and the material has been used by some 700++ graduates since its establishment and development in the early 1990s. The material was enhanced and developed further when the author moved to the Department of Electronic and Electrical Engineering at Loughborough University in 2003 and now forms part of the Department’s post-graduate programmes in Communication Systems Engineering. The original Masters programme included a taught component covering a period of six months based on two semesters, each Semester being composed of four modules. The material in this work covers the first Semester and its four parts reflect the four modules delivered. The material delivered in the second Semester is published as a companion volume to this work entitled Digital Image Processing, Horwood Publishing, 2005 which covers the mathematical modelling of imaging systems and the techniques that have been developed to process and analyse the data such systems provide. Since the publication of the first edition of this work in 2003, a number of minor changes and some additions have been made. The material on programming and software engineering in Chapters 11 and 12 has been extended. This includes some additions and further solved and supplementary questions which are included throughout the text. Nevertheless, it is worth pointing out, that while every effort has been made by the author and publisher to provide a work that is error free, it is inevitable that typing errors and various ‘bugs’ will occur. If so, and in particular, if the reader starts to suffer from a lack of comprehension over certain aspects of the material (due to errors or otherwise) then he/she should not assume that there is something wrong with themselves, but with the author

Space Programs Summary No. 37-36

Research in systems, guidance and control, space sciences, engineering, telecommunications and propulsion for space exploration program