Filter Design With Time Domain Mask Constraints: Theory and Applications

Applied Optimization

Book 56
Springer Science & Business Media
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Optimum envelope-constrained filter design is concerned with time-domain synthesis of a filter such that its response to a specific input signal stays within prescribed upper and lower bounds, while minimizing the impact of input noise on the filter output or the impact of the shaped signal on other systems depending on the application. In many practical applications, such as in TV channel equalization, digital transmission, and pulse compression applied to radar, sonar and detection, the soft least square approach, which attempts to match the output waveform with a specific desired pulse, is not the most suitable one. Instead, it becomes necessary to ensure that the response stays within the hard envelope constraints defined by a set of continuous inequality constraints. The main advantage of using the hard envelope-constrained filter formulation is that it admits a whole set of allowable outputs. From this set one can then choose the one which results in the minimization of a cost function appropriate to the application at hand. The signal shaping problems so formulated are semi-infinite optimization problems.
This monograph presents in a unified manner results that have been generated over the past several years and are scattered in the research literature. The material covered in the monograph includes problem formulation, numerical optimization algorithms, filter robustness issues and practical examples of the application of envelope constrained filter design.
Audience: Postgraduate students, researchers in optimization and telecommunications engineering, and applied mathematicians.
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Publisher
Springer Science & Business Media
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Published on
Mar 9, 2013
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Pages
330
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ISBN
9781475734096
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Language
English
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Genres
Computers / Information Technology
Computers / Software Development & Engineering / General
Mathematics / Applied
Mathematics / Optimization
Technology & Engineering / Electrical
Technology & Engineering / Electronics / Circuits / General
Technology & Engineering / Electronics / General
Technology & Engineering / Imaging Systems
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This content is DRM protected.
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Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as `controls'. Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit. Many results appear here for the first time in book form.
Audience: The book is written at the level of a first-year graduate course in optimization for students with varied backgrounds interested in modeling of real-life problems. It is expected that the reader has been exposed to a prior elementary course in optimization, such as linear or non-linear programming. The last section of the book requires some knowledge of functional analysis.
The 1980s and 1990s have seen a growing interest in research and practice in the use of methodologies within problem contexts characterised by a primary focus on technology, human issues, or power. During the last five to ten years, this has given rise to challenges regarding the ability of a single methodology to address all such contexts, and the consequent development of approaches which aim to mix methodologies within a single problem situation. This has been particularly so where the situation has called for a mix of technological (the so-called 'hard') and human centred (so-called 'soft') methods. The approach developed has been termed mixed-mode modelling. The area of mixed-mode modelling is relatively new, with the phrase being coined approximately four years ago by Brian Lehaney in a keynote paper published at the 1996 Annual Conference of the UK Operational Research Society. Mixed-mode modelling, as suggested above, is a new way of considering problem situations faced by organisations. Traditional technological approaches used in management science have suffered criticisms relating to their adequacy in the past few decades, and these hard approaches have been replaced by soft methods, which consider process more relevant than outcome. However, the sole use of human centred approaches to organisational problems has also proved to be inadequate. Mixed-mode modelling accepts the importance of both process and outcome, and provides enabling mechanisms for hard and soft investigation to be undertaken.
This volume contains refereed papers based on the lectures presented at the XIV International Conference on Mathematical Programming held at Matrahaza, Hungary, between 27-31 March 1999. This conference was organized by the Laboratory of Operations Research and Deci sion Systems at the Computer and Automation Institute, Hungarian Academy of Sciences. The editors hope this volume will contribute to the theory and applications of mathematical programming. As a tradition of these events, the main purpose of the confer ence was to review and discuss recent advances and promising research trends concerning theory, algorithms and applications in different fields of Optimization Theory and related areas such as Convex Analysis, Complementarity Systems and Variational Inequalities. The conference is traditionally held in the Matra Mountains, and housed by the resort house of the Hungarian Academy of Sciences. This was the 14th event of the long lasting series of conferences started in 1973. The organizers wish to express their thanks to the authors for their contributions in this volume, and the anonymous referees for their valu able comments. Special thanks are directed to our sponsors, the Hun garian Academy of Sciences, the National Committee for Technological Development, the Hungarian National Science Foundation, and last but not least, the Hungarian Operational Research Society. We would like to thank John Martindale from Kluwer Academic Publishers for helping us produce this volume, Eva Nora Nagy for cor rections and proof-readings, and Peter Dombi for his excellent work on typesetting and editing the manuscript.
The present book is the offspring of my Habilitation, which is the key to academic tenure in Austria. Legal requirements demand that a Ha bilitation be published and so only seeing it in print marks the real end of this biographical landmark project. From a scientific perspective I may hope to finally reach a broader audience with this book for a criti cal appraisal of the research done. Aside from objectives the book is a reflection of many years of research preceding Habilitation proper in the field of efficiency measurement. Regarding the subject matter the main intention was to fill an important remaining gap in the efficiency analysis literature. Hitherto no technique was available to estimate output-specific efficiencies in a statistically convincing way. This book closes this gap, although some desirable improvements and generalizations of the proposed estimation technique may yet be required, before it will eventually establish as standard tool for efficiency analysis. The likely audience for this book includes professional researchers, who want to enrich their tool set for applied efficiency analysis, as well as students of economics, management science or operations research, in tending to learn more about the potentials of rigorously understood efficiency analysis. But also managers or public officials potentially or dering efficiency studies should benefit from the book by learning about the extended capabilities of efficiency analysis. Just reading the intro duction may change their perception of value for money when it comes to comparative performance measurement.
Optimality and stability are two important notions in applied mathematics. This book is a study of these notions and their relationship in linear and convex parametric programming models. It begins with a survey of basic optimality conditions in nonlinear programming. Then new results in convex programming, using LFS functions, for single-objective, multi-objective, differentiable and non-smooth programs are introduced. Parametric programming models are studied using basic tools of point-to-set topology. Stability of the models is introduced, essentially, as continuity of the feasible set of decision variables under continuous perturbations of the parameters. Perturbations that preserve this continuity are regions of stability. It is shown how these regions can be identified. The main results on stability are characterizations of locally and globally optimal parameters for stable and also for unstable perturbations. The results are straightened for linear models and bi-level programs. Some of the results are extended to abstract spaces after considering parameters as `controls'. Illustrations from diverse fields, such as data envelopment analysis, management, von Stackelberg games of market economy, and navigation problems are given and several case studies are solved by finding optimal parameters. The book has been written in an analytic spirit. Many results appear here for the first time in book form.
Audience: The book is written at the level of a first-year graduate course in optimization for students with varied backgrounds interested in modeling of real-life problems. It is expected that the reader has been exposed to a prior elementary course in optimization, such as linear or non-linear programming. The last section of the book requires some knowledge of functional analysis.
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With its emphasis on the latest research results, Integrated Tracking, Classification, and Sensor Management is an invaluable guide for researchers and practitioners in statistical signal processing, radar systems, operations research, and control theory.

The 1980s and 1990s have seen a growing interest in research and practice in the use of methodologies within problem contexts characterised by a primary focus on technology, human issues, or power. During the last five to ten years, this has given rise to challenges regarding the ability of a single methodology to address all such contexts, and the consequent development of approaches which aim to mix methodologies within a single problem situation. This has been particularly so where the situation has called for a mix of technological (the so-called 'hard') and human centred (so-called 'soft') methods. The approach developed has been termed mixed-mode modelling. The area of mixed-mode modelling is relatively new, with the phrase being coined approximately four years ago by Brian Lehaney in a keynote paper published at the 1996 Annual Conference of the UK Operational Research Society. Mixed-mode modelling, as suggested above, is a new way of considering problem situations faced by organisations. Traditional technological approaches used in management science have suffered criticisms relating to their adequacy in the past few decades, and these hard approaches have been replaced by soft methods, which consider process more relevant than outcome. However, the sole use of human centred approaches to organisational problems has also proved to be inadequate. Mixed-mode modelling accepts the importance of both process and outcome, and provides enabling mechanisms for hard and soft investigation to be undertaken.
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