Издательство Marcel Dekker, 1995, -329 pp.
Virtually all physical systems are nonlinear. It is often possible to approximate them by linear models and so utilize the rich theory of linear systems in analyzing and predicting the behaviour of a physical system. When a good enough linear approximation does not exist, and one is forced to use nonlinear models, the analysis becomes much more demanding. It is well known that there are no general approaches to nonlinear systems and even for simple modeling and analysis one needs a wide variety of mathematical tools in his or her arsenal.
There are different strategies in the analysis and design of nonlinear filtering methods. One of the most useful ones is to concentrate on a fairly restricted class of systems which can be treated theoretically and optimized within this class of systems. Another useful strategy is to combine two powerful and well developed approaches to obtain new tools. An example of this approach is the combination of spectral methods with Boolean theory opening up several new possibilities, e.g. new and general methods for analyzing nonlinear systems, especially median-type filters. Modeling of complicated systems involving choices between different lines of action also necessitates a combination of logical and arithmetical operations.
The goal of this book is to give an introduction to the basic concepts and techniques of binary transforms in digital logic and nonlinear filtering. Binary transforms have many attractive features and have found applications in a number of fields. Their generalizations and implementations are simple and they have fast algorithms requiring only additions. They form a foundation of a new theory of nonlinear signal and image processing and can be used also in many other areas of applied mathematics.
This book was written from the practical point of view with detailed computational algorithms, primarily for engineers and scientists. However it can also be used as a textbook in nonlinear filtering. The level of the book is suitable for advanced undergraduate or graduate students.
Binary Polynomial Transforms.
Binary Polynomial Arithmetical and Logical Functions and Matrices.
Fast Algorithms and Complexity of Binary Polynomial Transforms.
Binary Polynomial Transforms and Digital Logic.
Logical Correlations and Binary Polynomial Transforms.
Spectral Methods in Analysis of Boolean Functions.
Spectral Methods in Minimization of Boolean Functions.
Applications in Nonlinear Digital Filtering.
Median and Order Statistic Filters.
Weighted Order Statistic and Stack Filters.
Statistical Properties of Stack Filters.
Virtually all physical systems are nonlinear. It is often possible to approximate them by linear models and so utilize the rich theory of linear systems in analyzing and predicting the behaviour of a physical system. When a good enough linear approximation does not exist, and one is forced to use nonlinear models, the analysis becomes much more demanding. It is well known that there are no general approaches to nonlinear systems and even for simple modeling and analysis one needs a wide variety of mathematical tools in his or her arsenal.
There are different strategies in the analysis and design of nonlinear filtering methods. One of the most useful ones is to concentrate on a fairly restricted class of systems which can be treated theoretically and optimized within this class of systems. Another useful strategy is to combine two powerful and well developed approaches to obtain new tools. An example of this approach is the combination of spectral methods with Boolean theory opening up several new possibilities, e.g. new and general methods for analyzing nonlinear systems, especially median-type filters. Modeling of complicated systems involving choices between different lines of action also necessitates a combination of logical and arithmetical operations.
The goal of this book is to give an introduction to the basic concepts and techniques of binary transforms in digital logic and nonlinear filtering. Binary transforms have many attractive features and have found applications in a number of fields. Their generalizations and implementations are simple and they have fast algorithms requiring only additions. They form a foundation of a new theory of nonlinear signal and image processing and can be used also in many other areas of applied mathematics.
This book was written from the practical point of view with detailed computational algorithms, primarily for engineers and scientists. However it can also be used as a textbook in nonlinear filtering. The level of the book is suitable for advanced undergraduate or graduate students.
Binary Polynomial Transforms.
Binary Polynomial Arithmetical and Logical Functions and Matrices.
Fast Algorithms and Complexity of Binary Polynomial Transforms.
Binary Polynomial Transforms and Digital Logic.
Logical Correlations and Binary Polynomial Transforms.
Spectral Methods in Analysis of Boolean Functions.
Spectral Methods in Minimization of Boolean Functions.
Applications in Nonlinear Digital Filtering.
Median and Order Statistic Filters.
Weighted Order Statistic and Stack Filters.
Statistical Properties of Stack Filters.