Every engineering professional needs a practical, convenient mathematics resource, without extensive theory and proofs. Mathematics for Circuits and Filters stresses the fundamental theory behind professional applications, making an excellent, flexible resource that enables easy access to the information needed to deal with circuits and filters.
The sections feature frequent examples and illustrations, reinforcing the basic theory. The examples also demonstrate applications of the concepts. References at the end of each section are drawn from not only traditional sources, but from relevant, nontraditional ones as well, including software, databases, standards, seminars, and conferences. This leads advanced researchers quickly to the data they may need for more specialized problems.
An international panel of experts developed the chapters for practicing engineers, concentrating on the problems that they encounter the most and have the most difficulty with. Mathematics for Circuits and Filters aids in the engineer's understanding and recall of vital mathematical concepts and acts as the engineer's primary resource when looking for solutions to a wide range of problems.
Author(s): Wai-Kai Chen
Publisher: CRC Press
Year: 2022
Language: English
Pages: 273
City: Boca Raton
Cover
Half Title
Title
Copyright
Preface
Contributors
Contents
1 Linear Operators and Matrices
1.1 Introduction
1.2 Vector Spaces Over Fields
1.3 Linear Operators and Matrix Representations
1.4 Matrix Operations
1.5 Determinant, Inverse, and Rank
1.6 Basis Transformations
1.7 Characteristics: Eigenvalues, Eigenvectors, and Singular Values
1.8 On Linear Systems
2 Bilinear Operators and Matrices
2.1 Introduction
2.2 Algebras
2.3 Bilinear Operators
2.4 Tensor Product
2.5 Basis Tensors
2.6 Multiple Products
2.7 Determinants
2.8 Skew Symmetric Products
2.9 Solving Linear Equations
2.10 Symmetric Products
2.11 Summary
3 The Laplace Transform
3.1 Introduction
3.2 Motivational Example
3.3 Formal Developments
3.4 Laplace Transform Analysis of Linear Systems
3.5 Conclusions and Further Reading
3.6 Appendix A: The Dirac Delta (Impulse) Function
3.7 Appendix B: Relationships among the Laplace, Fourier, and z-Transforms
4 Fourier Series, Fourier Transforms and the DFT
4.1 Introduction
4.2 Fourier Series Representation of Continuous Time Periodic Signals
4.3 The Classical Fourier Transform for Continuous Time Signals
4.4 The Discrete Time Fourier Transform
4.5 The Discrete Fourier Transform
4.6 Family Tree of Fourier Transforms
4.7 Selected Applications of Fourier Methods
4.8 Summary
5 z-Transform
5.1 Introduction
5.2 Definition of the z-Transform
5.3 Inverse z-Transform
5.4 Properties of the z-Transform
5.5 Role of the z-Transform in Linear Time-Invariant Systems
5.6 Variations on the z-Transform
5.7 Concluding Remarks
6 Wavelet Transforms
6.1 Introduction
6.2 Signal Representation Using Basis Functions
6.3 The Short-Time Fourier Transform
6.4 Digital Filter Banks and Subband Coders
6.5 Deeper Study of Wavelets, Filter Banks, and Short-Time Fourier Transforms
6.6 The Space of L1 and L2 Signals
6.7 Riesz Basis, Biorthogonality, and Other Fine Points
6.8 Frames in Hilbert Spaces
6.9 Short-Time Fourier Transform: Invertibility, Orthonormality, and Localization
6.10 Wavelets and Multiresolution
6.11 Orthonormal Wavelet Basis from Para unitary Filter Banks
6.12 Compactly Supported Orthonormal Wavelets
6.13 Wavelet Regularity
6.14 Concluding Remarks
7 Graph Theory
7.1 Introduction
7.2 Basic Concepts
7.3 Cuts, Circuits, and Orthogonality
7.4 Incidence, Circuit, and Cut Matrices of a Graph
7.5 Orthogonality Relation and Ranks of Circuit and Cut Matrices
7.6 Spanning Tree Enumeration
7.7 Graphs and Electrical Networks
7.8 Tellegen's Theorem and Network Sensitivity Computation
7.9 Arc Coloring Theorem and the No-Gain Property
8 Signal Flow Graphs
8.1 Introduction
8.2 Adjacency Matrix of a Directed Graph
8.3 Coates' Gain Formula
8.4 Mason's Gain Formula
Index
