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E-raamat: Mathematics for Circuits and Filters

Edited by (University of IIlinois, Chicago, USA)
  • Formaat: 280 pages
  • Ilmumisaeg: 16-Sep-2022
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781351838351
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Mathematics for Circuits and FiltersSuurem pilt
  • Formaat: 280 pages
  • Ilmumisaeg: 16-Sep-2022
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781351838351
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Reviews the key concepts, models, and equations that enable the practicing electrical engineer to analyze, design, and predict the behavior of large-scale circuits, devices, filters, and systems. The eight chapters cover linear operators and matrices, bilinear operators and matrices, the Laplace transform, the discrete Fourier transform, the z-transform, wavelet transforms, graph theory, and signal flow graphs. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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.

Arvustused

"Recommended for libraries associated with electrical engineering and applied math programs." --CHOICE Magazine



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Linear Operators and Matrices 1(19) Cheryl B. Schrader Michael K. Sain Introduction 1(1) Vector Spaces Over Fields 2(2) Linear Operators and Matrix Representations 4(2) Matrix Operations 6(2) Determinant, Inverse, and Rank 8(3) Basis Transformations 11(4) Characteristics: Eigenvalues, Eigenvectors, and Singular Values 15(2) On Linear Systems 17(2) Bilinear Operators and Matrices 19(18) Michael K. Sain Cheryl B. Schrader Introduction 19(1) Algebras 20(1) Bilinear Operators 21(1) Tensor Product 22(1) Basis Tensors 23(3) Multiple Products 26(1) Determinants 27(1) Skew Symmetric Products 28(3) Solving Linear Equations 31(2) Symmetric Products 33(2) Summary 35(2) The Laplace Transform 37(46) John R. Deller, Jr. Introduction 37(1) Motivational Example 38(6) Formal Developments 44(24) Laplace Transform Analysis of Linear Systems 68(10) Conclusions and Further Reading 78(1) Appendix A: The Dirac Delta (Impulse) Function 79(1) Appendix B: Relationships among the Laplace, Fourier, and z-Transforms 80(3) Fourier Series, Fourier Transforms and the DFT 83(30) W. Kenneth Jenkins Introduction 83(2) Fourier Series Representation of Continuous Time Periodic Signals 85(4) The Classical Fourier Transform for Continuous Time Signals 89(4) The Discrete Time Fourier Transform 93(4) The Discrete Fourier Transform 97(5) Family Tree of Fourier Transforms 102(2) Selected Applications of Fourier Methods 104(6) Summary 110(3) z-Transform 113(18) Jelena Kovacevic Introduction 113(1) Definition of the z-Transform 114(3) Inverse z-Transform 117(3) Properties of the z-Transform 120(4) Role of the z-Transform in Linear Time-Invariant Systems 124(2) Variations of the z-Transform 126(2) Concluding Remarks 128(3) Wavelet Transforms 131(86) P.P. Vaidyanathan Igor Djokovic Introduction 131(2) Signal Representation Using Basis Functions 133(13) The Short-Time Fourier Transform 146(7) Digital Filter Banks and Subband Coders 153(8) Deeper study of Wavelets, Filter banks, and Short-Time Fourier Transforms 161(1) The Space of L1 and L2 Signals 162(7) Riesz Basis, Biorthogonality, and Other Fine Points 169(7) Frames in Hilbert Spaces 176(4) Short-Time Fourier Transform: Invertibility, Orthonormality, and Localization 180(3) Wavelets and Multiresolution 183(13) Orthonormal Wavelet Basis from Paraunitary Filter Banks 196(9) Compactly Supported Orthonormal Wavelets 205(2) Wavelet Regularity 207(7) Concluding Remarks 214(3) Graph Theory 217(28) Krishnaiyan Thulasiraman Introduction 217(1) Basic Concepts 217(6) Cuts, Circuits, and Orthogonality 223(2) Incidence, Circuit, and Cut Matrices of a Graph 225(3) Orthogonality Relation and Ranks of Circuit and Cut Matrices 228(2) Spanning Tree Enumeration 230(3) Graphs and Electrical Networks 233(3) Tellegens Theorem and Network Sensitivity Computation 236(4) Arc Coloring Theorem and the No-Gain Property 240(5) Signal Flow Graphs 245(12) Krishnaiyan Thulasiraman Introduction 245(1) Adjacency Matrix of a Directed Graph 245(3) Coates Gain Formula 248(4) Masons Gain Formula 252(5) Index 257
Wai-Kai Chen (University of IIlinois, Chicago, USA)
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