| Description |
1 online resource (xix, 236 pages) |
| Physical Medium |
polychrome |
| Description |
text file |
| Bibliography |
Includes bibliographical references and index. |
| Summary |
"Discusses the mathematical concepts and their interpretations in the field of signal processing"-- Provided by publisher |
| Contents |
Cover; Mathematical Aspects of Signal Processing; Title; Copyright; Dedication; Contents; Figures; Tables; Foreword; Preface; Acknowledgments; 1 Paradigm of Signal Processing; 1.1 Introduction; 1.2 A Case Study: Spectral Estimation; 1.3 Outline Plan; Bibliography; 2 Function Representation; 2.1 Polynomial Interpolation and Lagrange Formula; 2.2 Error in Polynomial Interpolation and Chebyshev Interpolating Points; 2.3 Gregory-Newton Divided-Difference Formula and Hermite Interpolation; 2.3.1 Hermite Interpolation Method. |
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2.10.2 Simulation Study: Example 5 (`α-law Profile Fibre)Bibliography; 3 Generalized Inverse; 3.1 Simultaneous Linear Equations; 3.2 Generalized Inverse of Matrix; 3.3 Generalized Inverse by Orthogonal Bordering; 3.4 Generalized Inverse by Matrix Factorization; 3.4.1 Singular Value Decomposition; 3.5 Generalized Inverse by Matrix Partitioning; 3.6 Perturbation Analysis of Solution Vector; 3.7 Stability of Least Squares Solution; 3.8 Linear Operator Equation and Method of Orthogonal Projection; 3.8.1 Integral Equation and Method of Galerkin; 3.9 Conjugate Direction Methods. |
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2.4 Weierstrass Theorem and Uniform Convergence of Polynomial Approximation2.5 Best Approximation in Normed Linear Space; 2.6 Minimax Approximation and Exchange Algorithm; 2.7 Least Absolute Approximation and Linear Programming; 2.7.1 Linear Programming Method; 2.8 Least Squares Approximation and Orthogonal Polynomials; 2.8.1 Least Squares Approximation of Periodic Functions; 2.9 Signal Processing Applications I: Complex Exponential Signal Representation; 2.9.1 Prony's Method; 2.9.2 The Derivative Methods; 2.9.3 The Integral Method. |
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2.9.4 Linear Prediction Model for Noisy Data and Extended Order Modelling2.9.5 Transient Signal Analysis I; 2.9.6 Simulation Study: Example 1 (Non-uniform Sampling); 2.9.7 Smoothing; 2.9.8 Simulation Study: Example 2 (Noisy Signal); 2.9.9 Simulation Study: Example 3 (Parameter Estimation -- Non-uniform Sampling); 2.9.10 Simulation Study: Example 4 (Parameter Estimation -- Noisy Signal); 2.10 Signal Processing Applications II: Numerical Analysis of Optical Fibres; 2.10.1 Numerical Analysis of Optical Fibres with Arbitrary Refractive Index Profile. |
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3.10 Ill-posed Operator Equations and Regularization Theory3.10.1 Regularization Theory of Miller; 3.10.2 Landweber Iteration; 3.10.3 Regularization Method of Tikhonov; 3.11 Signal Processing Applications III: Non-uniform Sampling and Signal Parameter Estimation; 3.11.1 Transient Signal Analysis II; 3.11.2 Simulation Study: Example 1 (Numerical Stability); 3.11.3 Simulation Study: Example 2 (Extended-Order Modelling); Bibliography; 4 Modal Decomposition; 4.1 Schmidt Pair and Singular Value Decomposition; 4.2 Rank Property and Subspaces; 4.3 Matrix Inverse and Condition Number. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Signal processing -- Mathematics.
|
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Signal processing -- Mathematics. |
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TECHNOLOGY & ENGINEERING -- Mechanical. |
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Sircar, Pradip. Mathematical aspects of signal processing. Cambridge, United Kingdom ; New York : Cambridge University Press, 2016 9781107175174 (DLC) 2016019491 (OCoLC)951172560 |
| ISBN |
9781316811757 (electronic book) |
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1316811751 (electronic book) |
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9781107175174 |
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1107175178 |
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9781316796832 |
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1316796833 |
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