Discrete Signals and Inverse Problems
An Introduction for Engineers and Scientists
1st Edition
Published on 13. December 2005
364 pages
978-0-470-02188-0 (ISBN)
Description
Discrete Signals and Inverse Problems examines fundamentalconcepts necessary to engineers and scientists working withdiscrete signal processing and inverse problem solving, and placesemphasis on the clear understanding of algorithms within thecontext of application needs.
Based on the original 'Introduction to Discrete Signalsand Inverse Problems in Civil Engineering', this expandedand enriched version:
* combines discrete signal processing and inverse problem solvingin one book
* covers the most versatile tools that are needed to processengineering and scientific data
* presents step-by-step 'implementation procedures'for the most relevant algorithms
* provides instructive figures, solved examples and insightfulexercises
Discrete Signals and Inverse Problems is essentialreading for experimental researchers and practicing engineers incivil, mechanical and electrical engineering, non-destructivetesting and instrumentation. This book is also an excellentreference for advanced undergraduate students and graduate studentsin engineering and science.
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J. Carlos Santamarina | Dante Fratta
Discrete Signals and Inverse Problems - An Introduction for Engineers and Scientists
Software
06/2006
Wiley
€96.54
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J. Carlos Santamarina | Dante Fratta
Discrete Signals and Inverse Problems
An Introduction for Engineers and Scientists
Book
07/2005
1st Edition
Wiley
€188.50
Shipment within 10-20 days
Persons
J. Carlos Santamarina, Civil and Environmental Engineering,Georgia Institute of Technology, Atlanta, GA 30332-0355, USA
Dante Fratta, 3418H CEBA, Civil and EnvironmentalEngineering, Louisiana State University, Baton Rouge, LA 70803,USA
Content
- Intro
- Contents
- Preface
- Brief Comments on Notation
- 1 Introduction
- 1.1 Signals, Systems, and Problems
- 1.2 Signals and Signal Processing - Application Examples
- 1.3 Inverse Problems - Application Examples
- 1.4 History - Discrete Mathematical Representation
- 1.5 Summary
- Solved Problems
- Additional Problems
- 2 Mathematical Concepts
- 2.1 Complex Numbers and Exponential Functions
- 2.2 Matrix Algebra
- 2.3 Derivatives - Constrained Optimization
- 2.4 Summary
- Further Reading
- Solved Problems
- Additional Problems
- 3 Signals and Systems
- 3.1 Signals: Types and Characteristics
- 3.2 Implications of Digitization - Aliasing
- 3.3 Elemental Signals and Other Important Signals
- 3.4 Signal Analysis with Elemental Signals
- 3.5 Systems: Characteristics and Properties
- 3.6 Combination of Systems
- 3.7 Summary
- Further Reading
- Solved Problems
- Additional Problems
- 4 Time Domain Analyses of Signals and Systems
- 4.1 Signals and Noise
- 4.2 Cross- and Autocorrelation: Identifying Similarities
- 4.3 The Impulse Response - System Identification
- 4.4 Convolution: Computing the Output Signal
- 4.5 Time Domain Operations in Matrix Form
- 4.6 Summary
- Further Reading
- Solved Problems
- Additional Problems
- 5 Frequency Domain Analysis of Signals (Discrete Fourier Transform)
- 5.1 Orthogonal Functions - Fourier Series
- 5.2 Discrete Fourier Analysis and Synthesis
- 5.3 Characteristics of the Discrete Fourier Transform
- 5.4 Computation in Matrix Form
- 5.5 Truncation, Leakage, and Windows
- 5.6 Padding
- 5.7 Plots
- 5.8 The Two-Dimensional Discrete Fourier Transform
- 5.9 Procedure for Signal Recording
- 5.10 Summary
- Further Reading and References
- Solved Problems
- Additional Problems
- 6 Frequency Domain Analysis of Systems
- 6.1 Sinusoids and Systems - Eigenfunctions
- 6.2 Frequency Response
- 6.3 Convolution
- 6.4 Cross-Spectral and Autospectral Densities
- 6.5 Filters in the Frequency Domain - Noise Control
- 6.6 Determining H with Noiseless Signals (Phase Unwrapping)
- 6.7 Determining H with Noisy Signals (Coherence)
- 6.8 Summary
- Further Reading and References
- Solved Problems
- Additional Problems
- 7 Time Variation and Nonlinearity
- 7.1 Nonstationary Signals: Implications
- 7.2 Nonstationary Signals: Instantaneous Parameters
- 7.3 Nonstationary Signals: Time Windows
- 7.4 Nonstationary Signals: Frequency Windows
- 7.5 Nonstationary Signals: Wavelet Analysis
- 7.6 Nonlinear Systems: Detecting Nonlinearity
- 7.7 Nonlinear Systems: Response to Different Excitations
- 7.8 Time-Varying Systems
- 7.9 Summary
- Further Reading and References
- Solved Problems
- Additional Problems
- 8 Concepts in Discrete Inverse Problems
- 8.1 Inverse Problems - Discrete Formulation
- 8.2 Linearization of Nonlinear Problems
- 8.3 Data-Driven Solution - Error Norms
- 8.4 Model Selection - Ockham's Razor
- 8.5 Information
- 8.6 Data and Model Errors
- 8.7 Nonconvex Error Surfaces
- 8.8 Discussion on Inverse Problems
- 8.9 Summary
- Further Reading and References
- Solved Problems
- Additional Problems
- 9 Solution by Matrix Inversion
- 9.1 Pseudoinverse
- 9.2 Classification of Inverse Problems
- 9.3 Least Squares Solution (LSS)
- 9.4 Regularized Least Squares Solution (RLSS)
- 9.5 Incorporating Additional Information
- 9.6 Solution Based on Singular Value Decomposition
- 9.7 Nonlinearity
- 9.8 Statistical Concepts - Error Propagation
- 9.9 Experimental Design for Inverse Problems
- 9.10 Methodology for the Solution of Inverse Problems
- 9.11 Summary
- Further Reading
- Solved Problems
- Additional Problems
- 10 Other Inversion Methods
- 10.1 Transformed Problem Representation
- 10.2 Iterative Solution of System of Equations
- 10.3 Solution by Successive Forward Simulations
- 10.4 Techniques from the Field of Artificial Intelligence
- 10.5 Summary
- Further Reading
- Solved Problems
- Additional Problems
- 11 Strategy for Inverse Problem Solving
- 11.1 Step 1: Analyze the Problem
- 11.2 Step 2: Pay Close Attention to Experimental Design
- 11.3 Step 3: Gather High-quality Data
- 11.4 Step 4: Preprocess the Data
- 11.5 Step 5: Select an Adequate Physical Model
- 11.6 Step 6: Explore Different Inversion Methods
- 11.7 Step 7: Analyze the Final Solution
- 11.8 Summary
- Solved Problems
- Additional Problems
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- R
- S
- T
- U
- V
- W
