Signal Analysis
Time, Frequency, Scale, and Structure
1. Edition January 2004
960 Pages, Hardcover
Wiley & Sons Ltd
Short Description
Signal analysis attempts to arrive at a structural description of a signal so that later high-level algorithms can interpret its content. Responding to a need for a complete introduction to this growing field, this thorough overview discusses the major aspects of signal analysis, from analog and discrete signals, linear systems, and analog and discrete Fourier transforms to sampling theory and random signals.
Offers a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods
* Equally useful as a reference, an up-to-date review, a learning tool, and a resource for signal analysis techniques
* Provides a gradual introduction to the mathematics so that the less mathematically adept reader will not be overwhelmed with instant hard analysis
* Covers Hilbert spaces, complex analysis, distributions, random signals, analog Fourier transforms, and more
Acknowledgments.
1 Signals: Analog, Discrete, and Digital.
1.1 Introduction to Signals.
1.2 Analog Signals.
1.3 Discrete Signals.
1.4 Sampling and Interpolation.
1.5 Periodic Signals.
1.6 Special Signal Classes.
1.7 Signals and Complex Numbers.
1.8 Random Signals and Noise.
1.9 Summary.
References.
Problems.
2 Discrete Systems and Signal Spaces.
2.1 Operations on Signals.
2.2 Linear Systems.
2.3 Translation Invariant Systems.
2.4 Convolutional Systems.
2.5 The l¯p Signal Spaces.
2.6 Inner Product Spaces.
2.7 Hilbert Spaces.
2.8 Summary.
References.
Problems.
3 Analog Systems and Signal Spaces.
3.1 Analog Systems.
3.2 Convolution and Analog LTI Systems.
3.3 Analog Signal Spaces.
3.4 Modern Integration Theory.
3.5 Distributions.
3.6 Summary.
References.
Problems.
4 Time-Domain Signal Analysis.
4.1 Segmentation.
4.2 Thresholding.
4.3 Texture.
4.4 Filtering and Enhancement.
4.5 Edge Detection.
4.6 Pattern Detection.
4.7 Scale Space.
4.8 Summary.
References.
Problems.
5 Fourier Transforms of Analog Signals.
5.1 Fourier Series.
5.2 Fourier Transform.
5.3 Extension to L2(R).
5.4 Summary.
References.
Problems.
6 Generalized Fourier Transforms of Analog Signals.
6.1 Distribution Theory and Fourier Transforms.
6.2 Generalized Functions and Fourier Series Coefficients.
6.3 Linear Systems in the Frequency Domain.
6.4 Introduction to Filters.
6.5 Modulation.
6.6 Summary.
References.
Problems.
7 Discrete Fourier Transforms.
7.1 Discrete Fourier Transform.
7.2 Discrete-Time Fourier Transform.
7.3 The Sampling Theorem.
7.4 Summary.
References.
Problems.
8 The z-Transform.
8.1 Conceptual Foundations.
8.2 Inversion Methods.
8.3 Related Transforms.
8.4 Summary.
References.
Problems.
9 Frequency-Domain Signal Analysis.
9.1 Narrowband Signal Analysis.
9.2 Frequency and Phase Estimation.
9.3 Discrete filter design and implementation.
9.4 Wideband Signal Analysis.
9.5 Analog Filters.
9.6 Specialized Frequency-Domain Techniques.
9.7 Summary.
References.
Problems.
10 Time-Frequency Signal Transforms.
10.1 Gabor Transforms.
10.2 Short-Time Fourier Transforms.
10.3 Discretization.
10.4 Quadratic Time-Frequency Transforms.
10.5 The Balian-Low Theorem.
10.6 Summary.
References.
Problems.
11 Time-Scale Signal Transforms.
11.1 Signal Scale.
11.2 Continuous Wavelet Transforms.
11.3 Frames.
11.4 Multiresolution Analysis and Orthogonal Wavelets.
11.5 Summary.
References.
Problems.
12 Mixed-Domain Signal Analysis.
12.1 Wavelet Methods for Signal Structure.
12.2 Mixed-Domain Signal Processing.
12.3 Biophysical Applications.
12.4 Discovering Signal Structure.
12.5 Pattern Recognition Networks.
12.6 Signal Modeling and Matching.
12.7 Afterword.
References.
Problems.
Index.
DUNCAN W. MILLS received his BA in Physics from Wesleyan University, his MS in Electrical Engineering from George Washington University, and his PhD in Electrical Engineering from University of Texas at Dallas in 1992.