* 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
Autorentext
RONALD L. ALLEN received his BA in mathematics from the University of California, Berkeley in 1973, his MA in mathematics from the University of California, Los Angeles in 1975, and his MS and PhD in Computer Science from the University of Texas at Arlington in 1990 and 1993, respectively.
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.
Klappentext
Signal analysis from concept to application
Signal analysis, a method of arriving at a structural description of a signal so that later high-level algorithms can interpret its content, is a growing field with an increasing number of applications. Signal Analysis: Time, Frequency, Scale, and Structure opens a window into the practice of signal analysis by providing a gradual yet thorough introduction to the theory behind signal analysis as well as the abstract mathematics and functional analysis which may be new to many readers.
Making the material accessible for readers of different levels of mathematical background, the authors clarify the basic concepts and types of signals and slowly build up to mastering the mathematics of Hilbert spaces, complex analysis, distributions, random signals, and analog Fourier transforms. Chapters cover:
- Concepts of analog, discrete, and digital signals
- Discrete systems and signal spaces, including linear and convolutional systems and lp signal spaces
- Time domain signal analysis including segmentation and thresholding, filtering and enhancement, and edge and pattern detection
- Continuous, discrete, and generalized Fourier transforms
- The z-transform, time-frequency and time-scale signal transforms
- Frequency domain and mixed-domain signal analysis
Suitable as a professional reference, up-to-date review for practitioners, and a resource of signal analysis techniques, Signal Analysis: Time, Frequency, Scale, and Structure serves up a well-rounded, mathematical approach to problems in signal interpretation using the latest time, frequency, and mixed-domain methods.
Zusammenfassung
- 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
Inhalt
Preface.
Acknowledgments.
1 Signals: Analog, Discrete, and Digital.
1.1 Introduction to Signals.
1.1.1 Basic Concepts.
1.1.2 Time-Domain Description of Signals.
1.1.3 Analysis in the Time-Frequency Plane.
1.1.4 Other Domains: Frequency and Scale.
1.2 Analog Signals.
1.2.1 Definitions and Notation.
1.2.2 Examples.
1.2.3 Special Analog Signals.
1.3 Discrete Signals.
1.3.1 Definitions and Notation.
1.3.2 Examples.
1.3.3 Special Discrete Signals.
1.4 Sampling and Interpolation.
1.4.1 Introduction.
1.4.2 Sampling Sinusoidal Signals.
1.4.3 Interpolation.
1.4.4 Cubic Splines.
1.5 Periodic Signals.
1.5.1 Fundamental Period and Frequency.
1.5.2 Discrete Signal Frequency.
1.5.3 Frequency Domain.
1.5.4 Time and Frequency Combined.
1.6 Special Signal Classes.
1.6.1 Basic Classes.
1.6.2 Summable and Integrable Signals.
1.6.3 Finite Energy Signals.
1.6.4 Scale Description.
1.6.5 Scale and Structure.
1.7 Signals and Complex Numbers.
1.7.1 Introduction.
1.7.2 Analytic Functions.
1.7.3 Complex Integration.
1.8 Random Signals and Noise.
1.8.1 Probability Theory.
1.8.2 Random Variables.
1.8.3 Random Signals.
1.9 Summary.
1.9.1 Historical Notes.
1.9.2 Resources.
1.9.3 Looking Forward.
1.9.4 Guide to Problems.
References.
Problems.
2 Discrete Systems and Signal Spaces.
2.1 Operations on Signals.
2.1.1 Operations on Signals and Discrete Systems.
2.1.2 Operations on Systems.
2.1.3 Types of Systems.
2.2 Linear Systems.
2.2.1 Properties.
2.2.2 Decomposition.
2.3 Translation Invariant Systems.
2.4 Convolutional Systems.
2.4.1 Linear, Translation-Invariant Systems.
2.4.2 Systems Defined by Difference Equations.
2.4.3 Convolution Properties.
2.4.4 Application: Echo Cancellation in Digital Telephony.
2.5 The lp Signal Spaces.
2.5.1 lp Signals.
2.5.2 Stable Systems.
2.5.3 Toward Abstract Signal Spaces.
2.5.4 Normed Spaces.
2.5.5 Banach Spaces.
2.6 Inner Product Spaces.
2.6.1 Definitions and Examples.
2.6.2 Norm and Metric.
2.6.3 Orthogonality.
2.7 Hilbert Spaces.
2.7.1 Definitions and Examples.
2.7.2 Decomposition and Direct Sums.
2.7.3 Orthonormal Bases.
2.8 Summary.
References.
Problems.
3 Analog Systems and Signal Spaces.
3.1 Analog Systems.
3.1.1 Operations on Analog Signals.
3.1.2 Extensions to the Analog World.
3.1.3 Cross-Correlation, Autocorrelation, and Convolution.
3.1.4 Miscellaneous Operations.
3.2 Convolution and Analog LTI Systems.
3.2.1 Linearity and Translation-Invariance.
3.2.2 LTI Systems, Impulse Response, and Convolution.
3.2.3 Convolution Properties.
3.2.4 Dirac Delta Properties.
3.2.5 Splines.
3.3 Analog Signal Spaces.
3.3.1 Lp Spaces.
3.3.2 Inner Product and Hilbert Spaces.
3.3.3 Orthonormal Bases.
3.3.4 Frames.
3.4 Modern Integration Theory.
3.4.1 Measure Theory.
3.4.2 Lebesgue Integration.
3.5 Distributions.
3.5.1 From Function to Functional.
3.5.2 From Functional to Distribution.&l...