Author | Teolis, Anthony. author |
---|---|

Title | Computational Signal Processing with Wavelets [electronic resource] / by Anthony Teolis |

Imprint | Boston, MA : Birkhรคuser Boston, 1998 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-4142-3 |

Descript | XXIV, 324 p. online resource |

SUMMARY

This unique resource examines the conceptual, computational, and practical aspects of applied signal processing using wavelets. With this book, readers will understand and be able to use the power and utility of new wavelet methods in science and engineering problems and analysis. The text is written in a clear, accessible style avoiding unnecessary abstractions and details. From a computational perspective, wavelet signal processing algorithms are presented and applied to signal compression, noise suppression, and signal identification. Numerical illustrations of these computational techniques are further provided with interactive software (MATLAB code) that is available on the world wide web. Topics and Features: * Continuous wavelet and Gabor transforms * Frame-based theory of discretization and reconstruction of analog signals is developed * New and efficient "overcomplete" wavelet transform is introduced and applied * Numerical illustrations with an object-oriented computational perspective using the Wavelet Signal Processing Workstation (MATLAB code) available This book is an excellent resource for information and computational tools needed to use wavelets in many types of signal processing problems. Graduates, professionals, and practitioners in engineering, computer science, geophysics, and applied mathematics will benefit from using the book and software tools.

CONTENT

1 Introduction -- 1.1 Motivation and Objectives -- 1.2 Core Material and Development -- 1.3 Hybrid Media Components -- 1.4 Signal Processing Perspective -- 2 Mathematical Preliminaries -- 2.1 Basic Symbols and Notation -- 2.2 Basic Concepts -- 2.3 Basic Spaces -- 2.4 Operators -- 2.5 Bases and Completeness in Hilbert Space -- 2.6 Fourier Transforms -- 2.7 Linear Filters -- 2.8 Analog Signals and Discretization -- Problems -- 3 Signal Representation and Frames -- 3.1 Inner Product Representation (Atomic Decomposition) -- 3.2 Orthonormal Bases -- 3.3 Riesz Bases -- 3.4 General Frames -- Problems -- 4 Continuous Wavelet and Gabor Transforms -- 4.1 What Is a Wavelet? -- 4.2 Example Wavelets -- 4.3 Continuous Wavelet Transform -- 4.4 Inverse Wavelet Transform -- 4.5 Continuous Gabor Transform -- 4.6 Unified Representation and Groups -- Problems -- 5 Discrete Wavelet Transform -- 5.1 Discretization of the CWT -- 5.2 Multiresolution Analysis -- 5.3 Multiresolution Representation -- 5.4 Orthonormal Wavelet Bases -- 5.5 Compactly Supported (Daubechies) Wavelets -- 5.6 Fast Wavelet Transform Algorithm -- Problems -- 6 Overcomplete Wavelet Transform -- 6.1 Discretization of the CWT Revisited -- 6.2 Filter Bank Implementation -- 6.3 Time-Frequency Localization and Wavelet Design -- 6.4 OCWT Examples -- 6.5 Irregular Sampling and Frames -- Problems -- 7 Wavelet Signal Processing -- 7.1 Noise Suppression -- 7.2 Compression -- 7.3 Digital Communication -- 7.4 Identification -- 7.5 Conclusion -- Problems -- 8 Object-Oriented Wavelet Analysis with MATLAB 5 -- 8.1 Wavelet Signal Processing Workstation -- 8.2 MATLAB Coding -- 8.3 The sampled_signal Object -- 8.4 Wavelet Transform Implementation -- 8.5 The wavelet Object -- 8.6 Processing Example -- 8.7 Supporting Functions and Globals -- References

Mathematics
Fourier analysis
Computer mathematics
Applied mathematics
Engineering mathematics
Electrical engineering
Mathematics
Fourier Analysis
Computational Mathematics and Numerical Analysis
Appl.Mathematics/Computational Methods of Engineering
Signal Image and Speech Processing
Communications Engineering Networks
Computational Science and Engineering