Riassunto
The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques. Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data. Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLABä. Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned. Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background.
Contenuti
Haar Wavelets
The Haar Transform
Conservation and Compaction of Energy
Removing Noise from Audio Signals
Haar Wavelets
Multiresolution Analysis
Compression of Audio Signals
Removing Noise from Audio Signals
Notes and References
Daubechies Wavelets
The Daub4 Wavelets
Conservation and Compaction of Energy
Other Daubechies Wavelets
Compression of Audio Signals
Quantization, Entropy, and Compression
Denoising Audio Signals
Two-Dimensional Wavelet Transforms
Compression of Images
Fingerprint Compression
Denoising Images
Some Topics in Image Processing
Notes and References
Frequency Analysis
Discrete Fourier Analysis
Correlation and Feature Detection
Object Detection in 2-D Images
Creating Scaling Signals and Wavelets
Notes and References
Beyond Wavelets
Wavelet Packet Transforms
Applications of Wavelet Packet Transforms
Continuous Wavelet Transforms
Gabor Wavelets and Speech Analysis
Notes and References
Appendix: Software for Wavelet Analysis
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