This book presents connections between the different aspects of wavelet and subband theory. Specifically, it provides an understanding of the link between the continuous wavelet transform, the fast wavelet transform, and subband decomposition. Theory is intertwined with practical examples implementing MATLAB and applications of wavelets in ultrasonic and biomedical domains. Special emphasis is given to applications in signal and image processing, communications, and control and systems analysis.

Contenu

Introduction.- 1.1 Historical Review: From Fourier Analysis to Wavelet Analysis and Subband.- 1.2 Organization of This Book.- 1.3 References.- I: Fundamentals.- 2. Wavelet Fundamentals.- II: Wavelets and Subbands.- 3. Time and Frequency Analysis of Signals.- 4. Discrete Wavelet Transform: From Frames to Fast Wavelet Transform.- 5. Theory of Subband Decomposition.- 6. Two-Dimensional Wavelet Transforms and Applications.- III: Applications.- 7. Applications of Wavelets in the Analysis of Transient Signals.- 8. Applications of Subband and Wavelet Transform in Communication Systems.- 9. Real-Time Implementations of Wavelet Transforms.- A. Fourier Transform.- B. Discrete Fourier Transform.- C. z-Transform.- D. Orthogonal Representation of Signals.