Ripples in Mathematics

This book gives an introduction to the discrete wavelet transform and some of its applications. It is based on a novel approach to discrete wavelets called lifting. The first part is a completely elementary introduction to the subject, and the prerequisites for this part are knowledge of basic calculus and linear algebra. The second part requires some knowledge of Fourier series and digital signal analysis. The connections between lifting and filter theory are presented and the wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals. The problems with finite length signals are treated in detail. MATLAB is used as the computational environment for examples and implementation of transforms. The book is well suited for undergraduate mathematics and electrical engineering students and engineers in industry. TOC:1. Introduction.- 2. A First Example.- 3. The Discrete Wavelet Transform via Lifting.- 4. Analysis of Synthetic Signals.- 5. Interpretation.- 6. Two Dimensional Transforms.- 7. Lifting and Filters I.- 8. Wavelets Packets.- 9. The Time-Frequency Plane.- 10. Finite Signals.- 11. Implementation.- 12. Lifting and Filters II.- 13. Wavelets in Matlab.- 14. Applications and Outlook.- References.- Index.