Course Content
Introduction to time frequency analysis; the how, what and why about wavelets. Short-time Fourier transform, Wigner-Ville transform. Continuous time wavelet transform, Discrete wavelet transform, tiling of the time-frequency plane and wavepacket analysis. Construction of wavelets. Multiresolution analysis. Introduction to frames and biorthogonal wavelets. Multirate signal processing and filter bank theory. Application of wavelet theory to signal denoising, image and video compression, multi-tone digital communication, transient detection.
Text / References
- 1 Y.T. Chan, Wavelet Basics, Kluwer Publishers, Boston, 1993.I. Daubechies, Ten Lectures on Wavelets, Society for Industrial and Applied Mathematics, Philadelphia, PA, 1992.C. K. Chui, An Introduction to Wavelets, Academic Press Inc., New York, 1992. Gerald Kaiser, A Friendly Guide to Wavelets, Birkhauser, New York, 1995.P. P. Vaidyanathan, Multirate Systems and Filter Banks, Prentice Hall, New Jersey, 1993. A.N. Akansu and R.A. Haddad, Multiresolution signal Decomposition: Transforms, Subbands and Wavelets, Academic Press, Oranld, Florida, 1992. B.Boashash, Time-Frequency signal analysis, In S.Haykin, (editor), Advanced Spectral Analysis, pages 418--517. Prentice Hall, New Jersey, 1991.