E9 213: Time-Frequency Analysis
Last offered: January - April 2016
References
L. Cohen, Time-Frequency Analysis. Prentice Hall, 1995.
S. Mallat, A Wavelet Tour of Signal Processing - The Sparse Way. Elsevier, Third Edition, 2009.
M. Vetterli, J. Kovacevic, and V. K. Goyal, Fourier and Wavelet Signal Processing. Book site: http://fourierandwavelets.org/terms.php
M. Unser, "Sampling - 50 Years After Shannon," Proceedings of IEEE, vol. 88, No. 4, April 2000. Download from: http://bigwww.epfl.ch/publications/unser0001.html
M. Unser, "Splines - A Perfect Fit for Signal and Image Processing," IEEE Signal Processing Magazine, pp. 22-38, Nov. 1999. Download from: http://bigwww.epfl.ch/publications/unser9902.html
D. Gabor, "Theory of communication," pp. 429-457, Proceedings of IEE, pp. 429-457, 1946. A scanned copy of this document is available for download from http://bigwww.epfl.ch/sekhar/gaborscannedpages.pdf
Course content
Local/global averages, Time-frequency distributions
[1] Chapters 1 - 9, Chapters 13 & 14; [2] Chapter 4 (Sections 4.1, 4.2, 4.4.1, 4.4.2, 4.5); Gabor transform ([5], Part 1 only)
Spaces and bases
Hilbert spaces, Banach spaces ([2], Appendix on mathematical complements), Riesz bases [2,3], Biorthogonal bases, orthogonal bases, orthonormal bases - ([2], Appendix on mathematical complements), Shift-invariant spaces [3], Basis-splines [3], Frames: [2] Chapter 5 (definitions of frame and dual frame), Sections 5.3 and 5.4
Wavelets
[2] Chapter 4 (Section 4.3), Chapter 5 (Section 5.2), Chapter 7 (Sections 7.1 to 7.4)
Computational resources
Time-frequency toolbox (MATLAB) is available for download from http://tftb.nongnu.org/