Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
|Fourier series and transforms, the Shannon sampling theorem|
|Discrete Fourier, cosine, and sine transforms|
|Karhunen-Loeve transform and principal component analysis|
|Frames and sparse representations|
|The uncertainty principle|
|Windowed (or short-time) Fourier transform|
|Gabor (Weyl-Heisenberg) systems|
|Continuous and Discrete wavelet algorithms|
|Multiresolution analysis and fast wavelet algorithms|
|Applications to signal/image processing and communication|
- S. Mallat, A Wavelet Tour of Signal Processing, 3rd Ed., Academic Press, 2009.
- I. Daubechies, Ten Lectures on Wavelets, SIAM, 1992.
- S. Jaffard, Y. Meyer, and R. Ryan, Wavelets: Tools for Science and Technology, SIAM, 2001.
- K. Groechenig, Foundations of Time-Frequency Analysis, Birkhauser, 2001.
- W. L. Briggs and V. E. Henson, The DFT: An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995.