MATH 648W / MAIT 679W

Topics in Harmonic Analysis:
Wavelet Theory and Waveform Design

Dr. John J. Benedetto

Fall 2008
University of Maryland, College Park

Lecture Recordings

Video recordings of the classroom lectures are available here. There's no streaming web interface; to view the lecture recordings, download the files to your hard drive first. The recordings should be viewable using Microsoft Media Player, however I recommend using the program avidemux, available here:

Avidemux is a free software video editing tool, but it also can be used as a video player. I prefer it over Media Player because avidemux updates the video window as you drag the slidebar, while Media Player doesn't update until you let go, so it's a lot easier to skim through the entire recording and find the part you want with avidemux. If you install it, you'll find two versions of the program available on the Start Menu; use the 'gtk' version (not the 'cli' version). Also, the first time you start the program, go to Edit/Preferences/Video and set Video display to DirectX, or else your performance will be lousy.

Lecture 1: 02sep2008a.avi (557 MB) 02sep2008b.avi (322 MB)
Note: This lecture is encoded in a slightly different format from the others.

Lecture 2: 09sep2008a.avi (594 MB) 09sep2008b.avi (413 MB)

Lecture 3: 16sep2008a.avi (646 MB) 16sep2008b.avi (382 MB)

Lecture 4: 23sep2008a.avi (452 MB) 23sep2008b.avi (474 MB)

Lecture 5: 07oct2008a.avi (607 MB) 07oct2008b.avi (264 MB)

Lecture 6: 14oct2008a.avi (466 MB) 14oct2008b.avi (488 MB)

Lecture 7: 21oct2008a.avi (695 MB) 21oct2008b.avi (271 MB)

Lecture 8: 28oct2008a.avi (460 MB) 28oct2008b.avi (406 MB)

Lecture 9: 04nov2008a.avi (427 MB) 04nov2008b.avi (399 MB)

Lecture 10: 11nov2008a.avi (622 MB) 11nov2008b.avi (339 MB)

Lecture 11: 18nov2008a.avi (608 MB) 18nov2008b.avi (460 MB)

Lecture 12: 25nov2008a.avi (679 MB) 25nov2008b.avi (306 MB)

Lecture 13: 01dec2008a.avi (155 MB) 01dec2008b.avi (179 MB)

Lecture 14: 09dec2008a.avi (550 MB) 09dec2008b.avi (404 MB)

Supplemental Materials

Brent Baccala's Hölder and Minkowski Inequalities (LaTeX source)

Benedetto and Zimmermann, Sampling multipliers and the Poisson Summation Formula, The Journal of Fourier Analysis and Applications, Volume 3, Number 5, 1997, pp. 505-523

Bruce Driver's Analysis Book; Minkowski's inequality for integrals is on p. 168

Christopher Heil's Basis Theory Primer; from the Preface:

This manuscript grew out of a set of notes originally prepared in 1987 at the instigation of my Ph.D. thesis advisor, Professor John Benedetto of the University of Maryland, College Park. At that time, the now-ubiquitous field of wavelets was in its infancy. An important goal of the new theory was the construction of "good" bases or basis-like systems called frames for function spaces such as L²(R). A solid understanding of basis theory was therefore needed, and these notes are the offspring of that need.

Gabor's original paper; proof of the Gabor inequality is on p. 440 (p. 12 in the PDF)

PDF slides from Emily King's talk

Georg Zimmermann's translation of Haar's 1910 paper