Faculty of Engineering and Science
The International Doctoral School of Technology and Science
March 4, 2005
The lectures dealt with the discrete Fourier transform and its properties.
I also presented the Uncertainty Principle in the discrete case
The material presented and its relation to the book
BNB, and comments on what to read, follows below:
- Section 6.1
- Covered in abbreviated form. The book contains a lot of
- Section 6.2
- Covered in detail. I also went through exercise 6.2.5, using the
book by Strang and Nguyen. See below.
- Section 6.3
- Section 6.4
- This material was covered using the book by Strang and
Nguyen. See below.
- The discrete uncertainty principle
- Covered using articles by Donoho et al., see below.
Additional Course Material
I have used the following additional course material:
- DFT and FFT: The pages 61-68 and 265-271 from Strang and Nguyen:
Wavelets and Filter Banks. Copies have been distributed.
- Uncertainty principles: I have used material from the following
These two papers contain a lot of material and are good starting
points, if you want to see how the uncertainty principles can be
used in signal recovery. They are somewhat more advanced than
- D. Donoho, P. Stark: Uncertainty principles and signal
SIAM J. Appl. Math. 49 (1989), no. 3, 906--931.
- D. Donoho, X. Huo: Uncertainty principles
and ideal atomic decomposition.
IEEE Trans. Inform. Theory 47 (2001), no. 7, 2845--2862.
Problem set 4
There will be no problem set 4 concerning the discrete Fourier transform.
The following exercise is suggested:
- Maple exercise
- Look at the way one can deal with the discrete Fourier transform
- Matlab exercise
- Compare the above with the possibilities in matlab.
Updated March 8, 2005, by Arne Jensen.