MMA410 course diary

Course diary

Here I will try to keep an updated account of what has been done so far in the course.

date what we did comments

27/10

This was just an introduction to some of the topics of the course, corresponding to page 1-7 of the lecture notes.

28/10

This lecture corresponds to page 7.5-12 of the lecture notes: some basic properties of the Fourier transform, and the function class S.

30/10

This lecture corresponds to page 13-20 of the lecture notes, except that I did not say very much about the note on page 14. The exercise on page 14.5 will be covered in exercise classes, as will the example on p. 15.
please make a detailed proof that DT is a tempered distribution (see p. a18)

1/11-10-11

the diary for these days have been lost ... if anyone has copied them, please send me a mail.

10/11

The discrete Fourier transform

11-13/11

We studied more properties of the DFT, and the Fast Fourier Transform.

Note that there is an error in the lecturenotes concerining the down-sampling and addition theorems.

14/11

17/11

We worked through the Heisenberg uncertainty relation. Then: discrete signals, filters, the DFT and Z-transform, linear time invariant filters, FIR and IIR filters. The lecture corresponds to pp. 51-57 in the lecture notes

20/11

The full morning was dedicated to filter banks: the Haar basis, perfect reconstruction, orthogonal filter banks. In the lecture notes, pp. 58-69.

24/11

Beginning of Multi Resolution Analysis and Wavelet analysis of functions: Closed subspaces of Hilbert spaces, projections, definition of an MRA. In the lecture notes: pp. 70-77.

27/11

We covered MRA, scaling functions and scaling equations, the direct sum of vector subspaces, wavelet expansion of functions in L², orthogonal wavelets, and conditions on the scaling equation that lead to orthogonal wavelets. We also covered the continuous wavelet transform.

1/12

4/12

Fourier transforms in higher dimension; homogeneous functions and distributions; the Hankel transform; the Abel transform and the Radon transform.

date	what we did	comments
27/10	This was just an introduction to some of the topics of the course, corresponding to page 1-7 of the lecture notes.
28/10	This lecture corresponds to page 7.5-12 of the lecture notes: some basic properties of the Fourier transform, and the function class S.
30/10	This lecture corresponds to page 13-20 of the lecture notes, except that I did not say very much about the note on page 14. The exercise on page 14.5 will be covered in exercise classes, as will the example on p. 15.	please make a detailed proof that DT is a tempered distribution (see p. a18)
1/11-10-11	the diary for these days have been lost ... if anyone has copied them, please send me a mail.
10/11	The discrete Fourier transform
11-13/11	We studied more properties of the DFT, and the Fast Fourier Transform.	Note that there is an error in the lecturenotes concerining the down-sampling and addition theorems.
14/11
17/11	We worked through the Heisenberg uncertainty relation. Then: discrete signals, filters, the DFT and Z-transform, linear time invariant filters, FIR and IIR filters. The lecture corresponds to pp. 51-57 in the lecture notes
20/11	The full morning was dedicated to filter banks: the Haar basis, perfect reconstruction, orthogonal filter banks. In the lecture notes, pp. 58-69.
24/11	Beginning of Multi Resolution Analysis and Wavelet analysis of functions: Closed subspaces of Hilbert spaces, projections, definition of an MRA. In the lecture notes: pp. 70-77.
27/11	We covered MRA, scaling functions and scaling equations, the direct sum of vector subspaces, wavelet expansion of functions in L², orthogonal wavelets, and conditions on the scaling equation that lead to orthogonal wavelets. We also covered the continuous wavelet transform.
1/12
4/12	Fourier transforms in higher dimension; homogeneous functions and distributions; the Hankel transform; the Abel transform and the Radon transform.