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SF2702 Wavelets, 6hp 

Kursansvarlig/föreläsare:Jan-Olov Strömberg, 
janolov@math.kth.se
tel. 08-790 6676 
(12 gånger under period 1 -2)
Kursstart Torsdag den 3 september kl.10.15.
Föreläsningslokal:   Seminarierum 3721, Lindstedtsv. 25
Kurslitteratur: Bergh/Ekstedt/Lindberg: Wavelets.[Säljes på Kårbokhandel .]
Föreläsningsanteckningar (delas ut) 
Hemuppgifter.  Dataövningar på Matlab
Examensform: Inlämningsuppgifter under kursens gång 


  Preliminary course outline 
Here is a link to an outline for 12 wavelet lectures as they were given in this course a few years ago. We will basically follow the same plan (but not absolutely strict).
Here is a list of relevant chapters in Bergh/Ekstedt/Lindberg's book.

  First meeting  (September 3)


In this first couse meeting the were given some introductatary information about the administration of the course. 
Also ther were given some very general and very short description of wavelets as wave packages  and some application of it to imageprocessing were demonstrated.

In this wavelet course we will assume that the students have some knowledge in two basic
areas in mathematics:  1. Linera algebra,  with basis systems , specially orthormal basis.
                                   
2. Fourier series  and/or Fourier transforms.

The students are assumed to have accress to Matlab during the course



Homework assignment 1 is available here. It is published here on September 9 and is supposed to be handed in within a couple of weeks



Homework assignment 2 is available here. It is published here on September 30 and is supposed to be handed in within a couple of weeks



Homework assignment 3 is available here. It is published here on November 5 and is supposed to be handed in within a couple of weeks



Homework assignment 4 is available here. It is published here on November 16 and is supposed to be handed in within a couple of weeks




Homework assignment 5 is available here. It is published here on November 25 and is supposed to be handed in within a couple of weeks



Lecture 2 (September 11)
We saw that the expansion of function with the Haar filter corresponds to
filter operations on the sequence space l^2 with two filter  the Lowpass filter
h = (1,1)/sqrt(2)    and the  Highpass filter g=(-1,1)/sqrt(2) , arranging the
iterated filter operation in the Wavelet filter tree .
The filter h  and g  generatate the translation invariant ON-sets {T^2k g}_k
resp.   {T^2k g}_k .  Those two ON-sets are mutually orthogonal and makes
together an ON- basis for l^2.  The  Low-  and High- pass filter operation can
be seen as changing coordinates system to this new ON-basis.
This change of coordinates can be seen as locally doing an 45 degree  in
many copies of  R².   By  repeated local rotations (with specially selected angles)
 one will construct longer filters h and g with will generate similar translation invariant ON-sets and ON- basis.
Usually one selects the rotation angles  so that the constructed filter fullfill some moment conditions.








Avdelning Matematik Sidansvarig: Jan-Olov Strömberg  
Uppdaterad: 2009-06-09