Wavelettransformer (5hp), HT 2011

Kursstart: 26 oktober 15.15.

Kurskod 1MA082.

Kursplan.        Studentportalen

Lärare: Svante Janson

Kurslitteratur

"Formelsamling" (Formulae) and "Ordlista" (Vocabulary) may be used at the exam (but not Frazier).

Course content

The course consists essentially of Chapters 2, 3 and 4.5-4.7, 5.3-5.5 in Frazier.

Chapter 1 and 4.1-4.4, 5.1-5.2 contain background material from linear algebra and Fourier analysis. You should be able to use methods and results from those parts, but you are not required, for example, to prove any of them.

Chapter 6 is not part of the course.

Schedule        This week

Exam

Check exam schedule for changes.

Homework

Three homework assignments will be given. These form part of the examination, and should be solved individually. Correct solutions will give bonus points on the exam (up to 3 bonus points per set, i.e., total maximum 9). Solutions can be given to me at lectures, or in my mailbox at Ångström (floor 4), at the latest on the days shown below.
  1. 18 November.
  2. 30 November.
  3. 14 December.

Lectures

Here is a rough list of contents for the lectures, with approximate indications of sections in the textbook. Recommended exercises from Frazier are often given. They will be solved at a later lecture (marked PROBLEM SOLVING).
  1. 26/10: The Discrete Fourier transform. §2.1.
  2. 28/10: The Discrete Fourier transform. §2.1. Exerc. 2.1.3, 2.1.6
  3. 31/10: Translation invariant linear operators. §2.2. Exerc. 2.2.1, 2.2.2, 2.2.3, 2.2.9, 2.2.11, 2.2.16
  4. 10/11: The Fast Fourier Transform. §2.3. Exerc. 2.3.2, 2.3.4, 2.3.6
  5. 11/11: PROBLEM SOLVING.
  6. 15/11: First-stage wavelets on ZN. §3.1. Exerc 3.1.1-3.1.3, 3.1.5.
  7. 18/11: The iteration step. §3.1-3.2. Exerc. 3.1.13, 3.2.1, 3.2.2.
  8. 23/11: Discrete wavelet bases. Examples: Haar, Shannon and D6 wavelets. §3.2-3.3. Exerc. 3.2.5, 3.2.6, 3.3.1.
  9. 25/11: More on discrete wavelets. §3.2-3.3. PROBLEM SOLVING Exerc. 3.1.12, 3.2.12, 3.3.2, 3.3.4.
  10. 28/11: PROBLEM SOLVING
  11. 30/11: l1(Z), l2(Z). The Fourier transform on Z and T. Convolution on Z. First-stage wavelets on Z. (§4.1-4.4) 4.5. Exerc. 4.5.1, 4.5.3, 4.5.4.
  12. 2/12: The iteration step. Wavelet bases on Z. 4.6. Exerc 4.6.2.
  13. 7/12: The Fourier transform on R. Wavelets on R. (§5.1-5.2) 5.3-5.4. Exerc. 5.3.3, 5.3.5, 5.3.9, 5.3.13.
  14. 8/12: Wavelets with compact support on R. 5.4-5.5. Exerc. 5.4.3, 5.4.5, 5.5.5.
  15. 12/12: PROBLEM SOLVING Exam 2008-12-16.