Wavelettransformer (5hp), HT 2008

Kurskod 1MA082.    Kursplan.    Start: 30 oktober 13.15

Lärare: Svante Janson

The exam is corrected.

All 4 that took the exam have passed. The exams can be collected from me at my office on Thursday or Friday.

The result for the student that wants the result on Internet is:
810519: 38, grade 5.

Kurslitteratur

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

Course content

Chapter 1 and Sections 4.1-4.4, 5.1-5.2 in Frazier 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

Some 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. 17 November.
  2. 27 November.
  3. 5 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 also given. Some of these will be discussed at later lectures.
  1. 30/10: The Discrete Fourier transform. §2.1. Exerc. 2.1.3, 2.1.6
  2. 4/11: 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
  3. 6/11: The Fast Fourier Transform. §2.3. Exerc. 2.3.2, 2.3.4, 2.3.6
  4. 10/11: First-stage wavelets on ZN. §3.1. Exerc 3.1.1-3.1.3, 3.1.5.
  5. 13/11: The iteration step. §3.2. Exerc. 3.1.13, 3.2.1, 3.2.5.
  6. 17/11: Discrete wavelet bases. Haar wavelets. §3.3. Exerc. 3.2.2, 3.2.6, 3.3.1.
  7. 20/11: More examples of discrete wavelets: Shannon and D4, D6. Problem solving.
  8. 24/11: l1(Z), l2(Z). The Fourier transform on Z and T. Convolution on Z. Wavelets on Z. (§4.1-4.4) 4.5-4.6. Exerc. 4.5.1, 4.5.3, 4.5.4, 4.6.2
  9. 27/11: The Fourier transform on R. Wavelets on R. (§5.1-5.2) 5.3-5.4.
  10. 5/12: §4.7, 5.5. Problem solving (mainly old exams).

Old exams (from a similar but larger course)

Further exercises (from an old, similar but larger, course)

Övningar 1
Övningar 2
Övningar 3
Övningar 4