The Projection Theorem in Control and Signal Processing
Here you will find organizational matters, lecture notes and homework sets.
The lecture notes are made available in parts (because i'm writing them *now*).

HOME WORK SET 2 DEADLINE EXTENDED: HAND IN BEFORE THURSDAY 5 JULY

Organization

There will be two homework sets (each set counts for 20%) and one take-home exam (counting for 60-100%). The grade is determined by what is called the Magen rule. Lectures are scheduled for All lectures take place in room 442 (Lady Davis Bld).

Tentative schedule:
Time/Date Programme Comment
Monday 16 April, 15:30-18:30 Chapter 1 and 2 (upto page 10)
Monday 23 April....... No lecture this week
Monday 30 April, 17:30-20:30 Rest Chapter 2, sections 8.1 and 8.2, Chapter 9
Monday 7 May, 17:00-20:00 Chapter 3 (vector space) and Appendix (positive definite matrix) homework set 1
Monday 14 May, 17:00-20:00 Chapter 4 + a bit from Chapter 5
Monday 21 May Chapter 5
Monday 28 May Chapter 10
Monday 4 June Section 5.17, Chapter 6 and Sections 11.1, 11.2
Monday 11 June Rest Chapter 11
Monday 18 June Chapter 7 homework set 2
Monday 25 June Chapters 12 (which includes matched filters)
Monday 2 July Chapters 13 and 14 (jpeg and some wavelets) Take home exam is available (see at the end of this website)

Contents

The course lays the mathematical foundations of least squares and the more general projection theorem and then applies these ideas to a wide variety of problems from filtering, control and signal processing. The assignments will involve Matlab. Below is the list of covered chapters. A question mark means that the topic is covered only if time permits. The course splits into two parts: mathematical foundation and applications.

    Mathematical foundation:

  1. Intro: elementary geometry
  2. The dot product on Rn
  3. Vector space and subspace
  4. Linear transformations -- Operators
  5. Inner product, norm and orthogonal projection
  6. Fourier
  7. Intro to stochastic processes

    8. Applications:

  8. Least squares
  9. AR-models, Linear predictive coding
  10. Finite horizion LQ control
  11. H2-optimization
  12. Wiener filtering and matched filters
  13. JPEG -- two dimensional Fourier
  14. Orthogonal wavelets

Lecture notes

The current version of the notes is projectionstuff.pdf [latest version: 2 July; 173 pages; 1672 Kb.]

Change-log:

Homework and take-home exam

homework set 1 is available now.
homework set 2 is available now.
Take home exam is available now. You have to hand it in before Friday 20 July. You will also need these two files: coscos.m and leonid.jpg

Some matlab files

Probably I will make some matlab-files available here.