Department of Information Technology

# Spectral Processing of Signals

A schedule can be found here

## News:

2007-10-26: The fifth (and last) homework assignment has been corrected and is available in the out-box. You can see your results here.
2007-10-19: HW4 is now corrected and is available in the out box. The results are available online here. Note: You should NOT take the magnitude of the reconstructed signal when plotting it or using it to compute the MSE. Why so many people did this is a mystery to me...
2007-10-19: HW3 is now corrected and is available in the OUT-box. The results are available online here. (Note 1: Poles outside the unit circle does not matter when doing spectral analysis, since PSD = H(z)H^*(1/z^*). I.e., if the poles of H(z) are inside the unit circle, the poles of H^*(1/z^*) will be the mirrored poles of H(z) and thus outside the unit circle! Note 2: Always try to theoretically motivate your answers, e.g., if a method does not give proper results, explain why, do not just simply state that it does not work.)
2007-10-11: HW2 is now corrected and is available in the OUT-box. The results are available online here. (OBS: När ni studerar riktiga data så finns det inga exakta svar, utan det är era motiveringar som är det viktiga.)
2007-09-27: For HW2 you might want to use the file "armase.m" which handles the plotting of arma spectra. This function is available in the matlab package of the book, but it is "hidden" in the folder "extras" (or get it here).
2007-09-27: HW1 has been corrected, and is available in the OUT-box (no 45). The results are available online here. This time, we have not reduced the number of points for small errors in the frequency axis. Next time we will, so make sure you plot all spectra correctly!
2007-09-21: Note that some hints for the homeworks are available here.
2007-09-10: Suggestions for the applications to present on lecture 10 have been added.
2007-09-06: The name of the box on the 2nd floor in house 2 where you will put your homeworks is now Spectral proc. signals IN.
2007-08-21: Course homepage updated with most important info.

Course Level Study Period

## Educational programs:

Program Course Code Points Application Code
Engineering physics 1RT606 6hp 11807

## Goal:

To provide the student with the knowledge necessary to think in the "frequency domain" and to introduce the state-of-the-art methods and algorithms for computer-aided spectral analysis of temporal and spatial signals with applications in communications, signal analysis, radar systems, emitter location, signal recognition, and others. More information is available on this page.

Click to download a popular desciption of the course in ps or pdf format.

## Prerequisites:

Linear algebra, Fourier analysis, Discrete-time signals and systems.

## Contents:

1. Basic Definitions and the spectral estimation problem.
2. Periodogram and correlogram methods.
3. Improved periodogram-based methods.
4. Parametric methods for rational spectra.
5. Parametric methods for line spectra.
6. Filter-bank methods.
7. Spatial methods for array signal processing.

The course syllabus is available here. The course slides are available here (or locally in tar.gz-compressed format of in pdf format).

In lecture 10 the instructors will present several applications of spectral processing of signals. Similarly, the students have the possibility to get 20 credit points if they present short talks of approximately 20 minutes about some application of spectral processing of signals, either at their choice or by selecting one from the list below (NB: some of these paper might require being on the Uppsala University computer network in order to download):

## Homework assignments:

Periodogram methods C2.20/C2.22 Sept. 24 Here
Rational parametric methods C3.18/C3.20 Oct. 1 Here
Rational parametric methods for line spectra C3.17/C3.18 Oct. 8 Here
Parametric methods for line spectra C4.10/C4.14 Oct. 15 Here
Spatial methods C6.14/C6.17 Oct. 22 Here

(For information on the old/new book, see Literature below.)

The solutions should be put in the postbox marked Spectral proc. signals IN on floor 2 in house 2, and they will be returned via the adjacent OUT-box (box no:s 40 and 46).

Since the examination is based on the homeworks, discussing the solutions to the homework assignments with your colleagues or anybody else is strictly forbidden. Note that in grading the homework solutions we will put an emphasis on your interpretations of the results. Also, note that the deadlines are strict! This means that a homework which is handed in late may receive no points at all.

## Computer-Labs:

Lab Excercise (old/new book) Scheduled time Instructions
Periodogram methods C2.17/C2.19, C2.18/C2.20 Sept 18, 15-17 Lab1
Parametric methods for rational spectra C3.16/C3.17 Sept 20, 15-17 Lab2
Parametric methods for line spectra C4.9/C4.12 Sept 24, 13-15 Lab3
Filter bank methods C5.13/C5.13 Sept 28, 13-15 Lab4
Spatial methods C6.12/C6.15, C6.13/C6.16 Oct 9, 15-17 Lab5

(For information on the old/new book, see Literature below.)

The computer-labs are mandatory. If you for some reason cannot attend a specific session, please, contact the person responsible for the lab well in advance. If your absence was not predicted, make this contact as soon as possible. Make sure that you come prepared (see the course syllabus) for descriptions of the different lab sessions).

All computer labs are scheduled to be in room 2315 (house 2, 3rd floor) at Pollacksbacken.

IMPORTANT: For access to the PC-labs at the department, an account at UpUnet-S (the university computer network for students) is required. When logging in password C should be used! Make sure that you have this password! Information about UpUnet-S can be found at http://www.student.uu.se/upunets/.

From the computer labs at the IT-department you can access matlab scripts for all the labs (so you don't have to do any programming yourself). Those lab-files can be found in two ways. If you have a G: drive mounted when you log into the system you find the files under G:\Program\Systemteknik\Spektralanalys\. If you don't have G: mounted you can either mount it yourself (using "Map Network Drive") or you can find the files directly under "My Network Places"-"Entire Network"-"Microsoft Windows Network"-"It-Pclab"\Pegasus\Program\Systemteknik\Spektralanalys.

## Examination:

The students are required to pass all five labs. The exam consists of solving the five homework assignments. Each homework assignment gives a maximum of 20 points. The points required for the different grades are as follows.

For Master of Science students:

0-40 Fail
41-70 3
71-90 4
91-... 5

For PhD students: