Digital Signal Processing (TSRT78)
Course Information, 2025HT
Course Description
Welcome to the course page of TSRT78!
Signal processing is about extracting information from sensors and other data generating sources providing a stream of numerical time series data. Available methods are either non-parametric for extracting trends or frequency information in the data, or model-based parametric methods that can gain further insights of the data generation mechanisms.
This course describes the most important methods and algorithms for signal processing, and the course covers basic theory with tools from algebra, complex analysis and statistics to examples of real-world applications.
Topics include: discrete Fourier transform (DFT), signal modelling (both in the frequency and in the time domain), model estimation, spectral estimation, Wiener filtering, Kalman filtering and adaptive filtering.
As a motivation, the wildlife lecture below shows some examples of how the course knowledge can be used to protect wildlife.
Course Structure
This course gives 6 HP (of which 1 HP are labs). The course structure is as follows:
- Lectures: 14 (including invited speakers from the industry)
- Exercises sessions: 12
- Labs: 2 mandatory labs
- Exam: Exam (4 hours), including both written and computer problems
Further information about the labs is available on Lisam under course TSRT78.
- The use of computers is highly integrated in the course and more than half of the exercises take place in ISY’s computer labs. More information about the computer labs is available here.
- The computer and Matlab are “allowed aids” during the exam. The exam takes place in ISY’s computer labs.
- All students will have personal accounts and in this way have unlimited access to the computer labs also outside the scheduled time. In order to enter the computer labs and Laboteket (where the two labs can be performed), you will need your LiU-card.
- Many of the exercise problems require the use of Matlab for solving. Matlab can be downloaded from the student portal.
Lectures
Examiner and lecturer is Fredrik Gustafsson,
E-mail: fredrik.gustafsson@liu.se
| Lecture | Contents | Chapter | |
|---|---|---|---|
| 1 | Introduction, frequency description of signals | 1, 2.1-2.5 | le1.pdf |
| 2 | Frequency description continued, DFT | 2.6-2.6 | le2.pdf |
| 3 | Introducing stochastic signals and spectral estimation | 3 | le3.pdf |
| 4 | Design and use of filters | 4 | le4.pdf |
| 5 | Signal models | 5 | le5.pdf |
| 6 | Estimating signal models | 6 | le6.pdf |
| 7 | Wiener filter | 7 + appendix | le7.pdf |
| 8 | Wiener filter continued, Kalman filter derivation | 7-8 | le8.pdf |
| 9 | Kalman filter, theory | 8 | le9.pdf |
| 10 | Kalman filter, practice | 8 | le10.pdf |
| 11 | Adaptive filtering, theory | 9 | le11.pdf |
| 12 | Adaptive filtering, practice | 9 | le12.pdf |
| 13 | Summary | - | le13.pdf |
| 14 | Guest lectures from NIRA and Oticon | - |
Exercises
Teaching assistant is Rasmus Uhlin,
E-mail: rasmus.uhlin@liu.se
| Topic | Exercises | Extra Exercises | Notes |
|---|---|---|---|
| 01 DFT | 2.1bc, 2.3a, 2.12, 2.22a | 2.7, 2.15, 2.20a, 3.6 | - |
| 02 DFT (C) | 2.3bc, 2.5, 2.10, 2.22b | 2.4, 2.6, 2.8, 2.20b | - |
| 03 Spectrum/Filtering (C) | 2.25, 3.2, 4.16, 4.18 | 3.1, 4.19, 4.21, 4.22 | - |
| 04 Signal Models | 5.3, 5.9, 5.11, 5.12 | 6.11, 6.15 | - |
| 05 Signal Models (C) | 6.5, 6.18, 6.7 | 6.4, 6.6, 6.13, 6.17 | - |
| 06 Wiener Filter | 7.2, 7.7 | 7.5, 7.6 | - |
| 07 Wiener filter and Kalman filter | 8.1, 8.6, 8.11 | 8.2, 8.9, 8.13 | - |
| 08 Wiener filter and Kalman filter (C) | 7.8, 8.15 | 7.9, 8.4 | - |
| 09 Kalman filter (C) | 8.3, 8.17 | 8.16, 8.18 | - |
| 10 Adaptive filtering (C) | 9.4, 9.6, 9.12a | 9.8, 9.9 | - |
| 11 Adaptive filtering (C) | 9.7, 9.13, 9.10 | 9.2 | - |
Course material
The course material consists of,
- Gustafsson, F., Ljung, L. and Millnert, M. “Signal Processing”, 2011. A reprint is for sale at “LiU Tryck” for 562 kr. The MATLAB functions for the book are available here.
- Gunnarsson, F., Tjärnström, F. and Gustafsson, F. “Signal Processing - Exercises”, 2010. The exercises are from 2025 available as a pdf for screen view, and can be downloaded here (download and open with Acrobat, it does not work in your browser preview) The data files for the exercises can be downloaded here.
- Lab instructions are available here.
The course books are not available at Studentlitteratur anymore. If you use that edition, a list of errata in the equations is available. The text book is printed and sold locally at the LiU Tryck (see link above). The list of errata for the textbook has been corrected in this version, which is the same as 2024.
The exercise book will not be printed anymore, and will only be available in digital form with a link from this page when available.
Mailing list
If you registered for the course you are automatically on the list
tsrt78_2025ht_6t@student.liu.se. Information may also be
announced using this list.