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TSDT14 Signal Theory

Course Program Autumn 2017



Separate pages

General         General
Time         Time
Teachers and Staff         Teachers and Staff
Course Litterature         Course Litterature
Examination         Examination
Lectures         Lectures
Tutorials         Tutorials

1. General

TSDT14 Signal Theory is an introductory course in signal processing, dealing with both time-continuous and time-discrete signals, that are both deterministic and stochastic, real and complex. The focus is on stochastic signals. The signal processing systems are usually linear and time-invariant, but we also consider some momentary non-linear systems. One part of the course deals with multi-dimensional processes, where we concentrate on two-dimensional processes. We also consider traditional analog modulation methods and perform noise analysis of them. We are especially interested in transformations between time-continuous and time-discrete signals. A part of the course is estimation of power spectral densities using Fourier methods, where DFT is used. Signal Theory is a basis for further studies in signal processing, e.g. Tele(data)-communication, image processing, automatic control, et. cetera.

If you are reading a paper copy of this course program:
There is more information on the course web site: www.commsys.isy.liu.se/TSDT14. Among other things, you will find this course program there.

2. Time

Lectures: 12 × 2 h = 24 h
Problem Classes: 12 × 2 h = 24 h
Laborations: 4 × 2 h = 8 h

3. Teachers and Staff

During autumn 2016, the following people are involved in this course.

Lectures and Examination: Mikael Olofsson
tel. 281343
In English.
Tutorials: Mikael Olofsson
tel. 281343
Group A
  Håkan Johansson
tel. 281000
Group B
  Zheng Chen
tel. 282643.
Group C
Administrator Carina Lindström
tel. 284423

Those people are all i Building B, top floor, Corridor A, between entrances 27 and 29.

4. Course Litterature

The following litterature will be available at the two bookshops on campus.

  • Mikael Olofsson, Signal Theory, Studentlitteratur, 2011.
  • Mikael Olofsson, Tables and Formulas for Signal Theory, Studentlitteratur, 2011.

The following can be downloaded here.

Some additional material may be published on the course web later on.

5. Examination

The examinationen consists of two parts, that are reported separately to LADOK:

  • TEN1 (4 hp), which is a traditional written exam, and
  • LAB1 (2 hp), which consists of four lab assignments which is examined with a report.

For detailed information about the connection between the course aims and the examination, see the following page.

5.1 Written Exam (TEN1)

The written exam consists of two parts. First, there is a task with three simple subtasks that examine the following aims:

  • be able to clearly define central concepts regarding stochastic processes, using own words.
  • be able to reliably perform standard calculations regarding stochastic processes, e.g. LTI filtering (both time continuous and time discrete), sampling and pulse amplitude modulation.
  • be able to reliably perform standard calculations regarding stochastic processes being exposed to certain momentary non-linearities that are common in telecommunication, especially uniform quantization and monomial non-linearities of low degrees.

At least two of these three subtasks have to be solved correctly as a partial fulfillment to pass the written exam.

Then there are five tasks that are graded. Those tasks examine the following aim:

  • with some reliability be able to solve problems that demand integration of knowledge from different parts of the course.

The degree of difficulty of those tasks is as the most extensive tasks in the problem material. The solutions are given at most 5 points per task, i.e. you can at most get 25 points. Grading limits:

  • Grade 3 (pass): 10 points
  • Grade 4: 15 points
  • Grade 5: 20 points

The grade given for the exam is also the final grade for the course when both the written exam and the laborations are passed.

Allowed aids on the written exams:

  • Olofsson: Tables and Formulas for Signal Theory.
  • All kinds of pocket calculators, with empty memory.
  • A German 10-Mark note of the fourth series (1991-2001).
5.2 Laborations (LAB1)

The laborations are based on the Lab-Memo Time-Discrete Stochastic Signals, that you can download from the course webpages. The laborations examine the aims

  • be able to account for the connection between different concepts in the course in a structured way using adequate terminology.
  • be able to estimate the auto correlation function and power spectral density of a stochastic process based on a realization of the process. Also, clearly and logically account for those estimations and conclusions that can be drawn from them.

The laborations consist of the following four tasks:

  • Study 1: Modelling Signals
  • Study 2: Improving Spectrum Estimates
  • Study 3: Non-LTI-Systems
  • Study 4: Special Operations

Those tasks are solved in groups of two students, either on their own or at the scheduled lab occations. We recommend the latter. Each group is allowed to sign up for one two-hour occation per study. You can expect that you need to do additional work on your own to finish the labs.

You pass the laborations based on a report that is sent in to the examiner Mikael Olofsson, as a PDF document by email to

The lab report should be sent in no later than the last day in the exam period in October. Any additional details can be provided during HT2. Please include the course code TSDT14 and your LiU IDs in the filename. That simplifies our work.

For more instructions, see the Lab Memo.

6. Lectures

The plan below should be interpreted as an indication about approximately when the various course parts will be treated.

Lecture Contents Reference, Olofsson Extra-material
1 Introduction. Notation. Brief repetition of Signals and Systems, and stochastic variables. 2-3
2 Stochastic signals. 4.1-4.9
3 LTI filtering. White noise. Colored noise. 4.10-4.11, 5.1-5.3
4 Estimation. 10
5 Various: Cross-Correlation, Cross-Spectrum, Poisson processes. Prediction. 4.12, 5.4
6 Polynomial non-linearities. 7.1-7.4
7 Saturation and Quantization. 7.5-7.6
8 Modulation. AM, PM, FM. 8
9 Sampling and PAM. 6.1-6.2
10 Reconstruction. 6.3-6.4, 11
11 Multi-Dimensional Processes and Systems. 9
12 Complex processes. Yes

The extra material for lecture nine will be distributed in paper form, either before or at that lecture.

My recommendation is that you read the corresponding part of the course material through once before each lecture. If not, the lecture may not be as useful to you as you might wish.

7. Tutorials

These are suggested tasks, from the course book, suitable to solve during the tutorials in Signal Theory. Tasks in parentheses are recommended for home studies. All tasks in the book are good problems for the course. You should see this list as a suitable selection.

Tutorial Contents Examples
1 Repetition Signals & Systems 2.5b, 2.13b, 2.16c, 2.17c, 2.18c,
(2.4, 2.6b, 2.8, 2.22, 2.23)
Repetition Stochastic Variables 3.1, 3.5, 3.9, 3.15, (3.4, 3.14)
2 Stochastic Signals 4.2, 4.3, 4.4, 4.9, 4.10, 4.16, 4.17, (4.5, 4.6, 4.7, 4.12, 4.13, 4.14)
3 LTI Filtering, Time-Continuous 5.1, 5.3, 5.4, 5.5, 5.7, 5.12, 5.15, (5.2, 5.8, 5.11, 5.13, 5.17)
4 LTI Filtering, Time-Discrete 5.18, 5.20, 5.21, 5.22, 5.24, 5.25, (5.19, 5.23, 5.26, 5.27, 5.28)
5 Cross correlation & spectrum 5.9. More problems, see below.
Poisson processes Extra problem P1
Prediction 5.29, TSIT64/65 2001-04-24:3
Cross correlation and prediction Extra tasks
6 Non-linear filtering 7.1, 7.3, 7.5, 7.7, 7.10 (7.2, 7.6, 7.8, 7.9)
7 Non-linear filtering 7.11, 7.12, 7.13, 7.15
8 Modulation 8.1, 8.3, 8.4, 8.6 (8.2, 8.5)
9 Sampling and PAM 6.1, 6.3, 6.5, 6.6, 6.8, 6.9 (6.2, 6.4, 6.7)
10 Reconstruction 6.11, 6.12, 6.13
11 Multi-Dimensional Processes 9.1, 9.2, 9.5, 9.6, 9.9, (9.3, 9.4, 9.7, 9.10)
12 Complex processes. Will be distributed later.


Questions about solutions before the tutorials are welcome, and can be sent to your tutorial teacher (  ,  , or  ), via email, no later than the day before the tutorial. In that way you can help your teacher to plan the tutorials, and you may have more use of the tutorials.

Page responsible: Mikael Olofsson
Last updated: 2017 08 22   14:50