Signal and Image Processing, 6 credits (TSBB14)

Signal- och bildbehandling, 6 hp

Main field of study

Biotechnology Electrical Engineering


First cycle

Course type

Programme course


Maria Magnusson

Director of studies or equivalent

Lasse Alfredsson
Course offered for Semester Period Timetable module Language Campus VOF
6CTBI Engineering Biology, M Sc in Engineering 5 (Autumn 2019) 1, 2 3, 3 Swedish Linköping o

Main field of study

Biotechnology, Electrical Engineering

Course level

First cycle

Advancement level


Course offered for

  • Engineering Biology, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.


One- and multidimensional calculus, Programming.

Intended learning outcomes

The course intends to give fundamental knowledge about signal and image processing. It is then used to solve application oriented problems in technique, medicine and biology. This means that a student which has taken this course is expected to be able to:

  • Describe basics regarding 1-D signal processing: deterministic signals, convolution, continuous and discrete linear systems, continuous and discrete Fourier transform, sampling and reconstruction, the sampling theorem, aliasing, basic filters (low-pass, high-pass, and band-pass).
  • Perform computations on signals and systems by using the following techniques: convolution, Fourier series, Fourier transform and z-transform (simple problems).
  • Describe basics regarding the generalization from 1-D to 2-D signal processing: Continuous and discrete Fourier transform with accompanying theorems, sampling and reconstruction, convolution, re-sampling and interpolation.
  • Interpret the result of a 2-D Fourier transform of an image, such as what is a spatial frequency? Be acquainted with the most common convolution kernels and describe their appearance in the spatial and Fourier domain, respectively.
  • Describe some classical operations for image processing such as histogram, thresholding and morphological operations. Understand how measurements such as area, length and perimeter can be performed in images.
  • Produce an oral and Power-Point presentation in English or Swedish of an application related to the theory described in the course.

Course content


  • 1-D signal processing: Signals and their characteristics. Fourier series. Convolution. The Fourier transform and its accompanying theorems. TDFT and DFT. The Dirac impulse. Sampling and reconstruction. The z-transform. 1D correlation. Continuous and discrete linear systems. System characteristics such as linearity, time invariance, causality and stability.
  • 2-D signal processing: From 1-D to 2-D Fourier transform. Continuous and discrete Fourier transform, TDFT and DFT. Sampling and reconstruction. Convolution and filtering, translation, scaling, derivative, rotation, and other linear operations on digital images. Convolution kernels in the spatial and Fourier domain, low-pass, high-pass, and derivative (sobel). Edge detection using the magnitude of the gradient. Re-sampling and interpolation. Histogram and thresholding. Binary image processing. 2-D correlation.
  • Application examples: Signal processing of ECG-signal, computed tomography (CT), ultrasound images, 3-D visualization, JPEG image compression, phase vocoder, resampling of images, and image analysis applications like "counting of blood cells", segmentation of cell kernels" and "measurements on plants".

Teaching and working methods

The course consists of lectures, lessons, laboratory assignments based on Matlab, and a group project concerning an application studied by literature and laboratory Matlab work. The group project is examined with an oral and Power-Point presentation in English or Swedish.
The course runs over the entire autumn semester.


LABALaboratory workU, G2.5 credits
TENAWritten examinationU, 3, 4, 53.5 credits


Four-grade scale, LiU, U, 3, 4, 5

Other information

Admission courses: Courses about signal processing, image processing, image analysis, computer vision, etc.


Institutionen för systemteknik

Director of Studies or equivalent

Lasse Alfredsson


Maria Magnusson

Education components

Preliminär schemalagd tid: 71 h
Rekommenderad självstudietid: 89 h

Course literature

Maria Magnusson, Kompendium i Signal- och bildbehandling

Compendium in signal- and image processing (in Swedish).


1) Lecture slides.

2) Extract on the z-transform from the book by Svärdström.

3) Lesson exercises.

4) Laboratory exercises.

5) Formula collection.

The literature above are available in pdf-format on the course home page.



Maria Magnusson, Kompendium i Signal- och bildbehandling

Compendium in signal- and image processing (in Swedish).


1) Lecture slides.

2) Extract on the z-transform from the book by Svärdström.

3) Lesson exercises.

4) Laboratory exercises.

5) Formula collection.

The literature above are available in pdf-format on the course home page.

LABA Laboratory work U, G 2.5 credits
TENA Written examination U, 3, 4, 5 3.5 credits

Course syllabus

A syllabus has been established for each course. The syllabus specifies the aim and contents of the course, and the prior knowledge that a student must have in order to be able to benefit from the course.


Courses are timetabled after a decision has been made for this course concerning its assignment to a timetable module. A central timetable is not drawn up for courses with fewer than five participants. Most project courses do not have a central timetable.

Interrupting a course

The vice-chancellor’s decision concerning regulations for registration, deregistration and reporting results (Dnr LiU-2015-01241) states that interruptions in study are to be recorded in Ladok. Thus, all students who do not participate in a course for which they have registered must record the interruption, such that the registration on the course can be removed. Deregistration from a course is carried out using a web-based form: 

Cancelled courses

Courses with few participants (fewer than 10) may be cancelled or organised in a manner that differs from that stated in the course syllabus. The board of studies is to deliberate and decide whether a course is to be cancelled or changed from the course syllabus. 

Regulations relating to examinations and examiners 

Details are given in a decision in the university’s rule book:

Forms of examination


Written and oral examinations are held at least three times a year: once immediately after the end of the course, once in August, and once (usually) in one of the re-examination periods. Examinations held at other times are to follow a decision of the board of studies.

Principles for examination scheduling for courses that follow the study periods:

  • courses given in VT1 are examined for the first time in March, with re-examination in June and August
  • courses given in VT2 are examined for the first time in May, with re-examination in August and October
  • courses given in HT1 are examined for the first time in October, with re-examination in January and August
  • courses given in HT2 are examined for the first time in January, with re-examination at Easter and in August.

The examination schedule is based on the structure of timetable modules, but there may be deviations from this, mainly in the case of courses that are studied and examined for several programmes and in lower grades (i.e. 1 and 2). 

  • Examinations for courses that the board of studies has decided are to be held in alternate years are held only three times during the year in which the course is given.
  • Examinations for courses that are cancelled or rescheduled such that they are not given in one or several years are held three times during the year that immediately follows the course, with examination scheduling that corresponds to the scheduling that was in force before the course was cancelled or rescheduled.
  • If teaching is no longer given for a course, three examination occurrences are held during the immediately subsequent year, while examinations are at the same time held for any replacement course that is given, or alternatively in association with other re-examination opportunities. Furthermore, an examination is held on one further occasion during the next subsequent year, unless the board of studies determines otherwise.
  • If a course is given during several periods of the year (for programmes, or on different occasions for different programmes) the board or boards of studies determine together the scheduling and frequency of re-examination occasions.

Registration for examination

In order to take an examination, a student must register in advance at the Student Portal during the registration period, which opens 30 days before the date of the examination and closes 10 days before it. Candidates are informed of the location of the examination by email, four days in advance. Students who have not registered for an examination run the risk of being refused admittance to the examination, if space is not available.

Symbols used in the examination registration system:

  ** denotes that the examination is being given for the penultimate time.

  * denotes that the examination is being given for the last time.

Code of conduct for students during examinations

Details are given in a decision in the university’s rule book:

Retakes for higher grade

Students at the Institute of Technology at LiU have the right to retake written examinations and computer-based examinations in an attempt to achieve a higher grade. This is valid for all examination components with code “TEN” and "DAT". The same right may not be exercised for other examination components, unless otherwise specified in the course syllabus.

Retakes of other forms of examination

Regulations concerning retakes of other forms of examination than written examinations and computer-based examinations are given in the LiU regulations for examinations and examiners,


For examinations that involve the writing of reports, in cases in which it can be assumed that the student has had access to other sources (such as during project work, writing essays, etc.), the material submitted must be prepared in accordance with principles for acceptable practice when referring to sources (references or quotations for which the source is specified) when the text, images, ideas, data, etc. of other people are used. It is also to be made clear whether the author has reused his or her own text, images, ideas, data, etc. from previous examinations.

A failure to specify such sources may be regarded as attempted deception during examination.

Attempts to cheat

In the event of a suspected attempt by a student to cheat during an examination, or when study performance is to be assessed as specified in Chapter 10 of the Higher Education Ordinance, the examiner is to report this to the disciplinary board of the university. Possible consequences for the student are suspension from study and a formal warning. More information is available at


The grades that are preferably to be used are Fail (U), Pass (3), Pass not without distinction (4) and Pass with distinction (5). Courses under the auspices of the faculty board of the Faculty of Science and Engineering (Institute of Technology) are to be given special attention in this regard.

  1. Grades U, 3, 4, 5 are to be awarded for courses that have written examinations.
  2. Grades Fail (U) and Pass (G) may be awarded for courses with a large degree of practical components such as laboratory work, project work and group work.

Examination components

  1. Grades U, 3, 4, 5 are to be awarded for written examinations (TEN).
  2. Grades Fail (U) and Pass (G) are to be used for undergraduate projects and other independent work.
  3. Examination components for which the grades Fail (U) and Pass (G) may be awarded are laboratory work (LAB), project work (PRA), preparatory written examination (KTR), oral examination (MUN), computer-based examination (DAT), home assignment (HEM), and assignment (UPG).
  4. Students receive grades either Fail (U) or Pass (G) for other examination components in which the examination criteria are satisfied principally through active attendance such as other examination (ANN), tutorial group (BAS) or examination item (MOM).

The examination results for a student are reported at the relevant department.

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at 

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