Mathematics for signal and image processing
2010-2011 - IMT4991 - 5 ECTS

On the basis of

The following topics must be mastered:

  • Fundamental calculus including trigonometric functions, logarithms and the exponential function
  • Fundamental linear algebra
  • Fundamental complex calculus including the complex exponential function
  • Series

These topics are more than covered by the following courses:

  • REA1042 Mathematics 10
  • REA1051 Mathematics 15
  • REA2051 Mathematics 20

Expected learning outcomes

Having completed the course, the students will

  • Have knowledge and understanding of the mathematical methods commonly used for representing, compressing and processing signals and images.
  • Be able to apply the mathematical techniques to simplified problems with relevance to signal and image processing.
  • Be able to implement the mathematical methods in suitable programming languages.


  • Vector spaces, signals, and images
  • The discrete Fourier transform (DFT)
  • The discrete cosine transform (DCT)
  • Convolution and filtering
  • Filter banks
  • Wavelets and the discrete wavelet transform (DWT)

Teaching Methods

Laboratory work
Net Support Learning

Teaching Methods (additional text)

The course will be offered both as an ordinary campus course and as a course that is offered in a flexible way to off-campus students. Lecture notes, e-lectures and other types of e-learning material will be offered through an LMS. Communication between the teachers and the students, and among the students, will be facilitated by the LMS.

Form(s) of Assessment

Portfolio Assessment
Oral exam, individually

Form(s) of Assessment (additional text)

  • Portfolio (counts 60%)
  • Oral, individual exam (counts 40%)
  • Both parts must be passed

The portfolio consists of up to 6 assignments and is handed in individually. There is continuous assessment of each of the assignments before the final submission date of the portfolio. The portfolio will be given one single grade.

Grading Scale

Alphabetical Scale, A(best) – F (fail)

External/internal examiner

Two internal examiners

Re-sit examination

Re-sit examination of oral exam by appointment with the course responsible. No re-sit examination of the portfolio.

Teaching Materials

Broughton, S. Allen and Kurt Bryan (2008). Discrete Fourier Analysis and Wavelets - Applications to Signal and Image Processing. New Jersey: John Wiley & Sons, Inc.

Replacement course for


Additional information

100% overlap to REA4003.