Mathematics for signal and image processing
20102011

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.
Topic(s)
 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
Lectures
Laboratory work
Net Support Learning
Exercises
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 offcampus students. Lecture notes, electures and other types of elearning 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
Resit examination
Resit examination of oral exam by appointment with the course responsible. No resit 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
REA4003
Additional information
100% overlap to REA4003.