DT1130 Spectral Transforms 7.5 credits

Spektrala transformer

This course aims to give the participants basic understanding and experience of methods and applications of spectral transforms used in many types of advanced media technology, in areas such as speech- and music technology, audio technology, image processing and computer vision. The practical coursework is mostly done in Matlab, which gives the partcipants skills that will be of use also in other fields of engineering work.

  • Education cycle

    First cycle
  • Main field of study

  • Grading scale

    A, B, C, D, E, FX, F

Course offerings

Autumn 18 for programme students

Autumn 17 for programme students

Intended learning outcomes

The student should after the course be able to

    * analyse audio signals using spectrum/spectrogram and explain relations between spectrum, analysis window length, analysis bandwidth and resolution in time and frequency domains

    * explain and calculate the consequences of sampling and quantisation of analogue signals

    * express signals mathematically in terms of complex phasors, and utilise fourier series to describe periodic signals

    * analyse simple linear systems using the Z-transform, and calculate various properties of theese such as filter equation, transfer function, pole- and zero configuration, magnitude response and impulse response and relate these to each other

    * explain and apply convolution of signals in one and two dimensions

    * explain function and scope of use, and numerically compute the discrete fourier transform, and state the basic principle and computational properties of the FFT algorithm

    * account for basic principles and algorithms used in filtering and spectrally based compression of images

    * use Matlab for general computation and visualisation task, especially filtering and spectral treatment of sounds and images.

Course main content

Oscillations and complex phasors. Time-discrete signals, quantiszation and sampling. Linear systems, digital filters with and without feedback. Impluse response and step response. Frequency response and transfer function. Convolution. Z-transform. Periodic signals and fourier series. Dicrete fourier transform, FFT. Spectrum and spectrogram. Windowing. Source-filter models. Formants and fundamental frequency. Filtering, convolution and transforms in two dimensions. Discrete cosine transform and JPEG-based image compression.


For single course students: completed upper secondary education including documented proficiency in Swedish corresponding to Swedish B, English corresponding to English A. Furthermore: 15 hp in mathematics.

Recommended prerequisites

For those already studying at KTH: The courses SF1625 Calculus in One Variable and SF1624 Algebra and Geometry or corresponding.


Will be announced at least 4 weeks before the course starts at the web page for the course.


  • LABA - Laboratory Work, 3.0, grading scale: A, B, C, D, E, FX, F
  • TEN1 - Examination, 4.5, grading scale: A, B, C, D, E, FX, F

In this course all the regulations of the code of honor at the School of Computer science and Communication apply, see: http://www.kth.se/csc/student/hederskodex/1.17237?l=en_UK.

Requirements for final grade

One written examination (4,5 university credists) and a laboratory course (3 university credists) with two mandatory lab assignments and one programming assignment.

Offered by

CSC/Speech, Music and Hearing


Jonas Beskow, tel: 790 8965, e-post: beskow@kth.se


Jonas Beskow <beskow@kth.se>

Add-on studies

DT2212 Speech Technology Extended Course, DT2213 Musical Communication and Music Technology, DT1410 Audio Technology.


Course syllabus valid from: Autumn 2009.
Examination information valid from: Autumn 2014.