Single-Course English 5 ECTS

Signals and linear systems in discrete time

Overall Course Objectives

The general goal of the course is to introduce theory, analysis, and synthesis of discrete-time signals and systems, as they are used and needed for a broad variety of computer-based DSP applications. The students will make quantitative estimations as well as detailed written calculations. Exemplary technical applications will be examined in exercises and in Matlab simulations. Formative feedback will be given on submitted assignments.

Learning Objectives

  • explain the principles of sampling of continuous-time signals.
  • explain the connections and differences between the Fourier transform, the time-discrete Fourier transform and the discrete Fourier transform.
  • implement algorithms for the calculation of recursive and non-recursive filters in Matlab.
  • convert continuous-time filters into discrete-time filters using the bilinear transform.
  • use a spectrogram to analyse the time/frequency content of a signal.
  • calculate the spectral density of a stochastic signal.
  • analyse discrete-time signals and discrete-time systems in the time-, frequency- and z-domain.
  • design recursive and non-recursive digital filters
  • judge which sampling frequency, quantization depth and filter type is necessary to fulfill a simple problem specification.
  • implement computer programs and visualise results using Matlab.
  • apply English terminology in digital signal processing and write reports in English.
  • extract and combine information from different literature sources

Course Content

As an extension of course 31605/22050, Continuous-Time Signals and Linear Systems, this course introduces linear discrete-time signals and systems, digital filters and adaptive linear neural networks from a technical perspective. The algorithms can be applied to various fields of linear digital signal processing: acoustics, telecommunication, biomedical engineering, control theory. The following topics will be covered:
– Time-domain analysis and difference equations,
– Sampling theorem,
– Discrete-time Fourier transform (DTFT),
– Fast Fourier transforms (FFT),
– z-transform,
– IIR and FIR digital filters,
– The short-time Fourier transform
– Spectral density of a stochastic signal
– Noise reduction

Recommended prerequisites

31605/22050, The course is a continuation of course 22050 (previously 31605). Equivalent knowledge is expected for participation.
Prior knowledge in Matlab or another programming language (e.g. C) is beneficial.

Teaching Method

Lectures, Matlab or Python computer exercises


Matlab will be utilized in the course. Prior knowledge in Matlab or another programming language (e.g. C) is beneficial but not strictly required. Additional material will be provided if required.

E-learning is used in the form of podcast lectures, on-line quiz (home assignments), chat room, discussion board/blog, electronic correction system, web-based tools and digital whiteboard.

See course in the course database.





13 weeks


Health Tech


DTU Lyngby Campus

Course code 22051
Course type Bachelor
Semester start Week 35
Semester end Week 48
Days Thurs 13-17

7.500,00 DKK