Linear difference equations, characteristic equation, Discrete-time Fourier transfom, one- and double-sided z-transform, discrete-time systems and system properties, impulse response and convolution, transfer and frequency function, sine-in-sine-out, poles and zeros, stability criteria for discrete-time systems, sampling and reconstruction by pulse amplitude modulation, the sampling theorem, system realizations in Matlab.
EQ1120 Discrete Time Signals and Systems 6.0 credits
Linear difference equations. characteristic equation, discrete-time Fourier transform, single and double sided Z-transform, discrete-time systems and system properties, impulse response, convolution, transfer function, frequency function, sinus in sinus out, poles and zeroes, stability criteria for discrete time systems, sampling and reconstruction by pules amplitude modulation, sampling theorem, system realizations in Matlab.
The aim is to provide basic knowledge about discrete-time signals and systems, how they can be described and analyzed by using difference equations and transform methods, and be implemented in software like Matlab.Linear difference equations. characteristic equation, discrete-time Fourier transform, single and double sided Z-transform, discrete-time systems and system properties, impulse response, convolution, transfer function, frequency function, sinus in sinus out, poles and zeroes, stability criteria for discrete time systems, sampling and reconstruction by pules amplitude modulation, sampling theorem, system realizations in Matlab.
The aim is to provide basic knowledge about discrete-time signals and systems, how they can be described and analyzed by using difference equations and transform methods, and be implemented in software like Matlab.
Information per course offering
Choose semester and course offering to see current information and more about the course, such as course syllabus, study period, and application information.
Information for Spring 2025 Start 17 Mar 2025 programme students
- Course location
KTH Campus
- Duration
- 17 Mar 2025 - 2 Jun 2025
- Periods
- P4 (6.0 hp)
- Pace of study
33%
- Application code
60175
- Form of study
Normal Daytime
- Language of instruction
Swedish
- Course memo
- Course memo is not published
- Number of places
Places are not limited
- Target group
- No information inserted
- Planned modular schedule
- [object Object]
- Schedule
- Schedule is not published
Contact
Joakim Jalden (jalden@kth.se)
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus EQ1120 (Autumn 2021–)Content and learning outcomes
Course contents
Intended learning outcomes
The course gives basic knowledge of discrete-time signals and systems and how these can be described and analysed by using difference equations and transform methods and be implemented in software such as Matlab.
After approval in the course the student should be able to
- solve simple linear difference equations with and without initial conditions
- be able to implement and simulate discrete-time systems in Matlab numerically
- give an account of the definition and the meaning of system properties such as linearity, time invariance, causality and stability
- describe linear and time invariant systems by means of their impulse response, and through convolution be able to calculate the output signal for a system given an input signal
- calculate the discrete-time Fourier transform and its inverse for given signals based on definition and general properties for transforms
- calculate the double- and the one-sided z-transform for a given signal, use these transforms to solve difference equations and output signals of systems and through partial fraction decomposition and tables be able to recover the time domain description of solutions and output signals
- interpret the placements of poles and zeros in terms of the frequency domain properties of the discrete-time system
- decide the stability of causal LTI systems through the placement of the poles
- give an account of the concepts sampling and reconstruction through pulse amplitude modulation
- describe folding in the time and frequency domain
- describe the spectrum of a sampled signal in terms of the spectrum of the original signal and give an account of the importance of the Nyquist criterion (the sampling theorem)
- calculate the total transfer function for a sampled system
- describe in speech and writing how a system solves a given signal processing task
For higher grades, the student should also be able to
- demonstrate an understanding of the relationships between the different descriptions of discrete-time systems and their properties in the time and transform domain
- be able to choose appropriate solution methods for a given problem
- combine different concepts and methods from the course and apply them on more complex mathematical and technical problem formulations
Literature and preparations
Specific prerequisites
Knowledge in one variable calculus, 7.5 higher education credits, equivalent to completed course SF1625.
Active participation in a course offering where the final examination is not yet reported in LADOK is considered equivalent to completion of the course. Registering for a course is counted as active participation. The term 'final examination' encompasses both the regular examination and the first re-examination.
Recommended prerequisites
SF1624 Algebra and geometry
EQ1110 Continuous time signals and systems
Equipment
Literature
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- PRO1 - Project Work, 1.0 credits, grading scale: P, F
- PRO2 - Project Work, 1.0 credits, grading scale: A, B, C, D, E, FX, F
- TEN1 - Exam, 4.0 credits, grading scale: A, B, C, D, E, FX, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Other requirements for final grade
Approved examination in all course components.
Final mark is combined 80% based on TEN1 and 20% based on PRO2
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Offered by
Main field of study
Education cycle
Add-on studies
EL1??? Feedback systems
EQ1270 Stochastic signals and systems
Contact
Supplementary information
In this course, the EECS code of honor applies, see: http://www.kth.se/en/eecs/utbildning/hederskodex.