Discrete-time signal processing

Brief description

Influence of clock rate conversion with non-ideal filters

The lecture Discrete Time Signal Processing provides an introduction to elementary techniques of digital signal processing. Particular emphasis is placed on a description that is as clear and practice-orientated as possible. Students gain their own practical experience in the exercises through the use of Python.

Lecture contents

Discrete-time signals: elementary signals, even/odd signals, harmonic exponential oscillations
Fourier series of periodic discrete-time signals: Parseval theorem, symmetry relations
Discrete-time systems: LTI, impulse response
Fourier transform of discrete-time signals
Sampling theorem
Difference equations and z-transform
FIR and IIR filter design
DFT, FFT
Cyclic convolution, overlap-add and overlap-save
Multirate signal processing

Learning outcomes & professional competences

After completing this course, students will be able to

describe discrete-time signals and systems in the time and frequency domain using signal processing methods
analyse and evaluate discrete-time systems with regard to stability, transient response, etc.
design self-contained digital filters with specified properties
realise digital filters in software in a computationally efficient manner
implement more complex signal processing algorithms in Python in a computationally efficient manner

The students

have acquired extensive skills in Python, which can also be used outside the realisation of signal processing algorithms,
can design, implement and test a programme from a given task and evaluate, present and discuss the results obtained,
can analyse more extensive tasks together in a group, break them down into subtasks and work on them in a solution-oriented manner.

Methodical realisation

Lectures with predominantly blackboard use, occasional slide presentations
Classroom exercises with exercise sheets and demonstrations on the computer
Practical exercises with Python, in which students independently develop solutions and implement, test and analyse signal processing algorithms.