Signals and linear systems in discrete time

• 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.
• convert continuous-time filters into discrete-time filters using the bilinear transform.
• use a spectrogram to analyse the time/frequency content of a signal and calculate the spectral density of a stochastic signal.
• apply AI as a sparring partner in the solution of open problems with proper documentation
• 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.
• apply English terminology in digital signal processing and write reports in English.
• extract and combine information from different literatary sources.

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,
– Short-time Fourier transform
– Spectral density of a stochastic signal
– Noise reduction

31605/22050, The course is a continuation of course 22050 (previously 31605). Equivalent knowledge is expected for participation.
Prior knowledge in a programming language (e.g. MATLAB, C, Pyhton, Julia) is beneficial, but not a necessity. Additional material will be provided if required.

Lectures, group discussions, online material, computer exercises

The courses 22050, 22051, and 22052 constitute a specialization track in signal processing and should be taken in said order.

Matlab/PYTHON will be utilized in the course.

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.

Generative AI is used as supporting tool for exercises.