Course content / topics
Being able to analyse accurately functional brain signals is key to understand the underlying neural mechanisms. While signal processing toolboxes are nowadays widely available to neuroscientists, using them properly and correctly interpreting their outcome requires understanding fundamental principles of signal and system theory. The main goals of this course will be:
• Introduce and learn to manipulate the mathematical representations of signals (convolution, difference equations, z-transform, point-processes)
• Introduce key principles behind classical signal processing tools: filtering, spectral analysis, wavelets…
• Understand the capabilities and limitations of time series analysis approaches and how to use them safely.
The lectures will be evaluated with one exam (50% of final grade) with a focus on the lecture content (modalities to be defined depending on the covid situation), and two individual home assignments (each 25% of final grade) with a focus on applications of lectures involving Numpy (and possibly Matlab) programming and data analysis.
- Mathematical Principles of Signal Processing, P. Bremaud
- Digital Signal Processing, JG Proakis and DG Manolakis
- Spectral Analysis for Physical Applications, DB Percival and AT Walden
- Time series: theory and methods, PJ Brockwell and RA Davis
- A Wavelet Tour of Signal Processing, S Mallat
- Signal Processing for Neuroscientists, W van Drongelen
- Fourier Analysis and Applications: Filtering, Numerical Computation, Wavelets, C Gasquet and P Witomski
Although refreshers on these topics will be provided in the first lectures, we will have to build on basic notions of linear algebra (basis, matrices, scalar product), analysis (series, integrals, derivatives) and probabilities. Practical examples will be implemented using MatLab and NumPy, so elementary matrix/vector/indices manipulations functions from this software should be known.
Note: Please subscribe to the course on the ILIAS system and check there regularly.
ILIAS Online Course Link