Fiches de cours 2017-2018


Mathematical foundations of signal processing


Lecturer(s) :

Kolundzija Mihailo
Parhizkar Reza
Scholefield Adam James




Signal processing tools are presented from an intuitive geometric point of view which is at the heart of all modern signal processing techniques. Student will develop the mathematical depth and rigor needed for the study of advanced topics in signal processing.


From Euclid to Hilbert (vector spaces; Hilbert spaces; approximations, projections and decompositions; bases)

Sequences and Discrete-Time Systems (sequences; systems; discrete-time Fourier transform; z-transform; DFT; multirate sequences and systems; filterbanks)

Functions and Continuous-Time Systems (functions; systems; Fourier transform; Fourier series)

Sampling and Interpolation (sampling and interpolation with finite-dimensional vectors, sequences, functions and periodic functions)

Approximation and Compression (approximation by polynomials, splines, and series truncation)

Localization and Uncertainty (localization for functions, sequences and bases; local Fourier and wavelet bases; time, frequency and resolution in the real world)

Compressed Sensing (overview and definitions; reconstruction methods and applications)

Learning Prerequisites

Required courses

Circuits and Systems

Recommended courses

Signal processing for communications

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Ex cathedra with exercises

Expected student activities

Attending lectures, completing exercises

Assessment methods

Homeworks 20%, midterm (written) 30%, final exam (written) 50%


Office hours Yes
Assistants Yes
Forum No


Virtual desktop infrastructure (VDI)



M. Vetterli, J. Kovacevic and V. Goyal, "Signal Processing: Foundations", Cambridge U. Press, 2014.

Available in open access at

Ressources en bibliothèque
Moodle Link

In the programs

Reference week

      Exercise, TP
      Project, other


  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German