Signal theory: Part 1

• In-depth knowledge of linear systems theory and its application for signal processing.
  • Representations of linear time-invariant systems.
  • Converting one representation to another.
  • Realization theory (Kung's method).
  • Least-squares estimation (Kalman filtering).
  • System identification (subspace and optimization methods).
• Can formulate a precise mathematical problem from a given engineering specification.
• Can solve signal processing problems by converting them to already solved problems.
• Can solve signal processing problems numerically using Matlab/Octave.
• Can present solution of problems in a clear, well structured way.

(Extracted from the learning outcomes of the masters program in electronics and information technology engineering.)

• In-depth knowledge and understanding of exact sciences with the specificity of their application to engineering.
• Can reformulate complex engineering problems in order to solve them (simplifying assumptions, reducing complexity).
• Can present and defend results in a scientifically sound way, using contemporary communication tools, for a national as well as for an international professional or lay audience.
• Can collaborate in a (multidisciplinary) team.
• Has a creative, problem-solving, result-driven and evidence-based attitude, aiming at innovation and applicability in industry and society.
• Has a critical attitude towards one’s own results and those of others.
• Has an active knowledge of the theory and applications of information and communication technology.
• Has a profound knowledge of modelling and control.

1. Behavioral approach to signals and systems
2. Representations of linear time-invariant systems
3. Random signals and least-squares estimation

• Data compression
• Noise filtering
• Discovering signal in noise
• Making sensors faster
• Missing data estimation

• Behavioral approach
• Kernel, image, change of basis
• LTI system representations
• Autonomous systems