Signal theory: Part 1

Table of Contents

News

  • <2017-09-22 Fri> optional homework
    1. Given data \(\big(w(1),\ldots,w(T)\big)\) that is generated by a linear static system \(\mathcal{B}\), explain how to find a kernel representation ker\((R)\) of \(\mathcal{B}\).
    2. Test your solution on the data \(W = \begin{bmatrix} w(1) & \cdots & w(T) \end{bmatrix}\) saved in the mat-file W.mat. Compare your answer with the "true" data generating system \(\mathcal{B} = \text{ker}(\begin{bmatrix} 1 & 2 & 3 \end{bmatrix})\).

General information about the course

  • Lecturers:
    • Ivan Markovsky (part 1, weeks 1, 2, 3, 4)
    • Leo Van Biesen (part 2, weeks 4, 5, 6, 8)
  • Classes:
    • Tuesday, 10:00–12:00
    • Tuesday, 13:00–15:00
    • Friday, 10:00–12:00
  • Evaluation:
    • 100% final exam

Learning outcomes

Specific

  • 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.

General

(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.

Part 1 topics

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

Reader

Slides

Additional materials for Part 1