# Signal theory: Part 1

## 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