Linear and Time Invariant Systems

Based on the book $\text{Signal Representation}$, it is described how to mathematically capture the influence of a filter on deterministic signals.

• The book defines distortions and describes the Laplace transform for causal systems as well as the properties of electric leads.
• The filter influence on a random signal is covered later in Chapter 5 of the book $\text{Theory of Stochastic Signals}$ .

The subject matter corresponds to a  $\text{lecture with two semester hours per week (SWS) and another SWS of exercises}$.

First of all, here is an overview of the contents based on the  $\text{four main chapters}$  with a total of  $\text{twelve individual chapters}$.

Contents

Basics of System Theory

• System Description in Frequency Domain
• System Description in Time Domain
• Some Low-Pass Functions in Systems Theory

Signal Distortion and Equalization

• Classification of the Distortions
• Nonlinear Distortions
• Linear Distortions

Description of Causal Realizable Systems

• Conclusions from the Allocation Theorem
• Laplace Transform and p-Transfer Function
• Inverse Laplace Transform

Properties of Electrical Cables

• Some Results from Transmission Line Theory
• Properties of Coaxial Cables
• Properties of Balanced Copper Pairs

In addition to these theory pages, we also offer tasks and multimedia modules on this topic, which could help to clarify the teaching material:

• $\text{Exercises}$
• $\text{Learning videos}$
• $\text{Applets}$ 

$\text{Further links:}$

$(1)$    $\text{Bibliography for the book}$

$(2)$    $\text{General notes about the book}$   (authors,  other participants,  materials as a starting point for the book,  list of sources)

In addition to these theory pages, we also offer assignments and multimedia modules on this topic that could help clarify the subject matter:

• $\text{Educational videos}$
• $\text{Newly designed applets}$  (based on HTML5 and JavaScript, also executable on smartphones)
• $\text{Former applets}$  (based on SWF, executable only on WINDOWS with "Adobe Flash Player")

$\text{More links:}$

$(1)$    $\text{Recommended reading for the book}$

$(2)$    $\text{General notes on the Book}$   (authors,  other contributors,  materials as a starting point of the book,  list of references)