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 Realisable 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 assignments and multimedia modules on this topic that could help clarify the subject matter:

• $\text{Exercises}$
• $\text{Educational videos}$
• $\text{Newly designed applets}$  (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)