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   $\text{lecture with two semester hours per week and another hour per week of exercises}$.

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 Line Transmission Theory
• Properties of Coaxial Cables
• Properties of Balanced Copper Pairs

In addition to these theory pages,  we also offer exercisess 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)