1.1. SystemsΒΆ
In these lecture notes we restrict ourselves to the most simple systems: SISO systems. Systems with one input signal (Single Input) and one output signal.
When the system is fed with an input signal \(x(t)\) it outputs the signal \(y(t)\). For now a system is just a black box for us. We will often use the block diagram representation of systems. sdasd
A one input, one output (SISO) system
![\bXInput{A}
\bXBloc[8]{B}{System}{A}
\bXLink[{Input $x(t)$}]{A}{B}
\bXOutput[8]{C}{B}
\bXLink[{Output $y(t)$}]{B}{C}](../_images/tikz-30db632e39a193707240bc477db3405fb6efa052.png)
More complex systems have multiple inputs and multiple outputs: MIMO systems.
We will often find the need to use several systems and combine them into a new systems.
- Cascaded Systems
Two systems connected in such a way that the output of one system is the input to the second system are cascaded or connected in series.
![\bXInput{A}
\bXBloc[4]{B}{$S_1$}{A}
\bXLink[$x(t)$]{A}{B}
\bXBloc[4]{C}{$S_2$}{B}
\bXLink[$y(t)$]{B}{C}
\bXOutput[4]{D}{C}
\bXLink[$z(t)$]{C}{D}](../_images/tikz-2f7afb31a1339d308b3d4eec10edf086bd310c27.png)
Cascaded (or serial) Systems
In a later section when we restrict ourselves to linear systems we will look again at the block diagrams to construct composite systems.