Systems
=======

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

   .. tikz:: 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}

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.

      .. tikz:: Cascaded (or serial) Systems 

	 \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}

.. Addition / Subtraction
   One signal $x(t)$ can be splitted to function as the input of two
   systems $S_1$ and $S_2$. The output of the two systems can then, for
   instance, be added together to result in one signal again.

  

.. Feedback Loops
  


In a later section when we restrict ourselves to linear systems we
will look again at the block diagrams to construct composite systems.