\docname{sess4.4}
\doctitle{Systems, Signals, Input, Response}

\mylhead
\myrhead

\title{\doctitle}
\maketitle

\section{Introduction}
\hbcom{How do we refer to previous documents in the same session?  I'm
  deleting the ``(4.2)'' here.}

In the bank example we modeled the amount in my account by:
\[\overdot x-Ix=q(t).\]

Notice that the right-hand side does not depend on $x$. The left-hand
side represents what happens at the bank. The right-hand side
represents what comes into the bank. We will borrow the language of
engineering to describe the pieces of our model.

The left-hand side represents the {\bf system} (the bank). The
right-hand side represents an outside influence on the system: it's a
{\bf signal} -- the {\bf input signal}.

In general, a signal is just a function of $t$. Here it is the rate of
savings. The system {\bf responds} to the input signal and yeilds the
function $x(t)$, which we call the {\bf output signal} or {\bf system response}.

Solving the ODE means finding the unknown $x$. In this new language it means finding the response of the system to the input signal $q(t)$.

\section{Block Diagrams}

\TODO
\begin{figure}[h]
\begin{verbatim}
                        initial condition
                               |
                               |
                               |
                               V
                         ______________
                        |              |
        --------------> |    System    | -------------->
                        |______________|

           input                               output

\end{verbatim}
\caption{Engineers use block diagrams to describe
  systems.}\label{fig4.4.1}
\end{figure}

\begin{figure}[h]
\begin{verbatim}
                              x(0)
                               |
                               |
                               |
                               V
                         ______________
                        |              |
        --------------> |    Bank      | -------------->
            q(0)        |______________|       x(t)
\end{verbatim}
\caption{This diagram shows the input signal $q(t)$ and initial condition $x(0)$ going into the system and the output signal $x(t)$ coming out.}\label{fig4.4.2}
\end{figure}