Exercises
=========

#. Write Python functions to plot signals/functions. You should be
   able to plot real as well as complex signals and CT as well as DT
   signals. You will be using this functionality quite a lot in this
   course.

   
#. Plot the following functions:

   #. Step functions $u(t)$ and $u[n]$.

   #. Translated stepfunctions $u(t-2)$ and $u[n-2]$

   #. Scaled and translated step function $3\, u(\frac{t-2}{3})$

      
#. Plot the $x_a$ function for several values of $a$. See for yourself
   that it starts to look as the pulse function.

   
#. Defining the CT pulse function as the limit of the $x_a$ function
   is not a unique definition. If we take the function $g_s(t)$ being
   the Gaussian function (you may well remember...) and look at the
   limit for $s\rightarrow0$ you will see that in the limit we arrive
   at the pulse function too. Plot the $g_s$ for several values of $s$
   to see for yourself.