Coaxial Cable acts as differentiator In order to determine the characteristic impedance of a coaxial cable, I put a resistance on the one end and connected the other end of the cable to a signal generator and an oscilloscope.
This worked fine when using a sine signal as I just had to find the resistance, for which the returning signal was (almost) gone. However, I also wanted to try this with a square signal.
The result was first a positive sharp peak decreasing similar to an exponential function followed by a negative peak of the same form.
Why does this happen?
My first thought was a differentiator since the sine signal kept its form and the sides of the square signal resulted in sharp peaks with the constant middle part being changed to $0$ voltage.
After some reading I found out, that an RL-circuit can be looked at as an differentiator. So my assumption is that the coaxial cable's inductance makes the experiment a RL-circuit.
However, where do you draw the inductor into the circuit? My first guess would be to just add it in series with R:

Where V is the oscilloscope and the red parts are the coaxial cable.
This also produces the next question: I am measuring the voltage over R and the inductor while for the differentiator the voltage is taken over the inductor only:

I only made a sketch of the seen image on the oscilloscope:

The coaxial cable was $40\; \mathrm{m}$ long.
 A: An high-pass filter is characteristic of a capacitance in series with a signal. An unexpected high-pass filter is often diagnostic of a broken cable. For example, imagine the connector at one end of the cable gets separated from the ground sheath: that little gap is a capacitance interrupting your signal return path. This kind of problem is easy to cause by bumping the cable with your butt, and easy to fix by replacing the connector.
You say you have your function generator and oscilloscope close to each other, and your 40m cable going to a terminating resistor. If your termination were correct, the oscilloscope would see the signal produced by the function generator, and the part of the signal going down the transmission line would be swallowed by the resistor without evidence. You sketch a figure and give a rise time of 20 ns, so it looks like a time between start-of-rise and start-of-fall of about 70 ns, and a time between start-of-rise and the positive spike of a little over 200 ns.
One model which reproduces this signal is that the connection between the far end of the cable and its terminating resistor is bad. Instead of the echo being swallowed, it’s differentiated by a capacitive connection and returned to you.  A good estimate for signal speed in coaxial cable is $c/2$ or $2c/3$, so without taking your horizontal time scale too seriously it’s the right order of magnitude delay for an 80m round trip.
If your oscilloscope has two inputs, you might connect the near end of the cable on channel 1 and the far end on channel 2, to measure this delay time directly (including the time for the echo to return to channel 1, depending on how you terminate the scope connection at channel 2). This will also give you an excuse to touch all of the connectors and look for anything loose or weird.
A: The dominant characteristic of a piece of coax is its parallel capacitance per foot of length. This effect is significant and must be included in a model of the cable along with its series inductance (small) and series DC resistance (very small) per foot.
