How do I plot this periodic step function with GNUplot?

[randombill]

$$\sum_{k=0}^{∞} (t-2k) [u(t-2k)-u(t-2(k+1))] = f(t)$$

where $$u$$ is the step function and the graph of this is supposed to be 45 degree lines repeating to infinity. Sort of like

/ / / / / / / / / ad infinitum. I took this equation out of this lecture note on page 10. Fig 5.4 is supposedly the graph of it and example 5.27 is where they ask to solve it.

 

[DrDu]

What do you know about the modulo operation?

 

[randombill]

A lot actually. Thats the % operator in C/C++ right? Actually I figured out that plotting this function is next to impossible in GNUplot based on my searches online and this was actually plotted with Maple. There is a free Maple (clone) called Sage and runs in Oracle VirtualBox but I haven't tried it. What I did figure out is that it would be easier to use iteration (for loop, while, etc) in a modern programming language such as C and substitute that for the summation part of the problem. From there the problem falls together by simply plotting the numerical result from a dat file in GNUplot. I think that solves it.

 

[DrDu]

I don't think it is difficult to plot this function in gnuplot once you use the modulo operation (which is also in gnuplot represented by the % sign) as it is nothing else than f(t)=t%2

 

[randombill]

Okay but what about the periodic part using the summation. That usually requires two independent variables but most 2d graphers can only do one. For the summation you would need k and t to be both variables dynamically changing. I can easily graph one line using 2t but I would still need to repeat it iteratively using summation over k. And shouldn't it be f(t)=k%2?