Constructing a periodic piecewise (piecemeal) function in Maple.

Question

I'm trying to make a piecewise function that will have period $12$. That is, it repeats every $12$ units across the $x$-axis.

I managed to do one cycle successfully with

plot(piecewise(0<=t and t<2, 4,2<=t and t<12,0), t=0..13);

But I'm not sure how to do it periodically. I thought about using modular arithmetic in the conditions and setting up something like

H(t)=piecewise(0<=modp1(f(t),12) and modp1(f(t),12)<2, 4,2<=modp1(f(t),12) and modp1(f(t),12)<12,0);

but this clearly doesn't work.

Some direction or advice would be appreciated.

Answer 1

Create a trigonometric polynomial P(t), of period 12, that approximates the characteristic function of [2,12]. Use enough terms to ensure P(t)>=1/2 on [2,12].

Then you can define your piecewise periodic function

$H(t) = piecewise(P(t)<1/2, 4 , P(t) \geq 1/2,0)$