Waveforms: pulse and sawtooth
Approximation of the following waveforms:
Reverse sawtooth wave:
$$
2 + \sum_{k=1}^\infty (-1)^k\frac{\sin(2\pi k t)}{k}
$$
Pulse wave:
$$
(-2) + \sum_{k=1}^\infty \frac{\sin(2 \pi (2k-1)k t)}{(2k-1)}
$$
Web references:
// Define the id of your board in BOARDID
const board = JXG.JSXGraph.initBoard(BOARDID, {
axis: true, boundingbox: [-6, 5, 6, -5]
});
var s = board.create('slider', [[0.75, -2], [4.5, -2], [0, 0, 10]], {name: 'S', snapWidth: 1});
board.create('functiongraph', [
function(t) {
var val = 0, sv = s.Value() + 1, k;
for (k = 1; k <= sv; k++) {
val += Math.pow(-1, k) * Math.sin(2 * Math.PI * k * t) / k;
}
return val + 2;
}, -10, 10
], {strokeColor: '#bb0000'});
board.create('functiongraph', [
function(t) {
var val = 0, sv = s.Value() + 1, k;
for (k = 1; k <= sv; k++) {
val += Math.sin(2 * Math.PI * (2 * k - 1) * t) / (2 * k - 1);
}
return val - 2;
}, -10, 10
], {strokeColor: '#cc5520'});
This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note that you have to mention The Center of Mobile Learning with Digital Technology in the credits.