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Source
The whole widget is these files; the repository has their history.
widget.json
{
"name": "correlation-rig",
"title": "Correlation rig",
"version": 1,
"claim": "The average of the pointwise product of a signal and a template is large when their signs stay aligned and cancels toward zero when they drift in and out of alignment.",
"summary": "Set the template and signal frequencies in whole cycles per window; the top band overlays the two waveforms and the bottom band shades their pointwise product, whose net area is the correlation readout.",
"topics": [
"signals/correlation",
"math/vectors"
],
"aliases": [
"correlation",
"dot product",
"inner product",
"similarity"
],
"params": {
"templateFreq": {
"type": "integer",
"default": 5,
"min": 1,
"max": 12,
"label": "template frequency (cycles per window)"
},
"signalFreq": {
"type": "integer",
"default": 5,
"min": 1,
"max": 12,
"label": "signal frequency (cycles per window)"
}
},
"check": [
{
"q": "Correlation multiplies signal and template pointwise, then averages. A large positive result means…",
"options": [
"the signal is louder than the template",
"the two waveforms are identical",
"the signal contains many frequencies",
"the two tend to have the same sign at the same times"
],
"answer": 3,
"why": "Same-sign products are positive and opposite-sign products are negative, so persistent alignment is what survives the average; any aligned, scaled copy correlates strongly, not only an identical one."
}
],
"capabilities": [],
"height": 510,
"requires": [],
"forkedFrom": null,
"authors": []
}
index.html
<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Correlation rig</title>
<style>
:root {
color-scheme: light dark;
--bg: #f7f3ea;
--bg-card: #efe9da;
--border: #d8cfba;
--text: #211d14;
--text-dim: #6e6553;
--accent: #31597f;
--accent2: #b04e1b;
--hot: #a82433;
--ok: #3d6b4f;
--ink-rgb: 33, 29, 20;
--paper-rgb: 247, 243, 234;
--accent-rgb: 49, 89, 127;
--accent2-rgb: 176, 78, 27;
--hot-rgb: 168, 36, 51;
--ok-rgb: 61, 107, 79;
--serif: "Iowan Old Style", "Palatino Linotype", Palatino, "Book Antiqua", Georgia, serif;
--mono: ui-monospace, "SF Mono", Menlo, Consolas, monospace;
}
@media (prefers-color-scheme: dark) {
:root {
--bg: #161410;
--bg-card: #1e1b15;
--border: #383225;
--text: #e9e3d3;
--text-dim: #9c917c;
--accent: #8fb8e0;
--accent2: #dd9355;
--hot: #df7a88;
--ok: #82bd97;
--ink-rgb: 233, 227, 211;
--paper-rgb: 22, 20, 16;
--accent-rgb: 143, 184, 224;
--accent2-rgb: 221, 147, 85;
--hot-rgb: 223, 122, 136;
--ok-rgb: 130, 189, 151;
}
}
* { box-sizing: border-box; }
html, body { margin: 0; }
body { background: transparent; color: var(--text); font-family: var(--serif); font-size: 15px; line-height: 1.5; }
.widget { background: var(--bg-card); border: 1px solid var(--border); border-radius: 4px; padding: 22px; }
.control-row { display: flex; align-items: center; gap: 14px; flex-wrap: wrap; margin-bottom: 14px; }
.control-row label { font-size: 14px; color: var(--text-dim); white-space: nowrap; }
.control-row.sym { display: grid; grid-template-columns: 88px 1fr 1fr; gap: 12px 16px; align-items: center; }
.control-row.sym.single { grid-template-columns: 88px 1fr; }
.ctl { display: flex; align-items: center; gap: 10px; min-width: 0; }
.ctl input[type="range"] { flex: 1; min-width: 0; }
.ctl .val { flex: none; width: 64px; text-align: right; font-size: 13px; }
@media (max-width: 600px) {
.control-row.sym { grid-template-columns: 64px 1fr; }
.control-row.sym .ctl:nth-of-type(2) { grid-column: 2; }
}
input[type="range"] { flex: 1; min-width: 110px; accent-color: var(--accent); }
.toggle { display: inline-flex; align-items: baseline; gap: 7px; font-size: 13.5px; color: var(--text-dim); cursor: pointer; }
.toggle input { accent-color: var(--accent2); }
.control-row .toggle { white-space: normal; }
.mono { font-family: var(--mono); }
.dim { color: var(--text-dim); font-size: 12.5px; }
.chips { display: flex; flex-wrap: wrap; gap: 8px; margin-bottom: 16px; }
.chip, .btn {
font-family: var(--mono); font-size: 12.5px; color: var(--text); background: transparent;
border: 1px solid var(--border); border-radius: 3px; padding: 6px 13px; cursor: pointer;
transition: border-color 0.15s, color 0.15s;
}
.chip:hover, .btn:hover { border-color: var(--accent); color: var(--accent); }
.btn.primary { border-color: var(--accent); color: var(--accent); }
.btn.playing, .btn.playing:hover { border-color: var(--hot); color: var(--hot); }
.btn.off { border-color: var(--hot); color: var(--hot); opacity: 0.85; }
.btn:disabled { opacity: 0.35; cursor: default; }
.btn:disabled:hover { border-color: var(--border); color: var(--text); }
.chip.sel-chip { border-color: var(--accent); color: var(--accent); }
.readout-row { display: flex; gap: 28px; flex-wrap: wrap; margin: 14px 0 0; }
.readout { text-align: left; }
.readout.inline { margin-left: auto; text-align: right; }
.readout .big { display: block; font-size: 30px; font-weight: 600; color: var(--accent); line-height: 1.1; min-width: 5ch; }
.readout.accent .big { color: var(--accent2); }
.readout .big.hot { color: var(--hot); }
.readout small { color: var(--text-dim); font-size: 12.5px; }
@media (max-width: 560px) { .readout .big { font-size: 25px; } }
.plot { display: block; width: 100%; height: 220px; margin-top: 8px; }
.plot.tall { height: 280px; }
.plot.duo { height: 320px; }
.plot.phasor { height: 400px; }
.plot.spec { height: 230px; }
.mono, .ctl .val, .readout .big, .readout small { font-variant-numeric: tabular-nums; }
</style>
</head>
<body>
<div class="widget">
<div class="control-row sym single">
<label for="corr-f1">template freq</label>
<span class="ctl wide"><input type="range" id="corr-f1" min="1" max="12" value="5"><span class="mono val" id="corr-f1-label">5 cyc</span></span>
</div>
<div class="control-row sym single">
<label for="corr-f2">signal freq</label>
<span class="ctl wide"><input type="range" id="corr-f2" min="1" max="12" value="5"><span class="mono val" id="corr-f2-label">5 cyc</span></span>
</div>
<canvas id="corr-canvas" class="plot duo"></canvas>
<div class="readout-row">
<div class="readout">
<span class="big mono" id="corr-val">0.500</span>
<small>correlation · average of the product</small>
</div>
</div>
</div>
<script src="/w/_sdk/host.js?v=1"></script>
<script src="/w/_lib/dsp.js?v=1"></script>
<script src="widget.js?v=1"></script>
</body>
</html>
widget.js
/* Correlation rig: template × signal pointwise, signed product area, averaged. */
(() => {
'use strict';
const $ = (id) => document.getElementById(id);
const { T, setupCanvas, hline, trace, okWash, hotWash, zero, signal } = DSP;
function render() {
const f1 = +$('corr-f1').value;
const f2 = +$('corr-f2').value;
$('corr-f1-label').textContent = f1 + ' cyc';
$('corr-f2-label').textContent = f2 + ' cyc';
const N = 700;
const probe = (t) => Math.sin(2 * Math.PI * f1 * t);
const sig = (t) => Math.sin(2 * Math.PI * f2 * t);
let corr = 0;
for (let i = 0; i < N; i++) corr += probe(i / N) * sig(i / N);
corr /= N;
$('corr-val').textContent = zero(corr).toFixed(3);
const { ctx, w, h } = setupCanvas($('corr-canvas'));
const x0 = 14;
const pw = w - 28;
const topMid = h * 0.26;
const topAmp = h * 0.18;
const botMid = h * 0.72;
const botAmp = h * 0.2;
ctx.clearRect(0, 0, w, h);
ctx.font = DSP.font(10);
hline(ctx, x0, w - 14, topMid, T.GRID);
hline(ctx, x0, w - 14, botMid, T.GRID);
trace(ctx, probe, { x0, pw, mid: topMid, amp: topAmp, color: T.ACCENT, lw: 1.8 });
trace(ctx, sig, { x0, pw, mid: topMid, amp: topAmp, color: T.ACCENT2, lw: 1.8 });
DSP.label(ctx, 'template (blue) · signal (orange)', x0 + 2, 12);
for (let x = 0; x <= pw; x++) {
const v = probe(x / pw) * sig(x / pw);
ctx.strokeStyle = v >= 0 ? okWash(0.4) : hotWash(0.4);
ctx.beginPath();
ctx.moveTo(x0 + x, botMid);
ctx.lineTo(x0 + x, botMid - botAmp * v);
ctx.stroke();
}
DSP.label(ctx, 'template × signal: net shaded area = correlation', x0 + 2, botMid - botAmp - 8);
}
['corr-f1', 'corr-f2'].forEach((id) => $(id).addEventListener('input', () => {
render();
signal('interaction', { control: id });
}));
function applyParams(p) {
if (Number.isInteger(p.templateFreq)) $('corr-f1').value = p.templateFreq;
if (Number.isInteger(p.signalFreq)) $('corr-f2').value = p.signalFreq;
render();
}
render();
DSP.onResize(render);
DSP.connect({ render, params: applyParams });
})();