Statistics & signal

Fits

addRegression draws a least-squares line with an optional ±band, or a LOESS curve when the relationship is not linear. The fit's r² lands in the legend, so the chart states its own quality.

addRegression(plot, { x, y, band: 2 });                  // OLS ± 2·stderr
addRegression(plot, { x, y, method: "loess", bandwidth: 0.3 });

Pure equivalents: linearRegression(x, y) → { slope, intercept, r2, stderr, predict }, linearTrend, loess.

Distributions

addEcdf(plot, { values }) draws the empirical CDF as a step line — the most honest way to compare two distributions, since it involves no binning choice at all. histogram, boxStats, kde and quantileSorted are exported as pure functions.

Correlation

addCorrMatrix(plot, { columns, names });   // diverging, locked to ±1
corrMatrix(columns);                       // the raw k×k matrix
correlation(a, b);                         // one pair

Spectra

addPsd runs Welch's method — averaged periodograms of overlapping windowed segments — so a noisy signal gives a readable spectrum instead of grass.

addPsd(plot, { signal, sampleRate: 500, segment: 1024, window: "hann" });

Pure: welch, windowFunction(name, n) (hann, hamming, blackman, bartlett, rectangular), fft, spectrogram.

Waterfall

addWaterfall is the streaming half of a spectrogram: frequency across, time down. Each pushed column becomes the newest row at the top, the history slides down a row, and the y axis reads as a clock.

const wf = addWaterfall(plot, {
  extent: [0, 160_000],        // the band one row spans
  cols: 512, rows: 400,        // cells across × rows of history
  rowSeconds: 0.08,            // seconds one row covers → 32s on screen
  domain: [-68, -6],           // fix it, or the colours breathe every push
  colormap: "plasma", name: "power (dB)",
  timeFormat: "hh:mm:ss",      // or "mm:ss.mmm", or (s) => your own label
  timeTitle: "time",
});

wf.push(psdInDb);              // one column per step; longer columns are block-maxed
wf.setTimeAxis({ format: "mm:ss.mmm" });   // relabel live
plot.render();

A column longer than cols is reduced by block maximum, so a peak two bins wide survives fitting a 200k-bin spectrum into a few hundred cells. Give the plot margin: { left: 72 } — clock labels are wider than plain numbers and the margin is not measured from them. history opens on a pre-computed grid (row 0 at the bottom) instead of an empty one.

Pure: waterfallTimeTicks(now, span, opts), formatDuration(seconds, style), niceTimeStep(span, count), blockMax(values, cols).

Smoothing & correlation in time

• savitzkyGolay(values, window, order) — least-squares polynomial smoothing that preserves peak height and width, unlike a moving average.
• crossCorrelate(a, b, maxLag) → { lags, values }. Normalised by default, so the peak lag reads directly as "b lags a by k". Pass the same array twice for an autocorrelation.
• zscore, ecdf for quick standardisation and ranking.