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[Autoloop: build-tsb-pandas-typescript-migration] Iteration 387: Add signal processing (FFT/STFT/Welch) and digital filters (FIR/Butterworth)
- src/stats/signal.ts: Cooley-Tukey radix-2 DIT FFT/IFFT/RFFT/IRFFT, fftFreq/rfftFreq, fftshift/ifftshift, 8 window functions (getWindow), STFT/ISTFT (overlap-add), Welch PSD (mean/median), periodogram. Mirrors numpy.fft + scipy.signal spectral utilities. - src/stats/filters.ts: FIR design via windowed-sinc (firwin), Butterworth IIR design (butter, SOS form), frequency response (freqz, sosfreqz), filter application (lfilter, filtfilt, sosfilt, sosfiltfilt). Mirrors scipy.signal filter utilities. - tests/stats/signal.test.ts: 50+ tests (unit + property-based) - tests/stats/filters.test.ts: 50+ tests (unit + property-based) - playground/signal.html, playground/filters.html: interactive tutorials - playground/index.html, src/stats/index.ts, src/index.ts: updated exports Metric: 183 → 185 (+2) Run: https://github.com/githubnext/tsb/actions/runs/28396990118 Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
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‎playground/filters.html‎

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<!DOCTYPE html>
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<html lang="en">
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<head>
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<meta charset="UTF-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1.0" />
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<title>tsb — Digital Filters</title>
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<style>
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:root {
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--bg: #0d1117;
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--surface: #161b22;
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--border: #30363d;
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--text: #e6edf3;
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--red: #f85149;
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--font-mono: "Cascadia Code", "Fira Code", "JetBrains Mono", monospace;
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}
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* { box-sizing: border-box; margin: 0; padding: 0; }
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body {
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background: var(--bg);
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color: var(--text);
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font-family: system-ui, -apple-system, sans-serif;
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line-height: 1.6;
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padding: 2rem;
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max-width: 900px;
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margin: 0 auto;
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}
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a { color: var(--accent); }
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h1 { color: var(--accent); margin-bottom: 0.5rem; }
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h2 { color: var(--text); margin: 2rem 0 0.5rem; border-bottom: 1px solid var(--border); padding-bottom: 0.3rem; }
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h3 { color: var(--accent); margin: 1.5rem 0 0.5rem; }
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pre {
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background: var(--surface);
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border-radius: 6px;
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padding: 1rem;
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overflow-x: auto;
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font-family: var(--font-mono);
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font-size: 0.85rem;
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line-height: 1.5;
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}
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code { font-family: var(--font-mono); font-size: 0.9em; }
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.example { margin: 1.5rem 0; }
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.output {
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background: #0a2a0a;
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border: 1px solid var(--green);
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border-radius: 6px;
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padding: 0.75rem 1rem;
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font-family: var(--font-mono);
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font-size: 0.85rem;
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margin-top: 0.5rem;
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white-space: pre-wrap;
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}
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table { border-collapse: collapse; width: 100%; margin: 1rem 0; }
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th, td { border: 1px solid var(--border); padding: 0.5rem 1rem; text-align: left; }
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th { background: var(--surface); color: var(--accent); }
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</style>
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</head>
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<body>
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<h1>🎛️ Digital Filters</h1>
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<p>FIR and IIR filter design and application — mirrors <code>scipy.signal</code>.</p>
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<h2>FIR Filters</h2>
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<h3>1. Low-pass FIR with firwin</h3>
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<div class="example">
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<pre>import { firwin, freqz, cAbs } from "tsb";
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// 51-tap Hamming-windowed low-pass at 0.3 * Nyquist
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const b = firwin(51, 0.3);
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console.log(`Coefficients: ${b.length} taps`);
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console.log(`DC gain: ${b.reduce((s, v) => s + v, 0).toFixed(6)}`);
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// Frequency response
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const { w, H } = freqz(b, [1], 512);
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const mag = H.map(cAbs);
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// DC (w=0): should be ≈ 1.0
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console.log(`Gain at DC: ${mag[0].toFixed(4)}`);
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// Nyquist (w=π): should be ≈ 0
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console.log(`Gain at Nyquist: ${mag[511].toFixed(4)}`);</pre>
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<div class="output" id="out1">Running…</div>
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</div>
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<h3>2. High-pass FIR</h3>
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<div class="example">
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<pre>import { firwin, freqz, cAbs } from "tsb";
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// 51-tap high-pass, pass_zero=false
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const b = firwin(51, 0.3, { pass_zero: false });
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const { H } = freqz(b, [1], 512);
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const mag = H.map(cAbs);
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console.log(`Gain at DC: ${mag[0].toFixed(4)} (should be ≈ 0)`);
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console.log(`Gain at Nyquist: ${mag[511].toFixed(4)} (should be ≈ 1)`);</pre>
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<div class="output" id="out2">Running…</div>
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</div>
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<h3>3. Apply FIR filter with lfilter and filtfilt</h3>
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<div class="example">
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<pre>import { firwin, lfilter, filtfilt } from "tsb";
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const fs = 512, n = 512;
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// Mix 20 Hz (keep) + 200 Hz (remove) signals
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const x = Array.from({ length: n }, (_, i) =>
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Math.sin(2 * Math.PI * 20 * i / fs) +
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Math.sin(2 * Math.PI * 200 * i / fs),
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);
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// Low-pass FIR: cutoff at 100 Hz
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const b = firwin(63, 100, { fs });
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// Causal filter (introduces phase delay)
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const yLf = lfilter(b, [1], x);
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// Zero-phase filter (no phase delay)
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const yFf = filtfilt(b, [1], x);
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const mid = 256;
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console.log(`Input at mid-point: ${x[mid].toFixed(4)}`);
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console.log(`lfilter output (causal): ${yLf[mid].toFixed(4)}`);
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console.log(`filtfilt output (no delay): ${yFf[mid].toFixed(4)}`);</pre>
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<div class="output" id="out3">Running…</div>
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</div>
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<h2>IIR Filters — Butterworth</h2>
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<h3>4. Design a Butterworth low-pass filter</h3>
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<div class="example">
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<pre>import { butter, sosfreqz, cAbs } from "tsb";
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// 4th-order Butterworth, cutoff at 0.3 * Nyquist
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const { sos, b, a } = butter(4, 0.3, "lowpass");
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console.log(`SOS sections: ${sos.length}`);
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console.log(`b coefficients: [${b.map(v => v.toFixed(6)).join(", ")}]`);
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console.log(`a coefficients: [${a.map(v => v.toFixed(6)).join(", ")}]`);
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// Frequency response via SOS
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const { H } = sosfreqz(sos, 512);
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const mag = H.map(cAbs);
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console.log(`DC gain: ${mag[0].toFixed(4)} (should be ≈ 1.0)`);
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console.log(`At cutoff (~bin 77): ${mag[77].toFixed(4)} (≈ 0.707 = -3dB)`);</pre>
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<div class="output" id="out4">Running…</div>
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</div>
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<h3>5. Apply Butterworth filter with sosfilt</h3>
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<div class="example">
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<pre>import { butter, sosfilt, sosfiltfilt } from "tsb";
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const fs = 1000, n = 1000;
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// Noisy 50 Hz signal
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const x = Array.from({ length: n }, (_, i) =>
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Math.sin(2 * Math.PI * 50 * i / fs) +
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0.5 * Math.sin(2 * Math.PI * 300 * i / fs), // high-freq noise
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);
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// 4th-order Butterworth low-pass at 150 Hz
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const { sos } = butter(4, 150 / (fs / 2), "lowpass");
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// Causal
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const y1 = sosfilt(sos, x);
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// Zero-phase
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const y2 = sosfiltfilt(sos, x);
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const mid = 500;
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const ref = Math.sin(2 * Math.PI * 50 * mid / fs);
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console.log(`Reference (50 Hz): ${ref.toFixed(4)}`);
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console.log(`sosfilt output: ${y1[mid].toFixed(4)}`);
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console.log(`sosfiltfilt output: ${y2[mid].toFixed(4)} (zero-phase, closer to ref)`);</pre>
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<div class="output" id="out5">Running…</div>
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</div>
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<h3>6. High-pass Butterworth</h3>
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<div class="example">
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<pre>import { butter, sosfreqz, cAbs } from "tsb";
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const { sos } = butter(2, 0.3, "highpass");
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const { w, H } = sosfreqz(sos, 512);
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const mag = H.map(cAbs);
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console.log(`Gain at DC (w=0): ${mag[0].toFixed(4)} (should be ≈ 0)`);
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console.log(`Gain at Nyquist (w=π): ${mag[511].toFixed(4)} (should be ≈ 1.0)`);</pre>
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<div class="output" id="out6">Running…</div>
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</div>
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<h3>7. Filter frequency response — multiple orders</h3>
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<div class="example">
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<pre>import { butter, sosfreqz, cAbs } from "tsb";
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// Compare -3dB attenuation at cutoff for different orders
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const Wn = 0.3;
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console.log("Butterworth -3dB gain at cutoff frequency:");
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for (const N of [1, 2, 4, 6, 8]) {
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const { sos } = butter(N, Wn, "lowpass");
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// Evaluate at ω = Wn * π (the digital cutoff frequency)
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const { H } = sosfreqz(sos, [Wn * Math.PI]);
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const gain = cAbs(H[0]);
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const dB = 20 * Math.log10(gain);
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console.log(` N=${N}: gain=${gain.toFixed(4)} (${dB.toFixed(2)} dB)`);
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}</pre>
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<div class="output" id="out7">Running…</div>
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</div>
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<h2>API Reference</h2>
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<table>
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<tr><th>Function</th><th>Description</th><th>Mirrors</th></tr>
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<tr><td><code>firwin(n, cutoff, opts?)</code></td><td>FIR design (windowed-sinc)</td><td><code>scipy.signal.firwin</code></td></tr>
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<tr><td><code>butter(N, Wn, type?)</code></td><td>Butterworth IIR design</td><td><code>scipy.signal.butter</code></td></tr>
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<tr><td><code>freqz(b, a?, worN?)</code></td><td>FIR/IIR frequency response</td><td><code>scipy.signal.freqz</code></td></tr>
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<tr><td><code>sosfreqz(sos, worN?)</code></td><td>SOS frequency response</td><td><code>scipy.signal.sosfreqz</code></td></tr>
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<tr><td><code>lfilter(b, a, x)</code></td><td>Causal FIR/IIR filter</td><td><code>scipy.signal.lfilter</code></td></tr>
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<tr><td><code>filtfilt(b, a, x)</code></td><td>Zero-phase filter</td><td><code>scipy.signal.filtfilt</code></td></tr>
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<tr><td><code>sosfilt(sos, x)</code></td><td>Causal SOS filter</td><td><code>scipy.signal.sosfilt</code></td></tr>
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<tr><td><code>sosfiltfilt(sos, x)</code></td><td>Zero-phase SOS filter</td><td><code>scipy.signal.sosfiltfilt</code></td></tr>
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</table>
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<script type="module">
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import * as tsb from "https://esm.sh/tsb@latest";
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function run(id, fn) {
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const el = document.getElementById(id);
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try {
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const logs = [];
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const origLog = console.log;
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console.log = (...args) => { logs.push(args.map(String).join(" ")); origLog(...args); };
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fn(tsb);
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console.log = origLog;
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el.textContent = logs.join("\n") || "(no output)";
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el.style.borderColor = "#3fb950";
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} catch (err) {
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el.textContent = "Error: " + err.message;
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el.style.borderColor = "#f85149";
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}
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}
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run("out1", (tsb) => {
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const b = tsb.firwin(51, 0.3);
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console.log(`Coefficients: ${b.length} taps`);
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console.log(`DC gain: ${b.reduce((s, v) => s + v, 0).toFixed(6)}`);
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const { H } = tsb.freqz(b, [1], 512);
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const mag = H.map(tsb.cAbs);
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console.log(`Gain at DC: ${mag[0].toFixed(4)}`);
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console.log(`Gain at Nyquist: ${mag[511].toFixed(4)}`);
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});
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run("out2", (tsb) => {
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const b = tsb.firwin(51, 0.3, { pass_zero: false });
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const { H } = tsb.freqz(b, [1], 512);
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const mag = H.map(tsb.cAbs);
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console.log(`Gain at DC: ${mag[0].toFixed(4)} (should be ≈ 0)`);
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console.log(`Gain at Nyquist: ${mag[511].toFixed(4)} (should be ≈ 1)`);
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});
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run("out3", (tsb) => {
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const fs = 512, n = 512;
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const x = Array.from({ length: n }, (_, i) =>
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Math.sin(2 * Math.PI * 20 * i / fs) + Math.sin(2 * Math.PI * 200 * i / fs),
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);
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const b = tsb.firwin(63, 100, { fs });
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const yLf = tsb.lfilter(b, [1], x);
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const yFf = tsb.filtfilt(b, [1], x);
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const mid = 256;
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console.log(`Input at mid-point: ${x[mid].toFixed(4)}`);
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console.log(`lfilter output (causal): ${yLf[mid].toFixed(4)}`);
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console.log(`filtfilt output (no delay): ${yFf[mid].toFixed(4)}`);
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});
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run("out4", (tsb) => {
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const { sos, b, a } = tsb.butter(4, 0.3, "lowpass");
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console.log(`SOS sections: ${sos.length}`);
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console.log(`b: [${b.map(v => v.toFixed(6)).join(", ")}]`);
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console.log(`a: [${a.map(v => v.toFixed(6)).join(", ")}]`);
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const { H } = tsb.sosfreqz(sos, 512);
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const mag = H.map(tsb.cAbs);
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console.log(`DC gain: ${mag[0].toFixed(4)}`);
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});
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run("out5", (tsb) => {
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const fs = 1000, n = 1000;
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const x = Array.from({ length: n }, (_, i) =>
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Math.sin(2 * Math.PI * 50 * i / fs) + 0.5 * Math.sin(2 * Math.PI * 300 * i / fs),
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);
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const { sos } = tsb.butter(4, 150 / (fs / 2), "lowpass");
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const y1 = tsb.sosfilt(sos, x);
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const y2 = tsb.sosfiltfilt(sos, x);
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const mid = 500;
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const ref = Math.sin(2 * Math.PI * 50 * mid / fs);
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console.log(`Reference (50 Hz): ${ref.toFixed(4)}`);
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console.log(`sosfilt output: ${y1[mid].toFixed(4)}`);
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console.log(`sosfiltfilt output: ${y2[mid].toFixed(4)}`);
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});
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run("out6", (tsb) => {
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const { sos } = tsb.butter(2, 0.3, "highpass");
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const { H } = tsb.sosfreqz(sos, 512);
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const mag = H.map(tsb.cAbs);
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console.log(`Gain at DC: ${mag[0].toFixed(4)}`);
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console.log(`Gain at Nyquist: ${mag[511].toFixed(4)}`);
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});
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run("out7", (tsb) => {
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const Wn = 0.3;
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console.log("Butterworth -3dB gain at cutoff:");
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for (const N of [1, 2, 4, 6, 8]) {
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const { sos } = tsb.butter(N, Wn, "lowpass");
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const { H } = tsb.sosfreqz(sos, [Wn * Math.PI]);
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const gain = tsb.cAbs(H[0]);
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const dB = 20 * Math.log10(gain);
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console.log(` N=${N}: gain=${gain.toFixed(4)} (${dB.toFixed(2)} dB)`);
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}
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});
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</script>
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</body>
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</html>

‎playground/index.html‎

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<p>Shannon entropy, KL divergence, Jensen-Shannon divergence/distance, cross-entropy, mutual information, conditional entropy, normalised MI, variation of information, joint entropy, Rényi entropy, and Tsallis entropy. Mirrors <code>scipy.stats.entropy</code> and related utilities.</p>
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<div class="status done">✅ Complete</div>
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</div>
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<div class="feature-card">
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<h3><a href="signal.html" style="color: var(--accent); text-decoration: none;">📡 Signal Processing — FFT, STFT, Welch PSD</a></h3>
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<p>FFT/IFFT/RFFT (Cooley-Tukey radix-2), <code>fftFreq</code>, <code>fftshift</code>/<code>ifftshift</code>, 8 window functions (<code>getWindow</code>), Short-Time Fourier Transform (<code>stft</code>/<code>istft</code> with overlap-add), Welch power spectral density, and periodogram. Mirrors <code>numpy.fft</code> and <code>scipy.signal</code>.</p>
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<div class="status done">✅ Complete</div>
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</div>
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<div class="feature-card">
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<h3><a href="filters.html" style="color: var(--accent); text-decoration: none;">🎛️ Digital Filters — FIR, Butterworth IIR</a></h3>
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<p>FIR filter design via windowed-sinc (<code>firwin</code>), Butterworth IIR (<code>butter</code>), frequency response (<code>freqz</code>, <code>sosfreqz</code>), and filter application: <code>lfilter</code> (causal), <code>filtfilt</code> (zero-phase), <code>sosfilt</code>, <code>sosfiltfilt</code>. Mirrors <code>scipy.signal</code>.</p>
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<div class="status done">✅ Complete</div>
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</div>
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</div>
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<div class="features-grid">
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<div class="feature-card">

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