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z^{-2}}$\n\n**Pole radius**: $R = e^{-\\pi \\cdot bw / f_s}$ — controls bandwidth; $bw \\to 0$ gives infinite Q
\n**Peak gain**: always 0 dB by construction — the two zeros at $z = \\pm 1$ shape the numerator so $(1-R^2)/2$ normalizes the pole peak regardless of `fc`/`bw` (verified ±0.01 dB across `fc` ∈ {50, 440, 5000, 15000} Hz, `bw` ∈ {5, 20, 200} Hz)
\n**Origin**: Julius O. Smith III, *Introduction to Digital Filters with Audio Applications* — Two-Pole, \"Constant Peak-Gain Resonator\"\n\n```js\nresonator(buffer, { fc: 440, bw: 20, fs: 44100 })\n```\n\n| Param | Default | |\n|---|---|---|\n| `fc` | — | required, center frequency Hz |\n| `fs` | `44100` | sample rate, Hz |\n| `bw` | `50` | bandwidth, Hz — smaller = higher Q |\n\nPass the same `params` object on every call to persist the two-pole state across blocks. Internal cache fields are prefixed `_r*` (`_rFc`, `_rA1`, …) so `params` can double as a caller-owned object — e.g. `@audio/speech-formant` shares one params object per formant band.\n\n**Use when:** additive synthesis (bells, gongs), modal synthesis, formant bank building.\n\n**vs Peaking EQ**: resonator has fixed 0 dB peak; peaking EQ has variable gain — use resonator for synthesis, EQ for mixing.\n\n---\n\nPart of [@audio/filter](https://github.com/audiojs/filter) — the filter family umbrella. This README is generated from the umbrella docs.\n\nMIT © [audiojs](https://github.com/audiojs)\n","readmeFilename":"README.md"}