Lab · Computed reference
ComputedBiquad coefficients, solved
Every one of the eight RBJ filter types at every ISO third-octave centre from 20 Hz to 20 kHz — 248 designs, each with its 48 kHz coefficients, poles solved from the quadratic, and the word length it stops working at. Any other rate is one API call.
Pick a type
The last column is measured over each type's full sweep on this build, not quoted: it is the count of corners whose poles leave the unit circle once all five coefficients are rounded to a shared 16-bit scale. None of them fail at 24-bit.
31 corners
Low-pass
Passes everything below the corner and rolls off above it at 12 dB/octave.
worst pole 0.99815 · 3 fail at 16-bit
31 corners
High-pass
Rejects everything below the corner at 12 dB/octave and passes what is above it.
worst pole 0.99815 · 3 fail at 16-bit
31 corners
Band-pass
Passes a band centred on f0 at unity gain and rejects everything either side.
worst pole 0.99869 · 3 fail at 16-bit
31 corners
Notch
Removes one frequency and leaves the rest of the spectrum untouched.
worst pole 0.99869 · 3 fail at 16-bit
31 corners
All-pass
Leaves every magnitude alone and shifts phase, passing through −180° at f0.
worst pole 0.99869 · 3 fail at 16-bit
31 corners
Peaking EQ
Boosts or cuts a band around f0 and leaves both ends of the spectrum at unity.
worst pole 0.99907 · 5 fail at 16-bit
31 corners
Low shelf
Lifts or drops everything below f0 by a fixed amount and leaves the top flat.
worst pole 0.99844 · 4 fail at 16-bit
31 corners
High shelf
Lifts or drops everything above f0 by a fixed amount and leaves the bottom flat.
worst pole 0.99780 · 5 fail at 16-bit
The corner frequencies
ISO 266 third-octave centres, with one substitution: 60 Hz replaces 63 Hz, because at the bottom of the spectrum the frequency people design a filter at is the power line, and the two are 5% apart. A 63 Hz notch does not remove 60 Hz hum, so substituting was the safe direction. Each type's table above lists every corner with its coefficients: 20 Hz · 25 Hz · 31.5 Hz · 40 Hz · 50 Hz · 60 Hz · 80 Hz · 100 Hz · 125 Hz · 160 Hz · 200 Hz · 250 Hz · 315 Hz · 400 Hz · 500 Hz · 630 Hz · 800 Hz · 1 kHz · 1.25 kHz · 1.6 kHz · 2 kHz · 2.5 kHz · 3.15 kHz · 4 kHz · 5 kHz · 6.3 kHz · 8 kHz · 10 kHz · 12.5 kHz · 16 kHz · 20 kHz.
What these tables are, and are not
Solved, not sampled
Every figure comes from the RBJ Audio EQ Cookbook evaluated at each type and corner. Nothing is fetched, interpolated or recalled, so there is nothing here that can be out of date or wrong about the world — only right or wrong about the arithmetic, which is checked by asserting the shape of the response rather than comparing coefficients.
A coefficient set is not an implementation
The fixed-point columns model coefficient rounding and nothing else. Signal-path headroom, limit cycles, accumulator width and the topology you pick (Direct Form I vs transposed II) all matter and none of them are on these pages. A design that clears the table can still misbehave in your loop.
The tables use 48 kHz. The API also returns8 kHz, 16 kHz, 22.05 kHz, 32 kHz, 44.1 kHz, 96 kHz, 192 kHz, dropping any rate whose Nyquist limit the corner does not clear. Shelves fix the slope at S = 1, matching Web Audio's BiquadFilterNode, so Q is not read for those two types.
Taking a design with you
Every design is already an API call
curl "https://makerportal.ai/api/v1/biquad-design?type=highpass&freq=80&fs=48000"returns this lane's solve as JSON — the identical function that renders the page, not a second copy of it. No key, no account, CORS open, and &include=curveadds the 240-point response. Arbitrary inputs are accepted, not just the 248 published corners, and every answer names the page it belongs to. Embed a resulton your own site, or design a cascade in the interactive designer.
A coefficient set still is not a running filter
These pages stop at the numbers, deliberately — see the note above about headroom, limit cycles and topology. Biquadia — Local Neural DSP & Sound Laboratory, CoreML · Neural Engine (ANE) · Metal Shaders · Native Swift, iOS (iPhone + iPad) — is where the studio runs this class of DSP on the device instead of describing it.