biquad

NODE

EQ and filters. Eight response shapes, from a bell to a notch, all solved as a state-variable filter.

Parameters

FIELD	WHAT IT DECIDES	RANGE	REQUIRED
cutoff_hz	Cutoff / centre frequency [Hz]. The maximum is the internal Nyquist of the lower rate family.	0 〜 352,800	yes
gain_db?	Gain [dB]. Required for bell and the shelves, null or omitted for the other shapes.	-24 〜 24	no
q	Q.	0.05 〜 40	yes
shape	Response shape.	low_pass / high_pass / band_pass / notch / all_pass / bell / low_shelf / high_shelf	yes

? = the field may be omitted

{
  "cutoff_hz": 1000,
  "gain_db": 3,
  "q": 1,
  "shape": "bell",
  "type": "biquad"
}

How it is computed

g = tan(π · cutoff_hz / rate)     rate = 705,600 or 768,000 Hz
k = 1 / q                        (for a bell, 1 / (q · A))

the five coefficients (g, k and three mixing terms) are solved from
the shape, the cutoff, q and gain_db, then run as a TPT state-variable filter

A topology-preserving state-variable form is used rather than a direct-form biquad. At 768 kHz the ratio of cutoff to rate is very small, and direct-form coefficients degenerate there: the filter drifts toward the instability the validation exists to catch. In this form, any cutoff below Nyquist with a positive q stays stable however the coefficients round.

gain_db applies to bell, low_shelf and high_shelf. For the other shapes it must be omitted or null.
The coefficients are solved by the same code that draws the response curve in the app, so the curve you see and the filter you hear cannot disagree.
Coefficients are solved again at both internal rates, and the design has to be valid at both.

Using it

The cutoff can be set far above the audible band.
The maximum is the internal Nyquist of the lower family. That is deliberate: filters that shape what a nonlinear stage produced up there are a legitimate thing to write. What is refused is amplifying that band.
A high q is not refused, it is measured.
A very narrow filter with a large boost has a large peak gain, and the coefficient check measures exactly that. If it refuses, the numbers it returns tell you how far over you are.
It is linear, so it joins the loudness match.
A biquad that lifts a band raises the measured level of the chain, and the A/B matching accounts for it from the coefficients.