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Lab · Biquad design

Computed

All-pass filters, corner by corner

Leaves every magnitude alone and shifts phase, passing through −180° at f0. Every ISO third-octave centre from 20 Hz to 20 kHz, solved at 48 kHz and seven other sample rates.

All filter typesDesign a cascade →

Every corner, with what changes across the sweep

The pole radius column is the one worth reading down. It rises toward 1 as the corner drops relative to the sample rate, and it is what decides the last column: the 3 corners at and below 40 Hz do not survive 16-bit fixed point at 48 kHz.

CornerAt f₀Pole radius @ 48 kHz16-bit fixed point
20 Hz0.00 dB0.998692diverges
25 Hz0.00 dB0.998365diverges
31.5 Hz0.00 dB0.997940holds · ≤ 0.000 dB
40 Hz0.00 dB0.997385diverges
50 Hz0.00 dB0.996733holds · ≤ 0.000 dB
60 Hz0.00 dB0.996081holds · ≤ 0.000 dB
80 Hz0.00 dB0.994778holds · ≤ 0.000 dB
100 Hz0.00 dB0.993476holds · ≤ 0.000 dB
125 Hz0.00 dB0.991852holds · ≤ 0.000 dB
160 Hz0.00 dB0.989583holds · ≤ 0.000 dB
200 Hz0.00 dB0.986996holds · ≤ 0.000 dB
250 Hz0.00 dB0.983772holds · ≤ 0.000 dB
315 Hz0.00 dB0.979597holds · ≤ 0.000 dB
400 Hz0.00 dB0.974166holds · ≤ 0.000 dB
500 Hz0.00 dB0.967816holds · ≤ 0.000 dB
630 Hz0.00 dB0.959628holds · ≤ 0.000 dB
800 Hz0.00 dB0.949033holds · ≤ 0.000 dB
1 kHz0.00 dB0.936734holds · ≤ 0.000 dB
1.25 kHz0.00 dB0.921614holds · ≤ 0.000 dB
1.6 kHz0.00 dB0.900925holds · ≤ 0.000 dB
2 kHz0.00 dB0.877973holds · ≤ 0.000 dB
2.5 kHz0.00 dB0.850335holds · ≤ 0.000 dB
3.15 kHz0.00 dB0.816178holds · ≤ 0.000 dB
4 kHz0.00 dB0.774597holds · ≤ 0.000 dB
5 kHz0.00 dB0.730270holds · ≤ 0.000 dB
6.3 kHz0.00 dB0.680357holds · ≤ 0.000 dB
8 kHz0.00 dB0.629016holds · ≤ 0.000 dB
10 kHz0.00 dB0.590467holds · ≤ 0.000 dB
12.5 kHz0.00 dB0.578174holds · ≤ 0.000 dB
16 kHz0.00 dB0.629016holds · ≤ 0.000 dB
20 kHz0.00 dB0.774597holds · ≤ 0.000 dB

The other seven types

Low-pass

Passes everything below the corner and rolls off above it at 12 dB/octave.

High-pass

Rejects everything below the corner at 12 dB/octave and passes what is above it.

Band-pass

Passes a band centred on f0 at unity gain and rejects everything either side.

Notch

Removes one frequency and leaves the rest of the spectrum untouched.

Peaking EQ

Boosts or cuts a band around f0 and leaves both ends of the spectrum at unity.

Low shelf

Lifts or drops everything below f0 by a fixed amount and leaves the top flat.

High shelf

Lifts or drops everything above f0 by a fixed amount and leaves the bottom flat.

Method. RBJ Audio EQ Cookbook coefficients at Q = 1.0000, normalised to a₀ = 1. Pole radii are the roots of the denominator quadratic, not √|a₂| — the two disagree exactly when coefficient rounding pushes the poles onto the real axis, which is the case this table's last column is about. Every figure is solved; nothing is fetched.