Peaking EQ filters, corner by corner

Boosts or cuts a band around f0 and leaves both ends of the spectrum at unity. Every ISO third-octave centre from 20 Hz to 20 kHz, solved at 48 kHz and seven other sample rates.

All filter types Design 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 5 corners at and below 50 Hz do not survive 16-bit fixed point at 48 kHz.

Corner	At f₀	Pole radius @ 48 kHz	16-bit fixed point
20 Hz	+6.00 dB	0.999074	diverges
25 Hz	+6.00 dB	0.998842	diverges
31.5 Hz	+6.00 dB	0.998542	diverges
40 Hz	+6.00 dB	0.998148	diverges
50 Hz	+6.00 dB	0.997686	diverges
60 Hz	+6.00 dB	0.997224	holds · ≤ 0.046 dB
80 Hz	+6.00 dB	0.996300	holds · ≤ 0.598 dB
100 Hz	+6.00 dB	0.995377	holds · ≤ 0.382 dB
125 Hz	+6.00 dB	0.994225	holds · ≤ 0.444 dB
160 Hz	+6.00 dB	0.992614	holds · ≤ 0.099 dB
200 Hz	+6.00 dB	0.990777	holds · ≤ 0.065 dB
250 Hz	+6.00 dB	0.988485	holds · ≤ 0.188 dB
315 Hz	+6.00 dB	0.985514	holds · ≤ 0.095 dB
400 Hz	+6.00 dB	0.981643	holds · ≤ 0.016 dB
500 Hz	+6.00 dB	0.977111	holds · ≤ 0.032 dB
630 Hz	+6.00 dB	0.971255	holds · ≤ 0.038 dB
800 Hz	+6.00 dB	0.963660	holds · ≤ 0.004 dB
1 kHz	+6.00 dB	0.954817	holds · ≤ 0.001 dB
1.25 kHz	+6.00 dB	0.943910	holds · ≤ 0.002 dB
1.6 kHz	+6.00 dB	0.928924	holds · ≤ 0.001 dB
2 kHz	+6.00 dB	0.912221	holds · ≤ 0.002 dB
2.5 kHz	+6.00 dB	0.892012	holds · ≤ 0.002 dB
3.15 kHz	+6.00 dB	0.866912	holds · ≤ 0.001 dB
4 kHz	+6.00 dB	0.836215	holds · ≤ 0.000 dB
5 kHz	+6.00 dB	0.803389	holds · ≤ 0.000 dB
6.3 kHz	+6.00 dB	0.766413	holds · ≤ 0.000 dB
8 kHz	+6.00 dB	0.728526	holds · ≤ 0.000 dB
10 kHz	+6.00 dB	0.700294	holds · ≤ 0.000 dB
12.5 kHz	+6.00 dB	0.691348	holds · ≤ 0.000 dB
16 kHz	+6.00 dB	0.728526	holds · ≤ 0.000 dB
20 kHz	+6.00 dB	0.836215	holds · ≤ 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.

All-pass

Leaves every magnitude alone and shifts phase, passing through −180° at f0.

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 and +6 dB, 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.