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	b0 · b1 · b2 · a1 · a2 @ 48 kHz
20 Hz	+6.00 dB	0.999074	diverges	1.000921453 · -1.998141473 · 0.997226867 · -1.998141473 · 0.998148320
25 Hz	+6.00 dB	0.998842	diverges	1.001151550 · -1.997675241 · 0.996534388 · -1.997675241 · 0.997685938
31.5 Hz	+6.00 dB	0.998542	diverges	1.001450515 · -1.997068184 · 0.995634647 · -1.997068184 · 0.997085161
40 Hz	+6.00 dB	0.998148	diverges	1.001841196 · -1.996272714 · 0.994458883 · -1.996272714 · 0.996300079
50 Hz	+6.00 dB	0.997686	diverges	1.002300425 · -1.995334511 · 0.993076823 · -1.995334511 · 0.995377248
60 Hz	+6.00 dB	0.997224	holds · ≤ 0.046 dB	1.002759226 · -1.994393765 · 0.991696053 · -1.994393765 · 0.994455279
80 Hz	+6.00 dB	0.996300	holds · ≤ 0.598 dB	1.003675542 · -1.992504666 · 0.988938381 · -1.992504666 · 0.992613923
100 Hz	+6.00 dB	0.995377	holds · ≤ 0.382 dB	1.004590143 · -1.990605459 · 0.986185871 · -1.990605459 · 0.990776014
125 Hz	+6.00 dB	0.994225	holds · ≤ 0.444 dB	1.005730979 · -1.988217298 · 0.982752501 · -1.988217298 · 0.988483480
160 Hz	+6.00 dB	0.992614	holds · ≤ 0.099 dB	1.007323638 · -1.984847595 · 0.977959362 · -1.984847595 · 0.985283000
200 Hz	+6.00 dB	0.990777	holds · ≤ 0.065 dB	1.009137365 · -1.980959220 · 0.972500913 · -1.980959220 · 0.981638278
250 Hz	+6.00 dB	0.988485	holds · ≤ 0.188 dB	1.011394827 · -1.976043297 · 0.965707035 · -1.976043297 · 0.977101862
315 Hz	+6.00 dB	0.985514	holds · ≤ 0.095 dB	1.014313390 · -1.969561444 · 0.956923559 · -1.969561444 · 0.971236949
400 Hz	+6.00 dB	0.981643	holds · ≤ 0.016 dB	1.018102386 · -1.960931808 · 0.945520499 · -1.960931808 · 0.963622885
500 Hz	+6.00 dB	0.977111	holds · ≤ 0.032 dB	1.022519896 · -1.950560546 · 0.932225911 · -1.950560546 · 0.954745807
630 Hz	+6.00 dB	0.971255	holds · ≤ 0.038 dB	1.028197613 · -1.936731967 · 0.915138706 · -1.936731967 · 0.943336319
800 Hz	+6.00 dB	0.963660	holds · ≤ 0.004 dB	1.035511030 · -1.918074567 · 0.893128827 · -1.918074567 · 0.928639858
1 kHz	+6.00 dB	0.954817	holds · ≤ 0.001 dB	1.043953087 · -1.895320724 · 0.867722285 · -1.895320724 · 0.911675372
1.25 kHz	+6.00 dB	0.943910	holds · ≤ 0.002 dB	1.054258810 · -1.865708809 · 0.836707001 · -1.865708809 · 0.890965811
1.6 kHz	+6.00 dB	0.928924	holds · ≤ 0.001 dB	1.068225378 · -1.822190877 · 0.794674327 · -1.822190877 · 0.862899705
2 kHz	+6.00 dB	0.912221	holds · ≤ 0.002 dB	1.083528432 · -1.769718979 · 0.748619473 · -1.769718979 · 0.832147905
2.5 kHz	+6.00 dB	0.892012	holds · ≤ 0.002 dB	1.101673322 · -1.700388588 · 0.694012057 · -1.700388588 · 0.795685378
3.15 kHz	+6.00 dB	0.866912	holds · ≤ 0.001 dB	1.123642896 · -1.604737169 · 0.627894173 · -1.604737169 · 0.751537069
4 kHz	+6.00 dB	0.836215	holds · ≤ 0.000 dB	1.149660126 · -1.471597921 · 0.549594786 · -1.471597921 · 0.699254912
5 kHz	+6.00 dB	0.803389	holds · ≤ 0.000 dB	1.176443260 · -1.305410288 · 0.468990397 · -1.305410288 · 0.645433657
6.3 kHz	+6.00 dB	0.766413	holds · ≤ 0.000 dB	1.205327868 · -1.077521139 · 0.382061577 · -1.077521139 · 0.587389445
8 kHz	+6.00 dB	0.728526	holds · ≤ 0.000 dB	1.233513677 · -0.765374742 · 0.297235808 · -0.765374742 · 0.530749485
10 kHz	+6.00 dB	0.700294	holds · ≤ 0.000 dB	1.253587270 · -0.385746801 · 0.236823918 · -0.385746801 · 0.490411188
12.5 kHz	+6.00 dB	0.691348	holds · ≤ 0.000 dB	1.259782507 · 0.096663322 · 0.218179226 · 0.096663322 · 0.477961733
16 kHz	+6.00 dB	0.728526	holds · ≤ 0.000 dB	1.233513677 · 0.765374742 · 0.297235808 · 0.765374742 · 0.530749485
20 kHz	+6.00 dB	0.836215	holds · ≤ 0.000 dB	1.149660126 · 1.471597921 · 0.549594786 · 1.471597921 · 0.699254912

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.