Low-pass at 1000 Hz

Gain at corner
-3.01 dB
Gain at Nyquist
-334.7 dB
Group delay at corner
0.226 ms
Pole radius
0.9116

RBJ Audio EQ Cookbook coefficients solved in float64, with pole and zero radii from the quadratic roots (never from sqrt(|a2|)), the response curve, the real −3 dB crossings, and what 16/24/32-bit word lengths do to stability and in-band error. Pure mathematics — nothing is fetched and nothing is recalled.

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