RBJ cookbook biquads: pick a response, get MCU-ready coefficients and the curve.

The biquad — the workhorse of embedded DSP

A biquad is a second-order IIR section:

H (z) = \frac{b _{0} + b _{1} z ^{- 1} + b _{2} z ^{- 2}}{1 + a _{1} z ^{- 1} + a _{2} z ^{- 2}}

Five multiplies and four adds per sample, regardless of the response shape — which is why audio EQs, sensor conditioning chains and PLL loop filters are all built from cascaded biquads. The coefficient recipes here come from Robert Bristow-Johnson's Audio EQ Cookbook, the de-facto standard. Two embedded notes: use Direct Form I on fixed-point machines (it tolerates coefficient quantization better than Form II), and at very low $f_{0} / f_{s}$ ratios the poles crowd the unit circle — switch to double precision or cascade two gentler sections instead of one aggressive one.

Biquad Filter Designer

The biquad — the workhorse of embedded DSP