Parametric EQ Biquad Coefficients
Peaking filter:
A = 10^(gain_dB / 40)
ω₀ = 2π × f_center / f_s
α = sin(ω₀) / (2Q)
b₀ = 1 + α × A
b₁ = −2 × cos(ω₀)
b₂ = 1 − α × A
a₀ = 1 + α / A
a₁ = −2 × cos(ω₀)
a₂ = 1 − α / A
Normalize all by a₀.
Low-shelf filter:
A = 10^(gain_dB / 40)
ω₀ = 2π × f_c / f_s
α = sin(ω₀) / 2 × √((A + 1/A) × (1/S − 1) + 2)
(where S = shelf slope, typically 1.0)
b₀ = A × [(A+1) − (A−1)×cos(ω₀) + 2√A×α]
b₁ = 2A × [(A−1) − (A+1)×cos(ω₀)]
b₂ = A × [(A+1) − (A−1)×cos(ω₀) − 2√A×α]
a₀ = (A+1) + (A−1)×cos(ω₀) + 2√A×α
a₁ = −2 × [(A−1) + (A+1)×cos(ω₀)]
a₂ = (A+1) + (A−1)×cos(ω₀) − 2√A×α
Normalize all by a₀.
These are the "Audio EQ Cookbook" formulas — the standard reference for digital filter design, by Robert Bristow-Johnson.