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AD1953

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APPENDIX

Cookbook Formulae for Audio EQ Biquad Coefficients

(adapted from Robert Bristow-Johnson’s Internet posting)

For designing a Parametric EQ, follow the steps below.

1. Given:

Frequency

dB_Gain

sample_rate

2. Compute Intermediate Variables

A = 10^(dB_Gain/40)

omega = 2

π × Frequency/Sample_Rate

sn = sin(omega)

cs = cos(omega)

alpha = sn/(2

× Q)

3. Compute Coefficients

b0 = (1 + A

× alpha)/(1 + (alpha/A))

b1 = –2

× cs/(1 + (alpha/A))

b2 = (1 – (alpha/A))/(1 + (alpha/A))

a1 = 2

× cs/(1 + (alpha/A)) = –b1

a2 = –(1 – (alpha/A))/(1 + (alpha/A))

4. The transfer function implemented by the AD1953 is given by:

H(Z) = (b0 + b1

× Z–1 + b2 × Z–2)/(1 – a1 × Z–1 – a2 × Z–2)

Note the inversion in sign of a1 and a2 relative to the more standard form. This form is used in this document because the AD1953

implements the difference equation using the formula below.

Y(n) = a1

× y(n – 1) + a2 × y(n – 2) + b0 × x(n) + b1 × x(n – 1) + b2 × x(n – 2)

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