AD1953 Analog Devices, AD1953 Datasheet - Page 33

• Manufacturer Part Number: AD1953
• Description: SigmaDSP Digital Audio Processor
• Manufacturer: Analog Devices

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:
2. Compute Intermediate Variables
3. Compute Coefficients
4. The transfer function implemented by the AD1953 is given by:
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.
REV. 0
Y(n) = a1
Frequency
Q
dB_Gain
sample_rate
A = 10^(dB_Gain/40)
omega = 2
sn = sin(omega)
cs = cos(omega)
alpha = sn/(2
b0 = (1 + A
b1 = –2
b2 = (1 – (alpha/A))/(1 + (alpha/A))
a1 = 2
a2 = –(1 – (alpha/A))/(1 + (alpha/A))
H(Z) = (b0 + b1
×
×
×
cs/(1 + (alpha/A)) = –b1
y(n – 1) + a2
cs/(1 + (alpha/A))
×
×
π
×
alpha)/(1 + (alpha/A))
×
Q)
Frequency/Sample_Rate
×
Z
–1
+ b2
×
y(n – 2) + b0
×
Z
–2
)/(1 – a1
×
x(n) + b1
×
Z
–1
– a2
×
×
x(n – 1) + b2
Z
–2
)
–33–
×
x(n – 2)
AD1953