AN2874 Datasheet, PDF (1/6 Pages) STMicroelectronics – BQD filter design equations

AN2874
Applications note
BQD filter design equations
1
Introduction
A generalized set of equations is formulated for the design of first-order and second-order
low-pass and high-pass filters. A specialized set of equations is then given for the design of
parametric biquad EQ filters.
The parameters governing the characteristics of the filter are:
! filter cut-off frequency, f_C (-3 dB corner frequency)
! sampling rate (f_S).
! Q factor
! boost/cut gain value at f_C.
These parameters can be used to determine the coefficients of the filter transfer function.
The transfer function for a first-order filter in the digital z-domain can be written as:
H(z) = (b₀ + b₁.z^-1) / (a₀ + a₁.z^-1).
And for a second-order filter as:
H(z) = (b₀ + b₁.z^-1 + b₂.z^-2) / (a₀ + a₁.z^-1+ a₂.z^-2).
This document can be used in conjunction with all the ST digital audio devices having EAQ
filters onboard. These include STA309A, STA320, STA321, STA33xBW and several others.
February 2009
Rev 1
1/6
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