AN2874 datasheet(2/6 Pages) STMICROELECTRONICS

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Low-pass and high-pass filter design

AN2874

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Low-pass and high-pass filter design

First-order filter design

As a first step to obtain the coefficients for the 1st-order low-pass or high-pass filter equation

on page 1, the following equations can be used:

θC = 2 ∗ π ∗ fC / fS (= the normalized cut-off frequency)

K = tan(

θC / 2)

α = 1 + K.

The denominator coefficients are identical for both low-pass and high-pass filters designed

for the same cut-off frequency and are computed as follows:

a0 = 1

a1 = -(1 - K) / α.

The numerator coefficients for a low-pass filter can be calculated as follows:

b0 = K / α

b1 = K / α.

The numerator coefficients for a high-pass filter can be calculated as follows:

b0 = 1 / α

b1 = -1 / α.

Second-order filter design

As a first step to obtain the coefficients for the 2nd-order low-pass or high-pass filter

equation on page 1, the following equations can be used:

θC = 2 ∗ π ∗ fC / fS

K = tan(

θC / 2)

W = K2

α = 1 + K / Q + W.

The denominator coefficients are the same for both low-pass and high-pass filters designed

for the same cut-off frequency and are computed as follows:

a0 = 1

a1 = 2 * (W - 1) / α

a2 = (1 - K / Q + W) / α.

The numerator coefficients for a low-pass filter can be calculated as follows:

b0 = W / α

b1 = 2 * W / α

b2 = b0.

The numerator coefficients for a high-pass filter can be calculated as follow:

b0 = 1 / α

b1 = -2 / α

b2 = b0.

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