Biquad Calculator

A biquad is a second order IIR (Infinite Impulse Response) filter. It is used as the basic building blocks for complex filters due to the sensitivity of the biquad coefficients in higher order filters. This online calculator is used to find the biquad filter coefficients (a0, a1, a2, b1 and b2).

Biquad Filter Coefficient Calculation

Hz
Hz
dB
Biquad Filter Coefficients
a0
a1
a2
b1
b2

A biquad is a second order IIR (Infinite Impulse Response) filter. It is used as the basic building blocks for complex filters due to the sensitivity of the biquad coefficients in higher order filters. This online calculator is used to find the biquad filter coefficients (a0, a1, a2, b1 and b2).

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Biquads come in several forms. Direct form I, Direct form II, Transposed Direct Form II and Direct Form I with First Order Noise Shaping.

Example

Let consider the sample rate is 12Hz, frequency is 34Hz, bandwidth is 4 and gain is 3 of the lowpass filter, find the filter coefficients,

If frequency is greater than half value of sample rate, the frequency is half the value of sample rate,
Given,
F = 34, SR = 12, Q = 4, g = 3

Step : 1

F = SR / 2
F= 12 / 2 = 6

R = tan(π * F / SR)
R = tan(π * 6 / 12)
R = tan(1.5707963267948966)
R = 16331778728383844

Step : 2

Normal = 1 / (1 + / Q + R * R)
Normal = 1 / (1 + 16331778728383844 / 4 + 16331778728383844 * 16331778728383844)
Normal = 3.7491518045553436e-33

Step : 3

a0 = R * R * Normal
a0 = 16331778728383844 * 16331778728383844 * 3.7491518045553436e-33
a0 = 1

Step : 4

a1 = 2 * a0
a1 = 2 * 1
a1 = 2

Step : 5

a2 = a0
a2 = 1

Step : 6

b1 = 2 * (R * R - 1) * Normal
b1 = 2 * (16331778728383844 * 16331778728383844 - 1) * 3.7491518045553436e-33
b1 = 2

Step : 7

b2 = (1 - R / Q + R * R) * Normal
b2 = (1 - 16331778728383844 / 4 + 16331778728383844 * 16331778728383844) * 3.7491518045553436e-33
b2 = 1


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