# 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

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 : 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