Digital biquad filter

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For the analog implementation of a biquad filter, check biquad filter.

In signal processing, a digital biquad filter is a second-order recursive linear filter, containing two poles and two zeros. "Biquad" is an abbreviation of "biquadratic", which refers to the fact that in the Z domain, its transfer function is the ratio of two quadratic functions:

High-order recursive filters can be highly sensitive to quantization of their coefficients, and can easily become unstable. This is much less of a problem with first and second-order filters; therefore, higher-order filters are typically implemented as serially-cascaded biquad sections (and a first-order filter if necessary).

Contents 1 Implementation 1.1 Direct Form 1 1.2 Direct Form 2 2 References 3 See also

[edit] Implementation

[edit] Direct Form 1

The most straightforward implementation is the Direct Form 1, which has the following difference equation:

Here the b₀, b₁ and b₂ coefficients determine zeros, and a₁, a₂ determine the position of the poles.

Flow graph of biquad filter in Direct Form 1:

[edit] Direct Form 2

The Direct Form 1 implementation requires four delay registers. An equivalent circuit is the Direct Form 2 implementation, which requires only two delay registers:

The Direct Form 2 implementation is called the canonical form, because it uses the minimal amount of delays, adders and multipliers, yielding in the same transfer function as the Direct Form 1 implementation. The difference equations for DF2 are:

where

[edit] References

• Sen M Kuo, Bob H Lee: Real-Time Digital Signal Processing, Wiley & Sons Ltd, 2001
• Cookbook formulae for audio EQ biquad filter coefficients
• Biquad filter
• JOS BiQuad section

[edit] See also

• Biquad filter
• Digital filter