# Biquad transformation

The biquad transformation is the substitution

$$s = \frac{1}{K}\frac{z-1}{z+1}, \, K=tan(\frac{\omega_c}{2})$$

used to convert the representation of a continuous (or "analog", Laplace transform) system into the representation of a discrete (or "digital", Z transform) system.

The biquad transformation is similar to the bilinear transformation, but does not exhibit the same warping of the frequency domain as the bilinear transformation.

An example of applying the biquad transformation on the transfer function of an infinite impulse response filter can be found in the topic Shelving filter.

## Add new comment

### Filtered HTML

• Freelinking helps you easily create HTML links. Links take the form of [[indicator:target|Title]]. By default (no indicator): Click to view a local node.
• Web page addresses and e-mail addresses turn into links automatically.
• Lines and paragraphs break automatically.

### Plain text

• No HTML tags allowed.
• Web page addresses and e-mail addresses turn into links automatically.
• Lines and paragraphs break automatically.
CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.