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.

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