The only elements in Fig.3 needing modification for digitization are the two integrators, each having transfer function . Normally the preferred digitization method is the bilinear transform:
However, the bilinear transform cannot be used here due to the presence of feedback which would give a delay-free loop.
The Forward Euler (FE) finite-difference scheme introduces a sample of delay in the digitization of that avoids a delay-free loop:
where denotes the sampling interval in seconds. There is also a Backward Euler (BE) finite-difference scheme:
It can be effective to use FE and BE together in alternation to avoid delay build-up in either direction:
Digitizing the two integrators in Fig.3 via FE and BE respectively and removing the frequency normalization yields
The resulting digital filter is drawn in Fig.4. This structure is normally called the Chamberlin form digital filter section .