For what it's worth, it's not a resolver. It's rather a variation of a Sine quadrature encoder. It's implemented on a scale rather than on a rotary encoder. The sine/cosine signals are decoded in the Heidenhain controller with a AD converter of some resolution. For instance an 8-bit converter will break the sine wave into 256 parts and thus it will get a resolution multiplied by that amount compared to the scale resolution.
Considering the above, while you would be able to use a simple Schmitt trigger to produce digital quadrature signals from the sine/cosine ones, you would lose resolution to such an extent making the scale not efficient. A further electronic gearing circuit could be added, but that would make things much more complicated.