apparatus , and a related method , for converting digital signals directly to radio - frequency analog signals . the apparatus includes a single high - speed delta - sigma modulator and an integrated upsampler that increases the data rate of digital input samples by a selected factor , such as nine times . the delta - sigma modulator is configured to include a feedback multiplier coefficients that are selected to greatly facilitate operation of associated adders . at least one critical adder includes a carry - select adder modification that further speeds up the add operation and ensures that the apparatus operates at desirably high frequencies .