A modulator performs data processing operations such as interpolation and fractional delay adjustment on amplitude and/or phase data by performing shift operations in lieu of multiplication operations. In selected embodiments, the modulator samples input data at a first rate, processes the sampled input data using the first rate, and then interpolates the processed data to produce interpolated data. The modulator then samples the interpolated data at a second rate higher than the first rate and generates output data at the second rate.