A method is presented for converting the sine/cosine signals from an optical encoder into a high-resolution position signal for use by a position control system while eliminating common noise and error sources. The improved noise performance resulting from the alias-free demodulation of encoder signals improves precision and reduces power consumption in precision motion control applications. The adaptive compensation of harmonic distortion eliminates errors related to offset, gain and quadrature of the encoder channels. The interpolator is able to process encoder signals at extremely high resolution without the speed limitation of prior art encoder interpolators.