A direct interpolation method is described that reduces the distortion due to quantisation and linearity errors of practical analogue-to-digital convertors. In contrast with other interpolation systems, the analogue signal is not oversampled, and no feedback loops are required. Compared with the conventional use of 'dither', direct interpolation provides an increase in signal-to-noise ratio as well as a reduction in harmonic distortion. Computer simulations and experimental measurements are presented. The method is particularly suited to reducing high-order harmonics and increasing the effective resolution of an ADC.