We propose a new type of oversampled analog-to-digital converter. It uses digital extrapolators to predict the analog signal before it is converted, and a coarse quantizer to convert the prediction error. Such converters are expected to have reduced complexity in their analog circuitry, thanks to the processing in the digital domain. General linear extrapolation algorithms are derived from the spline theory, and can be easily implemented using digital filters. Simulations show that the speed-resolution trade-off is 2 bits per octave with simple linear extrapolation. Noise-shaping can be added using a matched analog preemphasis filter, in which case the converter behaves similar to a delta-sigma modulator of the same order.