Abstract: High speed interpolation machine for interpolating values in the transformation from one space to another. One important application is in the transformation from a transmission space to a display space for digital color television reproduction. The machine includes storage schemes for lookup table contents which permit parallel access to needed transformation coefficients during one clock cycle. The architecture results in a machine which can compute interpolation points quickly enough for real time digital television processing and requires a relatively small number of electronic components. The present invention will compute the interpolation function with approximately one eighth the memory requirements of a comparable high speed implementation. In one embodiment, the number of multiples is reduced and in another implementation, all of the multiplications can be eliminated. The transformation coefficients are stored in separate interpolation tables permitting parallel access.