On residue number A/D and D/A converters

A very simple analog to digital converter and digital to analog converter is described for residue number digital processing. These simple devices make it feasible to replace analog components with comparitively inexpensive digital processors that use residue, or modulus, arithmetic capable of operating at very high speeds. Using off-the-shelf integrated circuits, addition, subtraction or multiplication of about 15 bits of accuracy can easily be done in as little as fifty nanoseconds. Any function using these operations (polynomial expansions, linear filters, fast fourier transforms) can be economically implemented in a pipeline or other structure to get very fast systems. Moreover, a stage in the pipeline can correct for non-linearities in the A/D or D/A converters. The simple devices described herein make residue arithmetic digital processors extremely attractive for use in fast analog systems.