Algebraic-integer quantization an residue number system processing

The algebraic-integer number representation, in which the signal sample is represented by a set of (typically four to eight) small integers, combines with residue number system (RNS) processing to produce processors composed of simple parallel channels. The analog samples must first be quantized into the algebraic-integer representation, and the final algebraic-integer result converted back to an analog or digital form. In between these two conversions, the algebraic-integer representation must be converted into and out of two levels of RNS parallelism. The authors address these quantization and conversion problems and demonstrate their solution by implementing a 128-tap algebraic-integer filter using the moduli 17 and 31, with four parallel channels per modulus. This processor performs equivalently to an integer processor with 19 bits of dynamic range. It is concluded that the algebraic-integer representation is best suited to control the dynamic range requirements of integer processors in situations where there is a high sensitivity to quantization and roundoff errors, especially when there is a matching nonuniform input distribution