Variable word length DSP using serial-by-modulus residue arithmetic

The concept of a variable-word-length sum-of-products signal processing kernel is developed based on a serial-by-modulus (SBM) residue number system (RNS) architecture. Because the RNS is not a weighted number representation, if the instantaneous dynamic range requirement can be estimated it is possible to perform the computation with only enough residue digits to provide the necessary dynamic range. Although it is difficult to estimate instantaneous dynamic range requirements for arbitrary computational processes encountered in general-purpose computers, in well-defined signal processing tasks, such as the sum-of-products kernel found in digital filters and vector processors, it may be possible to take advantage of a variable-word-length design to improve computational efficiency for special-purpose processors. Computer experiments were performed in software written in C that was designed to emulate an SBM FIR (finite impulse response) filter.<>