Inner products computation using folded waveforms and distributed arithmetic principles

In this paper, inner products using a new number system called the Folding Residue Number System (FRNS) and Distributed Arithmetic (DA) principles is proposed. The advantage of this new number system is that it allows digital filters to be implemented directly from the analog signal by decomposing and folding it in several parallel channels. Folding Residues extracted together with the folding information obtained from the folding circuits are processed using DA principles in implementing the filtering algorithm. The FRNS has the same complexity of computation as that of the Residue Number System (RNS) but intermediate steps such as conversion of the analog signal into its binary equivalents and subsequently into residues required in RNS are eliminated. Moreover, smaller word length of the folding residues coupled with DA results in faster implementation of the filtering algorithms.