An optimum SNS-to-binary conversion algorithm and pipelined field-programmable logic design

The Optimum Symmetrical Number System (OSNS) formulation is a direct conseq uence of the need to extract the maximum amount of information from a symme trically folded waveform, and has found use in applications such as folding analog-to-digital converters and phase-sampled direction finding antenna a rchitectures, One of the keg problems in an OSNS hardware realization is re combining the OSNS symmetrical residues (s(1), s(2) , ... ,s(3)) to determi ne the unknown incoming value. The symmetrical residues cannot be converted (e.g,, using the Chinese Remainder Theorem) in a straightforward manner, s ince the integers within each modulus are ambiguous. This paper presents an OSNS-to-binary conversion algorithm for N = 3 moduli of the form m(1) = 2( k) + 1, m(2) = 2(k), and m(3) = 2(k) - 1, The algorithm consists of three m ain steps: 1) conversion of the symmetrical residues into complete residues ; 2) solving the resulting congruences in binary; and 3) determining the un known incoming value, A B = 14-bit pipelined field-programmable logic desig n (FPLD) using k = 6 is also presented to illustrate the algorithm. The num ber of bits throughout the FPLD are quantified and an example calculation i s worked out to numerically demonstrate the efficiency of the design.