Extended Closed-form Expressions for the Robust Symmetrical Number System Dynamic Range and An Efficient Algorithm for its Computation
Pace, Phillip E.
Luke, Brian L.
Tedesso, Thomas W.
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The robust symmetrical number system (RSNS) is a number theoretic transform based on N > 2 sequences that can extract the maximum amount of information from symmetrical folding waveforms. The sequences, based on coprime moduli, exhibit an integer Gray code property making the RSNS well-suited for many applications that benefit from an inherent error detection and correction capability such as analog-to-digital converters, direction fnding arrays and radar waveform design. To use the RSNS, it is necessary to know the greatest length of combined sequences without ambiguities, called the dynamics range, M, for which only a few closed-form expresions currently exist. In this paper, an efficient algorithm for computing M and its position within the combined set of sequences is presented and shown to be independent of the size of the moduli. The algortihm is used to generate the equations for several groups of additional moduli arrangements. Closed form expressions for M are conjectured and proved using the obtained congruence equations that define the ambiguity locations.
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