N-Sequence RSNS Redundancy Analysis

Without dispute, symmetrical folding waveforms are the most common type of waveform in engineering science (e.g., cosine, sine). symmetrical number systems (SNS) have been formed to extract the maximum amount of information from symmetrically folded waveforms. The robust symmetrical number system (RSNS) is formed using N ges 2 sequences and ensures that two successive RSNS vectors differ by only one digit. This Gray-code property reduces the possibility of encoding errors and makes the RSNS useful in applications such as folding analog-to-digital converters, direction finding antenna architectures and photonic processors. This paper determines the length of combined sequences that contain no ambiguities (Mcirc) which we call the RSNS dynamic range. The position of M is also derived. We first extend our two-sequence results to develop Mcirc for a three-sequence RSNS with moduli of the form 2 r - 1, 2 r , 2 r + 1. We then extend the results to solving the N-channel RSNS redundancy locations in general