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.
MetadataShow full item record
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.
RightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
Showing items related by title, author, creator and subject.
Techniques and benefits of shaping the pulses of binary sequences with application to spread spectrum radio communications. Mavranganis, Panayiotis G. (Monterey, California. Naval Postgraduate School, 1979-03);This research is concerned with binary sequences. Such two-level voltage waveforms are used in some types of spread spectrum systems. Of interest in this work is the effect of shaping the normally rectangular pulses of ...
Jauregui, Stephen Jr. (Monterey, California: U.S. Naval Postgraduate School, 1962-05);Complementary binary sequences were invented by Golay in an investigation of infra-red multi-slit spectrometry. This dissertation formalizes the basic results obtained by Golay and develops new concepts and techniques ...
Holdahl, Robert LaVern (Monterey, California. Naval Postgraduate School, 1983-06);Binary sequences have had application in communication systems for many years. Shift registers have been used in their generation, because of the ease and economy of their operation. For certain applications, nonlinear ...