Random Residue Sequences and the Number Theoretic Hilbert Transform
This work addresses sequence design for signal processing applications, but it appears incremental as it builds on existing transform methods without broad practical impact.
The paper introduced random residue sequences from the number theoretic Hilbert transform and showed they are self-orthogonal with zero autocorrelation for non-zero shifts, while cross-correlation computations reveal an inverse qualitative relationship for many residue sets.
This paper presents random residue sequences derived from the number theoretic Hilbert (NHT) transform and their correlation properties. The autocorrelation of a NHT derived sequence is zero for all non-zero shifts which illustrates that these are self-orthogonal sequences. The cross correlation function between two sequences may be computed with respect to the moduli of the either sequence. There appears to be some kind of an inverse qualitative relationship between these two different computations for many sets of residue sequences.