Modulatable orthogonal sequences and their application to SSMA systems
IEEE Transactions on Information Theory
Ten lectures on wavelets
Time-frequency representations
Time-frequency representations
Introduction to Coding Theory
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
Signal Design for Good Correlation: For Wireless Communication, Cryptography, and Radar
IEEE Transactions on Wireless Communications
Constructions of permutation arrays
IEEE Transactions on Information Theory
Characterization of Zak Space Support of a Discrete Chirp
IEEE Transactions on Information Theory
EURASIP Journal on Advances in Signal Processing - Special issue on recent advances in theory and methods for nonstationary signal analysis
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Previously, a discretization of the linear FM chirp of length N = KL2, L and KL ∈ Z, was given and the conditions for its minimal Zak space support were derived. Chirps satisfying these conditions are known as finite chirps. In this work, subsets of finite chirps of length N = L2, L a prime, are examined. The investigation leads to a new, Zak space construction of general polyphase sequence sets of size L - 1 with optimal auto and cross-correlation properties, known as perfect sequence sets. It is shown that perfect sequence sets are closely related to sets of finite chirps and, in particular, include the sets of Zadoff-Chu sequences (which are identical with subsets of finite chirps) and the sets of generalized Frank sequences (which are identical with sets of modulations of finite chirps), as special cases. The entire collection of perfect sequence sets is then given by a partition of the set of perfect auto correlation sequences, obtained by right coset decomposition of the group of all permutations with respect to a certain cyclic group. The construction suggests several further generalizations that can be obtained by operating exclusively on subgroups of the permutation group.