On Certain Sets of Polyphase Sequences With Sparse and Highly Structured Zak and Fourier Transforms
This paper describes a KM2 x M, K is an element of Q, M, KM is an element of Z, Zak space construction of zero correlation zone polyphase sequence sets, of sequence length KM3 and set size KM, with all-zero cross correlation. The construction includes the sets with an (M - 1)-point and (T2M - 1)-point zero autocorrelation zone, where T-2 is an arbitrary nontrivial factor of M. All sequences in these sets have sparse, highly structured, semipolyphase finite Zak transforms, with constant nonzero magnitude at M points and zero magnitude at selectable KM3 - M points, and sparse, semipolyphase KM3-point discrete Fourier transforms, with constant nonzero magnitude at M-2 points and zero magnitude at selectable KM3 - M-2 points.
polyphase sequence all-zero cross correlation bat chirp fast correlation finite zak transform (fzt) partial correlation perfect sequence set (pss) periodically complementary sequences spectral null code zero correlation zone (zcz)