Characterization of Zak space support of a discrete chirp

General conditions are derived for an (N = KL2)-point discrete chirp with chirp rate a and carrier frequency b to have minimal support on the L x KL Zak transform lattice. Earlier, it has been shown that when the normalized chirp parameters a = aK, a = aK(2), and 2b = 2bK are integers, the last two of the same parity, then the disciete chirp is supported at KL points. Here, this condition is relaxed, by allowing a to be a rational number, i.e., -a = 2, n/d epsilon Z, (n, d) = 1, and requiring d only that a and bL be integers of arbitrary parity. It is shown that the support of the Zak space chirp satisfying the new condition then increases to dKL points. The results provide foundations for future constructions of sophisticated radar and communications signal processing algorithms. Examples of direct applications of the Zak space conditions in chirp parameter estimation, chirp detection, and chirp de-noising are included.