Characterization of Zak Space Support of a Discrete Chirp

General conditions are derived for an (N=KL
²
)-point discrete chirp with chirp rate a and carrier frequency b to have minimal support on the LtimesKL Zak transform lattice. Earlier, it has been shown that when the normalized chirp parameters amacr= aK, amacr= aK
²
, and 2bmacr = 2bK are integers, the last two of the same parity, then the discrete chirp is supported at KL points. Here, this condition is relaxed, by allowing amacr to be a rational number, i.e., amacr = n/d, n, disin Z, (n,d)=1, and requiring only that amacr and bmacrL 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