A new discrete chirp Fourier transform

Discrete chirp Fourier transform (DCFT) can be used to match multiple chirp rates and constant frequency rates simultaneously. We propose a new kind of DCFT scheme and investigate its matched filter properties. Compared to DCFTs proposed previously, the new DCFT scheme keeps high chirp rate resolution on the detected signals and its signal detection range can cover the full signal space. Moreover, the robustness of the new DCFT on the chirp rate and constant frequency errors is investigated, and an explicit sufficient condition is presented on the stability of the new DCFT with chirp rate and constant frequency errors.