This paper aims to detect and characterize a signal coming from frequency modulation continuous wave radars. The radar signals are made of piecewise linear frequency modulations. The maximum chirplet transform (MCT), a simplification of the chirplet transform is proposed. A detection of the relevant maximum chirplets is proposed based on iterative masking, an iterative detection followed by window subtraction that does not require the recomputation of the spectrum. This detection is designed to provide a sparse subset of maximum chirplet coefficients. The chirplets are then gathered into linear chirps whose starting time, length, and chirprate are estimated. These chirps are then gathered again back into the different frequency modulation continuous wave signals, ready to be classified. An illustration is provided on synthetic data.