Abstract: The FRaction Fourier Transform (FRFT) is optimal in the detection and parameter estimation of Linear Frequency Modulation (LFM) signal, but it is suboptimal for Linear Frequency Modulation Continuous Wave (LFMCW). LFMCW signal is a periodic extension of an LFM signal. In virtue of?the energy congregation of FRFT for LFM signal and the coherent integrator in signal processing, this paper formulates a new detection and parameter algorithm for LFMCW signal, called the periodic FRFT. The theory analysis and simulation results show the proposed algorithm is asymptotically optimal in the detection and parameter estimation of LFMCW signal along with increasing observation time, and better than traditional FRFT algorithm.