Performance of methods based on the fractional Fourier transform for the detection of linear frequency modulated signals

Analysis of detectors of linear frequency modulated (LFM) signals based on the fractional Fourier transform (FrFT) is presented. This allows one to conduct a fair comparison of the performance of these methods with those based on the Fourier transform (FT). In order to facilitate this analysis, expressions for the distribution of the coefficients of the FrFT are presented. Analytic approximations for the FT of the LFM signals are also developed. It is shown that the FrFT methods achieve superior performance if the sweep rate is sufficiently fast or the data length is sufficiently large.