Higher-order statistics for fractional Fourier transform

The definition of the higher-order statistics associated with the fractional Fourier transform is presented in this paper. The proposed fractional higher-order statistics for order greater than two are blind to the additive white or colored Gaussian noise, which is similar to the conventional higher-order statistics; and it is suitable for the chirp signal. The proposed higher-order statistics can outperform the conventional higher-order statistics in the Fourier domain under the correlated Gaussian noises at lower SNR. Simulation results demonstrate the validity of this estimation method.