Analysis of the shading between multicomponent chirp signals in the fractional Fourier domain

Starting with the relationship between the fractional Fourier transform and the time-frequency distribution, we derives the approximate expression of the fractional Fourier spectrum intensity of a single chirp based on the digital computation of the fractional Fourier transform. The shading between the fractional Fourier spectra of two chirps with different chirp rates is analyzed, and a formula is obtained, which is illuminated by some figures and verified by a simulation. We find that the amplitude, chirp-rate and sampling interval determine the shading between the fractional Fourier spectra of multicomponent chirp signals. Prolonging the sampling interval can reduce the shading when amplitude and chirp-rate of multicomponent chirp signals are determined.