Gravitational redshifts in electromagnetic bursts occurring near Schwarzschild horizon

It was suggested earlier that the gravitational redshift formula can be invalid when the effect of the backscattering is strong. It is demonstrated here numerically, for an exemplary electromagnetic pulse that is (i) initially located very close to the horizon of a Schwarzschild black hole and (ii) strongly backscattered, that a mean frequency does not obey the standard redshift formula. Redshifts appear to depend on the frequency and there manifests a backscatter-induced blueshift in the outgoing radiation.