The characteristics of impulses reflected from a sech2electron-density profile and bandpass filtered

The signal reflected from a sech
²
electron-density profile and bandpass filtered was calculated for an incident plane wave with an impulsive time variation. For "wide" bandwidths, the envelope of the filter output decreases in duration with decreasing bandwidth, with some increase in peak amplitude For "narrow" bandwidths, the envelope of the filter output decreases in peak amplitude and increases in duration with decreasing bandwidth; the envelope also oscillates about its mean value after the peak. The critical bandwidth, at which the filter output changes from the "wide-" to the "narrow-" band behavior, was found to be associated with a characteristic pattern of the saddle points of the Fourier-transform integrand.