If you assume the pulse is Gaussian, it can be shown that the product of the FWHM and the half-power point (f-3dB ) of the frequency response =~ 0.31. If the pulse is Gaussian and represents the impulse response of the system, then its integral (a form of the error function, or erf) would approximate the step response of the system and the product of the 10-90% rise time and the half-power point of the frequency response =~ 0.34. For a Gaussian impulse, the FWHM corresponds to the 12-88% points of its integral.