The publication describing the original detection of the first known FRB (Lorimer, D. R., Bailes, M., McLaughlin, M. A., Narkevic, D. J. & Crawford, F.: A Bright Millisecond Radio Burst of Extragalactic Origin. arXiv:0709.4301) has a plot of the measurement that makes the effects of dispersion on this particular FRB nicely visible. Take a look at Fig. 2 in the paper.
The actual signal is less than 10 ms, while dispersion delays the signal by around 200 ms over the 200 MHz frequency range between 1.3 and 1.5 GHz (note that this relationship is nonlinear).
Your idea about algorithmically removing the effects of dispersion on the signal is regularly done in practice, search for "dedispersion". At our (hobbyist) observatory, we are using D. Lorimer's own sigproc package to do this, and it seems to be in widespread use amongst professional observers as well. The basic idea is to simulate a classical filterbank arrangement and shift each filter channel according to the DM.
From Lorimer et al. (cited above):
Figure 2: Frequency evolution and integrated pulse shape of the radio burst. The survey data, collected on 2001 August 24, are shown here as a two-dimensional ‘waterfall plot’ of intensity as a function of radio frequency versus time. The dispersion is clearly seen as a quadratic sweep across the frequency band, with broadening towards lower frequencies. From a measurement of the pulse delay across the receiver band using standard pulsar timing techniques, we determine the DM to be 375±1 cm−3 pc. The two white lines separated by 15 ms that bound the pulse show the expected behavior for the cold-plasma dispersion law assuming a DM of 375 cm−3 pc. The horizontal line at ∼ 1.34 GHz is an artifact in the data caused by a malfunctioning frequency channel. This plot is for one of the offset beams in which the digitizers were not saturated. By splitting the data into four frequency sub-bands we have measured both the half-power pulse width and flux density spectrum over the observing bandwidth. Accounting for pulse broadening due to known instrumental effects, we determine a frequency scaling relationship for the observed width W = 4.6 ms (f/1.4 GHz)−4.8±0.4 , where f is the observing frequency.
A power-law fit to the mean flux densities obtained in each sub-band yields a spectral index of −4 ± 1. Inset: the total-power signal after a dispersive delay correction assuming a DM of 375 cm−3 pc and a reference frequency of 1.5165 GHz. The time axis on the inner figure also spans the range 0–500 ms.
