Engineers prefer the direct approach and so let all the scaling appear in the inverse.
Simulation has shown that the latter expression can be well approximated by a rectangular window modifying the chirp. These quantities are adjusted in the output image by empirical calibration. It is apparent that the explicit computation of Fourier transforms may be very difficult or complex. Therefore, it is important to be able to approximate the transforms, given assumptions about the signal waveform. At other times the phase varies relatively rapidly so that positive and negative contributions to the integral cancel out.