The proper characterization of lightning electric and magnetic fields is very important for a number of reasons, such as the study and design of lightning protection and the validation of return stroke models. Also, an accurate late time response of the sensor used to record electric fields radiated by a lightning return stroke is very important to correctly detect, classify, and locate lightning discharges. Lightning fields are commonly obtained by integrating the output of antennas that produce replicas of the derivatives of the wanted quantities. The integration is carried out using either passive or active analog circuits that introduce a distortion in the form of a decay time constant that may affect the late-time response of the sensor. We derive the transfer function required for the reconstruction of signals integrated using a single-pole integrator commonly used in field and current waveform measurements. Making use of the convolution theorem, we propose an equation that changes a signal that resulted from integration with a given time constant, to the signal that would have been obtained if a different time constant had been used. Finally, we propose an equation to fully compensate a measured signal from an insufficient time constant of an analog integrator.