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This report describes the various techniques and algorithms developed to enhance the accuracy of the measurements of very fast transient electromagnetic fields generated during EMP testing. Some fundamentals of digital signal processing are presented and the practical aspects are highlighted. The response of some sensors to incident fields is studied. Appropriates algorithms for reconstructing the incident field from the measurements are developed. The effect of low frequency cut-off of some sensors is also studied. A method to design a digital filter to arbitrary transfer function is presented. It is applied to compensate for losses occurring in long cables and also to fine tune other filters. The Hilbert transform is introduced to relate the magnitude and phase component of a transfer function. An implementation of the transform is given, allowing the design of digital filters when only the magnitude of the transfer function is known.