Abstract: Measured CW amplitude spectrum data are often obtained in EMP research, especially in effects experiments and probe calibration. This paper investigates the minimum phase reconstruction of the transient waveform from amplitude spectrum data. This technique involves the use of Hilbert transform, an assumption of minimum phase and cepstrum. The reconstruction of minimum phase signal, such as the HEMP waveform, cosine or sine exponentially damped waveform etc, shows good agreement with the original. For nonminimum phase signal, the total energy, the approximate amplitude and shape of the waveform can be indicated although the rise (fall) time and peak value are different from the original.