The unfolding-synthesis technique is used in the development of digital pulse processing systems used in radiation measurements. This technique is applied to digital signals obtained by digitization of analog signals that represent the combined response of the radiation detectors and the associated signal conditioning electronics. The salient features of the unfolding-synthesis technique are first the unfolding of the digital signals into unit impulses, followed by the synthesis of digital signal processing systems with unit impulse responses equivalent to the desired pulse shapes. Part 1 of this paper covers the unfolding part of this technique.