This paper presents a new approach to the time- domain near-field far-field transformation technique recently introduced by Hansen and Yaghijan and is based either on a time-domain or frequency-domain scheme. The approach presented here attempts to overcome the main drawbacks of this technique related to the computer time and memory requirements, which could make unrealistic the application of the technique to cases of practical interest. To this end, the advanced representation of the (time and frequency domain) near field recently introduced by the authors, which requires a minimum number of nonequispaced field samples, are exploited. This leads to new relationship between the near-field measured samples and the far field, which requires a minimal set of time–space measurements. Various computational schemes are considered and compared showing that the presented algorithm requires a reduced measurement effort, computer time, and memory occupancy, while allowing a lower far-field reconstruction error for a fixed number of measurements.