  The detection of extensive air showers (EAS) through their radio signal is
becoming one of the most promising techniques for the study of Neutrinos and
Cosmic rays at the highest energies. For the design, optimization and
characterization of radio arrays, and of their associated reconstruction
algorithms, tens of thousands of Monte Carlo simulations are needed. Current
available simulation codes can take several days to compute the signals
produced by a single shower, making it impossible to produce the required
simulations in a reasonable amount of time, in a cost-effective and
environmental-conscious way. In this article we present a method to synthesize
the expected signals (the full time trace, not just the peak amplitude) at any
point around the shower core, given a set of signals simulated in a finite
number of antennas strategically located in a pattern that exploits the
signature features of the radio wavefront. The method can be applied
indistinctly to the electric field or to the antenna response to the electric
field, in the three polarization directions. The synthesized signal can be used
to evaluate trigger conditions, compute the fluence or reconstruct the shower
incoming direction, allowing for the production of one single library of
simulations that can be used and re-used for the characterization and
optimization of radio arrays and their associated reconstruction methods, for a
thousandth part of the otherwise required CPU time.
