  The radio detection technique of cosmic ray air showers has gained renewed
interest in the last two decades. While the radio experiments are very
cost-effective to deploy, the Monte-Carlo simulations required to analyse the
data are computationally expensive. Here we present a proof of concept for a
novel way to synthesise the radio emission from extensive air showers in
simulations. It is a hybrid approach which uses a single microscopic
Monte-Carlo simulation, called the origin shower, to generate the radio
emission from a target shower with a different longitudinal evolution, primary
particle type and energy. The method employs semi-analytical relations which
only depend on the shower parameters to transform the radio signals in the
simulated antennas. We apply this method to vertical air showers with energies
ranging from $10^{17}$ eV to $10^{19}$ eV and compare the results with CoREAS
simulations in two frequency bands, namely the broad [20, 500] MHz band and a
more narrow one at [30, 80] MHz. We gauge the synthesis quality using the
maximal amplitude and energy fluence contained in the signal. We observe that
the quality depends primarily on the difference in $X_{\text{max}}$ between the
origin and target shower. After applying a linear bias correction, we find that
for a shift in $X_{\text{max}}$ of less than 150 $\text{g}/\text{cm}^2$ ,
template synthesis has a bias of less than 2% and a scatter up to 6%, both in
amplitude, on the broad frequency range. On the restricted [30, 80] MHz range
the bias is similar, but the spread on amplitude drops down to 3%. These
fluctuations are on the same level as the intrinsic scatter we observe in
Monte-Carlo ensembles. We therefore surmise the observed scatter in amplitude
to originate from intrinsic shower fluctuations we do not explicitly account
for in template synthesis.
