  Cold dark matter axions produced in the post-inflationary Peccei-Quinn
symmetry breaking scenario serve as clear targets for their experimental
detection, since it is in principle possible to give a sharp prediction for
their mass once we understand precisely how they are produced from the decay of
global cosmic strings in the early Universe. In this paper, we perform a
dedicated analysis of the spectrum of axions radiated from strings based on
large scale numerical simulations of the cosmological evolution of the
Peccei-Quinn field on a static lattice. Making full use of the massively
parallel code and computing resources, we executed the simulations with up to
$11264^3$ lattice sites, which allows us to improve our understanding of the
dependence on the parameter controlling the string tension and thus give a more
accurate extrapolation of the numerical results. We found that there are
several systematic effects that have been overlooked in previous works, such as
the dependence on the initial conditions, contaminations due to oscillations in
the spectrum, and discretisation effects, some of which could explain the
discrepancy in the literature. We confirmed the trend that the spectral index
of the axion emission spectrum increases with the string tension, but did not
find a clear evidence of whether it continues to increase or saturates to a
constant at larger values of the string tension due to the severe
discretisation effects. Taking this uncertainty into account and performing the
extrapolation with a simple power law assumption on the spectrum, we find that
the dark matter mass is predicted in the range of $m_a \approx
95$-$450\,\mu\mathrm{eV}$.
