  An algorithm for calculating the spectral intensity of radiation due to the
coherent addition of many particles with arbitrary trajectories is described.
Direct numerical integration of the Lienard-Wiechert potentials, in the
far-field, for extremely high photon energies and many particles is made
computationally feasible by a mixed analytic and numerical method. Exact
integrals of spectral intensity are made between discretely sampled
trajectories, by assuming the space-time four-vector is a quadratic function of
proper time. The integral Fourier transform of the trajectory with respect to
time, the modulus squared of which comprises the spectral intensity, can then
be formed by piecewise summation of exact integrals between discrete points.
Because of this, the calculation is not restricted by discrete sampling
bandwidth theory, and hence for smooth trajectories, time-steps many orders
larger than the inverse of the frequency of interest can be taken.
