  Partial differential equations with highly oscillatory input terms are hardly
ever solvable analytically and their numerical treatment is difficult.
Modulated Fourier expansion used as an {\it ansatz} is a well known and
extensively investigated tool in asymptotic numerical approach for this kind of
problems. Although the efficiency of this approach has been recognised, its
error analysis has not been investigated rigorously for general forms of linear
PDEs. In this paper, we start such kind of investigations for a general form of
linear PDEs with an input term characterised by a single high frequency. More
precisely we derive an analytical form of such an expansion and provide a
formula for the error of its truncation. Theoretical investigations are
illustrated by computational simulations.
