  In this note is presented a method, given nodal values on multidimensional
nonconforming spectral elements, for calculating global Fourier-series
coefficients. This method is ``exact'' in that given the approximation inherent
in the spectral-element method (SEM), no further approximation is introduced
that exceeds computer round-off error. The method is very useful when the SEM
has yielded an adaptive-mesh representation of a spatial function whose global
Fourier spectrum must be examined, e.g., in dynamically adaptive fluid-dynamics
simulations.
