  In this paper an algorithm for the forward interval propagation on the
amplitude of the discrete Fourier transform (DFT) is presented. The algorithm
yields best-possible bounds on the amplitude of the DFT for real and complex
valued sequences. We show that computing the exact bounds for the amplitude of
the DFT can be achieved with an exhaustive examination of all possible corners
of the interval-shaped domain. However, because the number of corners increase
exponentially (in base 2) with the number of intervals, such method is
infeasible for large interval signals. We provide an algorithm that does not
need such an exhaustive search, and show that the best possible bounds for the
amplitude can be obtained propagating complex pairs only from the convex hull.
Because the convex hull is always tightly inscribed in the respective rigorous
bounding box resulting from interval arithmetic, we conclude that the obtained
bounds are guaranteed to yield the true bounds.
