We present an algorithm for the forward propagation of intervals through the discrete Fourier transform. The algorithm yields best-possible bounds when computing the amplitude of the Fourier transform for real and complex valued sequences. We show that computing the exact bounds of the amplitude can be achieved with an exhaustive examination of all possible corners of the interval domain. However, because the number of corners increases exponentially 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 can be obtained propagating complex pairs only from the convex hull of endpoints at each term of the Fourier series. 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 enclose the true values.

翻译：我们提出了一个通过离散的Fourier变异的远方传播间隔的算法。 算法在计算Fourier变异的振幅时产生最有可能的界限, 以真实和复杂的有价值序列计算。 我们显示计算振幅的准确界限可以通过对间域所有可能的角进行彻底的检查来实现。 但是,由于角数随着间隔数的倍增而成倍增长, 这种方法对于大的间隔信号是行不通的。 我们提供了一个不需要如此彻底的搜索的算法, 并且显示只能从Fourier系列每一期的端点的螺旋体的螺旋体中获得尽可能最佳的界限来传播复合组合。 因为对角的轮体总是严格地刻在由间隙算产生的各自的严格界限框中, 我们的结论是, 获得的界限保证包含真实的值 。