The need to Fourier transform data sets with irregular sampling is shared by various domains of science. This is the case for example in astronomy or sismology. Iterative methods have been developed that allow to reach approximate solutions. Here an exact solution to the problem for band-limited periodic signals is presented. The exact spectrum can be deduced from the spectrum of the non-equispaced data through the inversion of a Toeplitz matrix. The result applies to data of any dimension. This method also provides an excellent approximation for non-periodic band-limit signals. The method allows to reach very high dynamic ranges ($10^{13}$ with double-float precision) which depend on the regularity of the samples.

翻译：科学各领域普遍需要处理非均匀采样的数据集进行傅里叶变换，例如天文学和地震学领域。现有迭代方法可达到近似解，本文针对带限周期信号问题提出精确解：通过反演Toeplitz矩阵，可从非等距数据的频谱中导出精确频谱。该方法适用于任意维度的数据，且对非周期带限信号也能提供极佳的近似效果。实验表明，该方法可达到非常高的动态范围（双精度浮点数下可达$10^{13}$），其精度取决于样本的规则性。