We describe a family of iterative algorithms that involve the repeated execution of discrete and inverse discrete Fourier transforms. One interesting member of this family is motivated by the discrete Fourier transform uncertainty principle and involves the application of a sparsification operation to both the time domain and frequency domain data with convergence obtained when time domain sparsity hits a stable pattern. This sparsification variant has practical utility for signal denoising, in particular the recovery of a periodic spike signal in the presence of Gaussian noise. General convergence properties and denoising performance are demonstrated using simulation studies. We are not aware of prior work on such iterative Fourier transformation algorithms and have written this paper in part to solicit feedback from others in the field who may be familiar with similar techniques.

翻译：本文描述了一族迭代算法，其核心是重复执行离散傅里叶变换与逆离散傅里叶变换。该算法族中一个值得关注的变体受到离散傅里叶变换不确定原理的启发，通过对时域和频域数据施加稀疏化操作，并在时域稀疏性达到稳定模式时实现收敛。该稀疏化变体对信号去噪具有实际应用价值，尤其适用于在存在高斯噪声的情况下恢复周期性尖峰信号。通过仿真研究展示了其通用收敛特性及去噪性能。我们尚未发现关于此类迭代傅里叶变换算法的先前工作，撰写本文的部分目的是为了向该领域可能熟悉类似技术的同行征求反馈意见。