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 real domain and frequency domain data with convergence obtained when real 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 relative to existing methods are demonstrated using simulation studies. An R package implementing this technique and related resources can be found at https://hrfrost.host.dartmouth.edu/IterativeFT.

翻译：本文描述了一类迭代算法家族，其核心在于反复执行离散傅里叶变换及其逆变换。该家族中一个引人关注的成员受离散傅里叶变换不确定原理启发，通过对时域和频域数据施加稀疏化操作，当实域稀疏性达到稳定模式时实现收敛。该稀疏化变体在信号去噪（特别是从高斯噪声中恢复周期性尖峰信号）方面具有实用价值。通过仿真研究展示了其相对于现有方法的通用收敛特性与去噪性能。实现该技术的R语言程序包及相关资源可访问 https://hrfrost.host.dartmouth.edu/IterativeFT 获取。