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We describe a family of iterative algorithms that involve the repeatedexecution of discrete and inverse discrete Fourier transforms. One interestingmember of this family is motivated by the discrete Fourier transformuncertainty principle and involves the application of a sparsificationoperation to both the time domain and frequency domain data with convergenceobtained when time domain sparsity hits a stable pattern. This sparsificationvariant has practical utility for signal denoising, in particular the recoveryof a periodic spike signal in the presence of Gaussian noise. Generalconvergence properties and denoising performance are demonstrated usingsimulation studies. We are not aware of prior work on such iterative Fouriertransformation algorithms and have written this paper in part to solicitfeedback from others in the field who may be familiar with similar techniques.

Iterative execution of discrete and inverse discrete Fourier transforms with applications for signal denoising via sparsification