On Performance of Sparse Fast Fourier Transform and Enhancement Algorithm

Sparse fast Fourier transform (FFT) is a promising technique that can significantly reduce computational complexity. However, only a handful of research has been conducted on precisely analyzing the performance of this new scheme. Accurate theoretical results are important for new techniques to avoid numerous simulations when applying them in various applications. In this study, we analyze several performance metrics and derive the corresponding closed-form expressions for the sparse FFT including 1) inter sparse interference due to nonideal windowing effects, 2) the probability of sparse elements overlapping, and 3) the recovering rate performance. From the analytical results, we gain insights and propose a novel mode-mean estimation algorithm for improving the performance. Simulation results are provided to show the accuracy of the derived results as well as the performance enhancement. We also show how to determine parameters to achieve the lowest computational complexity using these theoretical results.