Performance evaluation and parameter optimization of sparse Fourier transform

The sparse Fourier transform (SFT) dramatically accelerates spectral analyses by leveraging the inherit sparsity in most natural signals. However, a satisfactory trade-off between the estimation performance and the computational complexity commonly requires sophisticated empirical parameter tuning. In this work, we attempt to further enhance SFT by optimizing the parameter selection mechanism. We first derive closed-form expressions of objective performance metrics. On top of this, a parameter optimization algorithm is designed to minimize the complexity, under the premise that the performance metrics can meet the specified requirements. The proposed scheme, termed as optimized SFT, is shown to be able to automatically determine the optimized parameter settings as per the a priori knowledge and the performance requirements in the numerical simulations. Experimental studies of continuous-wave radar detection are also conducted to demonstrate the potential of the optimized SFT in the practical application scenarios.