Abstract 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.

中文翻译：

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稀疏傅立叶变换的性能评估与参数优化

摘要 稀疏傅立叶变换 (SFT) 通过利用大多数自然信号中的继承稀疏性显着加速了频谱分析。然而，估计性能和计算复杂性之间的令人满意的折衷通常需要复杂的经验参数调整。在这项工作中，我们尝试通过优化参数选择机制来进一步增强 SFT。我们首先推导出客观性能指标的闭式表达式。在此基础上，设计了参数优化算法，在保证性能指标满足规定要求的前提下，将复杂度降到最低。所提出的方案，称为优化 SFT，显示能够根据先验知识和数值模拟中的性能要求自动确定优化的参数设置。还进行了连续波雷达检测的实验研究，以证明优化的 SFT 在实际应用场景中的潜力。