Abstract For the input signals that can be sparsely represented in the fractional Fourier domain, sparse discrete fractional Fourier transform (SDFrFT) has been proposed to accelerate the numerical computation of discrete fractional Fourier transform. While significantly alleviating the computational load, SDFrFT has narrow applicability since it is more suitable for large-scale input signals. In this regard, the objective of this work is to overcome the limitation and further optimize the numerical computation of SDFrFT by exploiting the underlying phase information. We first employ Neyman-Pearson approach to achieve a noise-robust detection. Then, we derive the probability distribution function of the phase error in the location stage and, accordingly, design a location error correction algorithm. The proposed algorithm, termed optimized sparse fractional Fourier transform (OSFrFT), can reduce the computational complexity while guarantee sufficient robustness and estimation accuracy. Simulation results are provided to validate the effectiveness of the proposed algorithm. A successful application of OSFrFT to continuous wave radar signal processing is also presented.

中文翻译：

---

优化稀疏分数傅立叶变换：原理与性能分析

摘要 针对可以在分数阶傅里叶域中稀疏表示的输入信号，提出了稀疏离散分数阶傅里叶变换（SDFrFT）来加速离散分数阶傅里叶变换的数值计算。在显着减轻计算量的同时，SDFrFT 更适合大规模输入信号，适用范围较窄。在这方面，这项工作的目标是通过利用基础相位信息克服限制并进一步优化 SDFrFT 的数值计算。我们首先采用 Neyman-Pearson 方法来实现噪声鲁棒检测。然后，我们推导了定位阶段相位误差的概率分布函数，并据此设计了定位误差校正算法。提出的算法，称为优化稀疏分数傅里叶变换（OSFrFT），可以降低计算复杂度，同时保证足够的鲁棒性和估计精度。仿真结果验证了所提出算法的有效性。还介绍了 OSFrFT 在连续波雷达信号处理中的成功应用。