The Fast Folding Algorithm (FFA) is a phase-coherent search technique for periodic signals. It has rarely been used in radio pulsar searches, having been historically supplanted by the less computationally expensive Fast Fourier Transform (FFT) with incoherent harmonic summing (IHS). Here we derive from first principles that an FFA search closely approaches the theoretical optimum sensitivity to all periodic signals; it is analytically shown to be significantly more sensitive than the standard FFT+IHS method, regardless of pulse period and duty cycle. A portion of the pulsar phase space has thus been systematically under-explored for decades; pulsar surveys aiming to fully sample the pulsar population should include an FFA search as part of their data analysis. We have developed an FFA software package, riptide, fast enough to process radio observations on a large scale; riptide has already discovered sources undetectable using existing FFT+IHS implementations. Our sensitivity comparison between search techniques also shows that a more realistic radiometer equation is needed, which includes an additional term: the search efficiency. We derive the theoretical efficiencies of both the FFA and the FFT+IHS methods and discuss how excluding this term has consequences for pulsar population synthesis studies.

中文翻译：

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最佳周期搜索：重新审视大规模脉冲星调查的快速折叠算法

快速折叠算法 (FFA) 是一种用于周期信号的相位相干搜索技术。它很少用于无线电脉冲星搜索，历史上已被计算成本较低的快速傅立叶变换 (FFT) 和非相干谐波求和 (IHS) 所取代。在这里，我们从基本原理推导出 FFA 搜索接近于对所有周期信号的理论最佳灵敏度；分析表明，无论脉冲周期和占空比如何，它都比标准 FFT+IHS 方法灵敏得多。因此，几十年来，脉冲星相空间的一部分一直没有得到系统的探索。旨在对脉冲星群体进行全面抽样的脉冲星调查应包括 FFA 搜索作为其数据分析的一部分。我们开发了一个FFA软件包，riptide，足够快，可以大规模处理无线电观测；riptide 已经发现使用现有 FFT+IHS 实现无法检测到的源。我们在搜索技术之间的灵敏度比较还表明，需要一个更现实的辐射计方程，其中包括一个额外的术语：搜索效率。我们推导出 FFA 和 FFT+IHS 方法的理论效率，并讨论排除该术语如何对脉冲星群合成研究产生影响。