标题： 引力波信号来自旋转中子星的数据分析。 V. 窄带全天空搜索 显示英文标题

标题： Data analysis of gravitational-wave signals from spinning neutron stars. V. A narrow-band all-sky search

摘要： 我们提出理论和算法，以在探测器的窄带数据中进行全天空相干搜索引力波的周期信号。 我们的搜索基于一个统计量，通常称为$\mathcal{F}$-统计量，该统计量来源于本系列论文第一篇中的最大似然原理。 我们简要回顾地面探测器对旋转中子星引力波信号的响应以及$\mathcal{F}$-统计量的推导。 我们提出了几种高效计算此统计量的算法。 特别是我们的算法使得可以在计算$\mathcal{F}$-统计量时利用快速傅里叶变换（FFT）的速度。 我们在参数空间中构建了一个网格，使得网格的节点与傅里叶频率重合。 我们提出了插值方法，将$\mathcal{F}$-统计量中的两个积分近似转换为傅里叶变换，以便在它们的求值中应用FFT算法。 我们已将这些方法和算法编写成计算机代码，并展示了用于测试这些代码的蒙特卡洛模拟结果。 显示英文摘要

摘要： We present theory and algorithms to perform an all-sky coherent search for periodic signals of gravitational waves in narrow-band data of a detector. Our search is based on a statistic, commonly called the $\mathcal{F}$-statistic, derived from the maximum-likelihood principle in Paper I of this series. We briefly review the response of a ground-based detector to the gravitational-wave signal from a rotating neuron star and the derivation of the $\mathcal{F}$-statistic. We present several algorithms to calculate efficiently this statistic. In particular our algorithms are such that one can take advantage of the speed of fast Fourier transform (FFT) in calculation of the $\mathcal{F}$-statistic. We construct a grid in the parameter space such that the nodes of the grid coincide with the Fourier frequencies. We present interpolation methods that approximately convert the two integrals in the $\mathcal{F}$-statistic into Fourier transforms so that the FFT algorithm can be applied in their evaluation. We have implemented our methods and algorithms into computer codes and we present results of the Monte Carlo simulations performed to test these codes.