一种提高高斯平稳噪声时间序列中瞬态源检测灵敏度的方法
A method of enhancing the detection sensitivity of transient sources in time series with Gaussian stationary noise
摘要：
强度时间序列的高斯相位噪声被证明是大大减少时，原始电压数据进行数字滤波，通过任意大量的$n$正交带通曲线（本征滤波器）共享相同的强度带宽，并由此产生的强度系列共同添加。具体地说，在一个相干时间或更少的分辨率下，求和序列的相对噪声方差随着$n$的增加而下降为$1/n$，尽管（与辐射计方程一致）当序列被箱平均到较低分辨率时，优势逐渐消失。因此，该算法被设计为增强检测瞬态的灵敏度，所述瞬态通过时间平均而平滑，并且太微弱而在有噪声的未平均时间序列中不可见，如通过模拟周期性性质或快速且不重复的脉冲的弱嵌入式时变信号所证明的。然后将该算法应用于VLA对脉冲星PSR 1937+21的10分钟观测，其中理论预测得到了数据的验证。此外，它示出的时间轮廓内的微观结构被更好地定义为所使用的滤波器的数量$n$的增加，和周期$1.86 \times 10^{-5}$ ~s（$53.9$ ~kHz）的周期信号被发现在脉冲轮廓。最后，我们将该算法应用于LIGO探测到的第一个二元黑洞合并，GW 150914。我们发现平均峰值强度的SNR随着$\sqrt{n}$而增加，并且LIGO-Hanford-Livingston探测器对之间的事件的互相关随着滤波器阶数$n$而增加。
英文摘要：
The Gaussian phase noise of intensity time series is demonstrated to be drastically reduced when the raw voltage data are digitally filtered through an arbitrarily large number $n$ of orthornormal bandpass profiles (eigen-filters) sharing the same intensity bandwidth, and the resulting intensity series are co-added. Specifically, the relative noise variance of the summed series at the resolution of one coherence time or less, goes down with increasing $n$ as $1/n$, although (consistent with the radiometer equation) the advantage gradually disappears when the series is bin averaged to lower resolution. Thus the algorithm is designed to enhance the sensitivity of detecting transients that are smoothed out by time averaging and too faint to be visible in the noisy unaveraged time series, as demonstrated by the simulation of a weak embedded time varying signal of either a periodic nature or a fast and unrepeated pulse. The algorithm is then applied to a 10 minute observation of the pulsar PSR 1937+21 by the VLA, where the theoretical predictions were verified by the data. Moreover, it is shown that microstructures within the time profile are better defined as the number $n$ of filters used increases, and a periodic signal of period $1.86 \times 10^{-5}$~s ($53.9$~kHz) is discovered in the pulse profile. Lastly, we apply the algorithm to the first binary black hole merger detected by LIGO, GW150914. We find the SNR of the mean peak intensity increases as $\sqrt{n}$ and cross correlation of the event between the LIGO-Hanford-Livingston detector pair increases with filter order $n$.
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