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 $n$.

中文翻译：

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一种提高具有平稳高斯噪声的时间序列暂态源检测灵敏度的方法

当原始电压数据通过共享相同强度带宽的任意大数 $n$ 正交带通剖面（本征滤波器）进行数字滤波时，强度时间序列的高斯相位噪声被证明显着降低，以及由此产生的强度序列是共同添加的。具体来说，在一个相干时间或更短的分辨率下，求和序列的相对噪声方差随着 $n$ 增加为 $1/n$ 而下降，尽管（与辐射计方程一致）当序列为 bin 时，优势逐渐消失平均到较低的分辨率。因此，该算法旨在提高检测瞬态的灵敏度，这些瞬态通过时间平均而变得平滑，并且在嘈杂的未平均时间序列中太微弱而无法看到，正如对具有周期性或快速且不重复的脉冲的弱嵌入时变信号的模拟所证明的那样。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，结果表明，随着使用的滤波器数量 $n$ 的增加，时间剖面内的微观结构被更好地定义，并且周期 $1.86 \times 10^{-5}$~s ($53.9$~kHz) 的周期信号是在脉冲轮廓中发现。最后，我们将该算法应用于 LIGO GW150914 检测到的第一个双黑洞合并。我们发现平均峰值强度的 SNR 随着 $\sqrt{n}$ 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 $n$ 增加。