论文标题
具有指定统计数据的随机信号的快速生成
Rapid Generation of Stochastic Signals with Specified Statistics
论文作者
论文摘要
我们演示了一种新型算法，用于生成具有指定功率频谱密度的固定随机信号（或通过Wiener-khinchin关系，指定的自相关函数），同时满足信号概率密度函数的约束。涉及非线性过滤的方法已经解决了一个紧密相关的问题，但是我们使用涉及优化和随机交换的根本不同的方法，该方法立即将其推广到具有更广泛统计范围的信号。优化和随机交换的这种组合消除了与任何一种方法隔离相关的缺点，改善了运行时的最佳尺度缩放时间，以生成$ \ Mathcal {o}（n^2）$的长度$ n $的信号。 $ \ MATHCAL {O}（N）$具有完整的并行化。我们通过实验证明了这一加速度，此外表明，我们生成的信号比随机互换产生的信号更准确地匹配所需的自相关。我们观察到，与优化产生的信号不同，我们生成的信号是固定的。
We demonstrate a novel algorithm for generating stationary stochastic signals with a specified power spectral density (or equivalently, via the Wiener-Khinchin relation, a specified autocorrelation function) while satisfying constraints on the signal's probability density function. A tightly related problem has already been essentially solved by methods involving nonlinear filtering, however we use a fundamentally different approach involving optimization and stochastic interchange which immediately generalizes to generating signals with a broader range of statistics. This combination of optimization and stochastic interchange eliminates drawbacks associated with either method in isolation, improving the best-case scaling in runtime to generate a signal of length $n$ from $\mathcal{O}(n^2)$ for stochastic interchange on its own to $\mathcal{O}(n \: \text{log} \: n)$ without parallelization or $\mathcal{O}(n)$ with full parallelization. We demonstrate this speedup experimentally, and furthermore show that the signals we generate match the desired autocorrelation more accurately than those generated by stochastic interchange on its own. We observe that the signals we produce, unlike those generated by optimization on its own, are stationary.
