样本间距约束对非规则采样谱估计的影响
Effect of inter-sample spacing constraint on spectrum estimation with irregular sampling
摘要：
连续时间平稳随机过程的谱估计中的一个实际约束是连续观测样本之间的最小间隔。当底层过程不受带宽限制时，以任何均匀速率采样都会导致混叠，而某些随机采样方案，包括泊松过程采样，由于最小间隔的约束而变得不可行。本文证明，在这个约束条件下，没有一个点过程采样方案对所有谱的类是无混叠的。事实证明，在此约束下的点过程采样可以是带限频谱的无混叠。然而，通常的一致性谱估计器的构造在这种情况下不起作用。模拟表明，一个常用的估计，这是一致的，在没有这个约束，表现不佳时，约束存在。这些结果应有助于从业者在合理化他们的期望从点过程采样频谱估计而言，并激励研究人员寻找合适的带限谱估计。
英文摘要：
A practical constraint that comes in the way of spectrum estimation of a continuous time stationary stochastic process is the minimum separation between successively observed samples of the process. When the underlying process is not band-limited, sampling at any uniform rate leads to aliasing, while certain stochastic sampling schemes, including Poisson process sampling, are rendered infeasible by the constraint of minimum separation. It is shown in this paper that, subject to this constraint, no point process sampling scheme is alias-free for the class of all spectra. It turns out that point process sampling under this constraint can be alias-free for band-limited spectra. However, the usual construction of a consistent spectrum estimator does not work in such a case. Simulations indicate that a commonly used estimator, which is consistent in the absence of this constraint, performs poorly when the constraint is present. These results should help practitioners in rationalizing their expectations from point process sampling as far as spectrum estimation is concerned, and motivate researchers to look for appropriate estimators of bandlimited spectra.
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