论文标题
在带限制功能中使用衍生物采样的敏锐结果
Sharp results on sampling with derivatives in bandlimited functions
论文作者
论文摘要
我们讨论了独特性，采样和重建的问题，该问题在带有限制功能的空间中使用衍生物。我们证明，如果x是实数的序列，那么两个连续样品之间的最大差距小于某些正常常数c，则可以从涉及衍生物的非均匀样品中重建带宽σ的带宽函数。我们还证明，如果最大差距小于或等于C，则x是一组唯一性，当涉及K-1衍生物的样品时，带宽σ的带宽函数函数的唯一性。作为副产品，我们获得了涉及第一衍生物的样品的尖锐最大间隙条件。
We discuss the problems of uniqueness, sampling and reconstruction with derivatives in the space of bandlimited functions. We prove that if X is sequence of real numbers such that the maximum gap between two consecutive samples is less than certain positive constant c, then bandlimited function of bandwidth σ can be reconstructed uniquely and stably from its nonuniform samples involving derivatives. We also prove that if the maximum gap is less than or equal to c, then X is a set of uniqueness for the space of bandlimited functions of bandwidth σ when the samples involving k-1 derivatives. As a by-product we obtain the sharp maximum gap condition for samples involving first derivatives.
