加权再生核空间中信号的随机采样稳定性

Random sampling stability of signals in weighted reproducing kernel spaces

针对一般概率分布获取的独立随机样本,在核函数不满足对称性的条件下,在加权再生核子空间中研究了信号的随机采样稳定性。首先,基于加权再生核子空间的框架刻画,在有界区域上用有限维子空间逼近加权再生核空间。其次,通过研究加权再生核子空间中信号的无穷范数与p范数的关系,估计标准化有限维子空间的覆盖数。最后,证明了当采样量足够大时,能量集中于立方体上的加权再生核信号的随机采样稳定性以高概率成立。

For the independent random samples obtained according to the general probability distribution,the random sampling stability of signals is studied in the weighted reproducing kernel subspace under the condition that the kernel function does not satisfy the symmetry.Firstly,based on the framework characterization of the weighted reproducing kernel subspace,the finite dimensional subspace is used to approximate the weighted reproducing kernel space on the bounded region.Secondly,by studying the relationship between the infinite norm and p norm of signals in the weighted reproducing kernel subspace,the covering number of the normalized finite dimensional subspace is estimated.Finally,it is proved that the random sampling stability of the weighted reproducing kernel signals with energy concentrated on the cube is valid with high probability when the sampling quantity is large enough.