高斯白噪声中频谱有限函数的外推估计

EXTRAPOLATING ESTIMATION OF BAND-LIMITED FUNCTIONS IN GAUSSIAN WHITE NOISE

设f(t)是一σ-频谱有限函数和g(t)=f(t)+n(t)在(-T,T)区间内的值被观测到,其中n(t)是高斯白噪声。本文给出基于g(t)的f(t)的极大似然估计。还讨论了当f(t)为随机σ-频谱有限函数时,它与g(t)的均方距离达到最小的估计。

Suppose f(t) is a σ-band limited function and g(t)=f(t)+n(t) is observed in the interval (-T, T), where n(t) is a Gaussian white noise. The maximum likelihood estimation of f(t) based on g(t) is presented in this paper. It is also discussed that the estimation minimizes the mean square distance to g(t) when f(t) is a random σ-bandlimited function.