摘要
本文提出４个线性预测问题，并求出了它们的预测误差及预测值。这４个线性预测问题分别推广了预测问题２（即不对称半平面的线性预测）［２，３，９］，预测问题６［５］。
Let {x(m,n)} be a homogeneous random field with discrete parameters. Generally, linear prediction problems of a homogeneous random field with discrete parameters are as follows: Let T and T′ are two sets of (m,n) , {x(m,n)} have been observed if (m,n)∈T . But {x(m′,n′)} are unknown quantities if (m′,n′)∈T′ . We want to predict x(m′,n′) (m′,n′)∈T′ by the linear combination of the {x(m,n),(m,n)}∈T and its limite in terms of square mean, such that its error of square mean is minimum. In this paper, linear predictions of four types are discussed. 1. Let l(l =1, or 2, or 3, …) be a constant, T={(m,n),-∞<m<∞,n≤-1}∪{(lk,0),k=…,-3,-2,-1},T′={(0,0)}. 2. Let l(l =1, or 2, or 3,…) be a constrant, T={(m,n),-∞<m<∞,n≤-1}∪{(lk,0),k=±1,±2,±3,…},T′={(0,0)} 3. Let l(l =1, or 2, or 3,…) be a constrant, T={(m,n), -∞<m<∞, n≠0}∪{(lk,0),k=…,-3,-2,-1},T′={(0,0)} . 4. Let l(l =1, or 2, or 3, …) be a constrant, T={(m,n),-∞<m<∞,n≠0}∪{(lk,0),k=±1,±2,±3,…},T′={(0,0)}
