Suppose that a process x(n) has been recorded, but there is a missing gap of data over the interval [N1, N2], i.e., x(n) is unknown over this interval.
(a) Derive the optimum estimate of x(N1) using the data in the semi-infinite interval (-∞, N, - l].
(b) Derive the optimum estimate of x(N1) using the data in the semi-infinite interval [N2 + 1, ∞).
(c) Derive the optimum estimate of x(N1) that is formed by combining together the two estimates found in parts (a) and (b ).
(d) Generalize your result in part (c) to find the optimum estimate of x(n) at an arbitrary point n in the interval [N1, N2].