Sufficient condition of extendibility for two-dimensional quadrant-symmetric autocorrelations

A sufficient condition for extendibility of two-dimensional (2-D) quadrant-symmetric measured correlations is derived via matrix decomposition. It is very simple to test whether such measured correlations satisfy this sufficiency condition because the test boils down to a positive definiteness checking of a set of Toeplitz form matrices. However, there are cases that the condition does not give any result due to the fact that it is only sufficient.