Sufficient codition for extendibility and two-dimensional power spectrum estimation

A sufficient condition for the extendibility of two-dimensional (2-d) quadratically symmetric autocorrelation samples is derived based on matrix decomposition approaches. This condition is very simple to test because it boils down to a positive definiteness checking of a set of Toeplitz form matrices. It is shown by means of examples that this sufficient condition can be very useful, in some cases, by making the tedious extendibility test unnecessary. This paper also presents a method which can approximate with small error a given quadratically symmetric autocorrelation function (a.c.f) over a square with a new a.c.f that is guaranteed to be extendible. This method is also based on a matrix decomposition approach and employs an iterative gradient algorithm. Its implications to the estimation of a 2-d power spectrum is demonstrated.