A rank property of the generalized Hankel matrix for 2D sinusoidal sequences

Recently, a theory of Hankel operators associated with two-dimensional (2D) linear time-invariant systems has been developed. It is applicable to the class of noncausal systems with rational transfer functions. An algorithm for model order estimation and parameter identification has been developed based upon the singular value decomposition of a generalized Hankel Matrix. Applications are found in system identification and autoregressive moving average (ARMA) spectrum estimation. The characterization of the 2D Hankel operator constructed from sinusoidal data is discussed. In this case, the rank behavior is shown to be markedly different from that which holds for rational data. This fact, different from the case in 1D, suggests a method to separate sinusoids in 2D from colored noise obeying a rational difference equation