Two-dimensional all-pass structure of the \(n\)th order (Q1977274)

The aim is to propose an orthogonal two-dimensional structure that has as input function an all-pass two-dimensional lossless bounded real function of \(n\)th-order. A recurrence formula for this input function is derived. The proposed two-dimensional structure is a minimal one since it involves two delay units for every order of the two-dimensional all-pass function. As an example to the introduced structure, the corresponding all-pass functions of first, second, and third order are computed.