On the selective counting of third-order products

A practical and efficient method is presented for the counting of third-order products generated by an arbitrary number of carriers with arbitrary power spectral shapes. In particular, three selective counting procedures (i.e. sorting by position, sorting by position and group, and sorting by position, group, and kind) are introduced in a systemic way, based upon a discrete third-order Volterra model. The advantage of the counting algorithm is that (1) the algorithm provides the exact counting of third-order products of all eleven possible groups; (2) the counting process requires only two multiplications for the selective counting of third-order products at each position, and the algorithm, which is thus efficient, can be easily implemented