On the Relation between NARX Clusters and Even/Odd Nonlinearities through Frequency-Domain Analysis

Table 1

Summary of the results.

Cluster	System type
	LO	LE	H		W
			O	E	O	E
, even		P				P
, odd	P				P
, even
, odd	P
, even
, odd	P

H—Hammerstein, W—Wiener, O—odd, and E—even. LE and LO according to Section 4. P implies that such cluster can appear in a polynomial NARX model, in contrast to . The symbol denotes that nothing can be assured about the cluster. indicates that only terms with the same lag are possible. implies .