Various other dependence functions can be reduced to the multilinear function
through various transformations.
Abusing notation, we let U denote also the mixed extension of U, that is, the unique multilinear function
U: [Sigma] [right arrow] R that agrees with the original U when we identify the elements of S with the corresponding vertices of [Sigma].
and the B(x, y) and C(x, y, z) are multilinear functions
and can be denoted as
There have been a number of methods to generalize existing classes of multilinear functions with a view to improving the power and flexibility of analysis for PPS , such as the generalized representation of phase derivatives (GRPD) , the generalized high-order phase functions (GHOPF) .
Wiltshire, "A new class of multilinear functions for polynomial phase signal analysis," IEEE Trans.
n]), and the multilinear functions
B(q, p) and C(p, q, r) are defined by