* 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
Wiltshire, "A new class of multilinear functions
for polynomial phase signal analysis," IEEE Transactions on Signal Processing, vol.
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) .
where <p, q> = [bar][p.sup.T]q is the standard scalar product in [C.sup.n] (also used in [R.sup.n]), and the multilinear functions
B(q, p) and C(p, q, r) are defined by