Generalized Brillinger-Like Transforms

We propose novel transforms of stochastic vectors, called the generalized Brillinger transforms (GBT1 and GBT2), which are generalizations of the Brillinger transform (BT). The GBT1 extends the BT to the cases when the covariance matrix and the weighting matrix are singular, and moreover, the weighting matrix is not necessarily symmetric. We show that the GBT1 may computationally be preferable over another related optimal technique, the generic Karhunen-Loève transform (GKLT). The GBT2 generalizes the GBT1 to provide, under the condition we impose, better associated accuracy than that of the GBT1. It is achieved because of the increase in a number of parameters to optimize compared to that in the GBT1.