Optimum linear transformation for a quadratic form of signals

This paper proposes the optimum skew linear transformation of signals which gives the minimum mean error of a positive definite quadratic form of the signals. the relation of this problem with hybrid coding is emphasized. Based on conventional orthogonal KLT, the condition for the optimum transformation is given in a generalized eigenvalue problem. We show the geometrical meaning and a solving method of the condition, and discuss the existence and the uniqueness of its solution. Numerical performance comparisons show superiority of this transformation to others such as KLT and DCT. Because this transformation is a generalization of KLT to a general quadratic form, it is as significant as KLT is.