Karhunen-Loeve-like expansions

Abstract

Investigates the problem of the optimal orthogonal signal expansion for providing both the best signal approximation and non-correlated coefficients of expansion. Without the latter condition, the well-known solution of the best signal representation is given by the classical Fourier basis. This additional condition, however, provides Karhunen-Loeve expansion-like properties which are very useful in applied signal processing. Therefore, it is of major practical importance to describe Karhunen-Loeve-like signal expansion bases. We present an iterative algorithm converging to the solution of this this problem. It is also proven that this solution is unique.<>