Nth-Order autocorrelations in pattern recognition

Abstract

Given a real-valued time function x(t), its nth-order autocorrelation function is defined by {if121-1}. It is easy to see that this function is translation invariant in the sense that x(t) and y(t) = x(t + τ) have the same nth-order autocorrelation function. In this paper we investigate the properties of these functions and their use in pattern recognition. Even for small values of n the dimensionality of nth-order autocorrelation space can become very high. We describe indirect methods of using nth-order autocorrelations without explicitly computing them. We also investigate conditions for uniqueness in the sense that equality of rx(τ1, ..., τn) and ry(τ1, ..., τn) implies that x(t) = y(t + τ) for some τ. Finally we present some experimental results on character recognition. © 1968 Academic Press Inc.