Calculation of the local cross-correlation function on the basis of the Laguerre transform

Abstract

A simple and computationally efficient mechanism for calculating a running or local cross-correlation function of two time-domain signals is presented. In order to obtain a running cross-correlation function, the signals must be windowed. It is argued that an appropriate window for a local cross correlation is an exponential function. To obtain a computationally efficient mechanism, the windowed functions are decomposed in a series of orthogonal functions. The set or orthogonal functions is matched to the chosen window and is a Laguerre-Fourier series. The cross correlation of the windowed functions is equal to a weighted summation of cross-correlated pattern functions. The weights are determined by cross correlating the Laguerre coefficients.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>