Higher order differential energy operators

Abstract

Instantaneous signal operators /spl Upsi//sub k/(x)=x/spl dot/x/sup (k-1)/-xx/sup (k)/ of integer orders k are proposed to measure the cross energy between a signal x and its derivatives. These higher order differential energy operators contain as a special case, for k=2, the Teager-Kaiser (1990) operator. When applied to (possibly modulated) sinusoids, they yield several new energy measurements useful for parameter estimation or AM-FM demodulation. Applying them to sampled signals involves replacing derivatives with differences that lead to several useful discrete energy operators defined on an extremely short window of samples.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>