HIGHER-ORDER DIFFERENTIAL ENERGY OPERATORS

Instantaneous signal operators Upsilon(k)(x) = xx((k-1)) - xx((k)) of integer orders k are proposed to measure the cross energy between a si gnal x and its derivatives, These higher order differential energy ope rators contain as a special case, for k = 2, the Teager-Kaiser operato r. When applied to (possibly modulated) sinusoids, they yield several new energy measurements useful for parameter estimation or AM-FM demod ulation. Applying them to sampled signals involves replacing derivativ es with differences that lead to several useful discrete energy operat ors defined on an extremely short window of samples.