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.