Example. the 'k'f Shift Operator

we present a general theory of $ilii~ear/ quadratic signal representations t h a t a l e coiianant to timefrequency (TF) displacement operators resentations are developed in the CY,,^') dQmaiiB and iio the e e o ~ ~ u ~ a ~ e case, covariant representa,tions can also be formulated in an eigenfunction parameter domain ( ( a , b ) domain). The relations connecting the (0, p), TF, and (U, b) domains axe e p ~ t o ~ ~ ~ ~ ~ by the dispEoeem.ent Jtmction and the localization f u n ~ t ~ o n . For conjugate operators, (a , p) covariance and (a , b ) covariance are equivalent.