WAVE PACKET SYSTEMS

In this paper, we present a sufficient condition for a generalized shift-invariant system to be a Bessel sequence or even a frame for L^2(R^d). In particular, this leads us to a sufficient condition for a wave packet system, systems in the form {DAjTFkEcmg}j,mϵZ,kϵZ^d , to form a frame. On the other hand, we show that certain natural conditions on the parameters of such a system exclude the frame property. We also characterize the dual pairs of these systems.

Keywords:

Frame , Bessel sequence , generalized shift-invariant systems , wave packet system , Affine system , Gabor system , wavelet system