Irregular Weyl–Heisenberg wave packet frames in L2(R)L2(R)

Let {fk}{fk} be a frame for a Hilbert HH and let {αj,k}{αj,k} be a sequence of scalars. Aldroubi (1995) [1] considered a linear combination of the form gj=∑k=1∞αj,kfk (j∈Nj∈N) and proved sufficient conditions on {αj,k}{αj,k} such that {gj}{gj} constitutes a frame for HH. In this paper we discuss linear combination of the irregular Weyl–Heisenberg wave packet frames for L2(R)L2(R). Necessary and sufficient conditions for a finite sum of irregular Weyl–Heisenberg wave packet frames to be a frame for L2(R)L2(R) are given.