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

Let {f(k)} be a frame for a Hilbert H and let {alpha(j,k)} be a sequence of scalars. Aldroubi (1995) [I] considered a linear combination of the form g(j) = Sigma(infinity)(k=1) alpha(j,k) f(k) (j is an element of N) and proved sufficient conditions on {alpha(j,k)} such that {g(j)} constitutes a frame for H. In this paper we discuss linear combination of the irregular Weyl-Heisenberg wave packet frames for L-2(R). Necessary and sufficient conditions for a finite sum of irregular Weyl-Heisenberg wave packet frames to be a frame for L-2 (R) are given. (C) 2014 Elsevier Masson SAS. All rights reserved.