This chapter delves into the study of frames in the Hilbert space. It focuses on the discretization of two classes of induced representations associated with the affine Lie group. The chapter revisits the well-established Gabor wavelets, which have been widely studied in the literature. It presents a solution of the discretization problem for the direct sum of two nonequivalent irreducible representations. The chapter also discusses a few theorems along with their proofs under the Gabor systems and the Heisenberg group.