Construction of -stage discrete periodic wave packet frames

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In this paper, our main goal is to introduce the construction of the -stage periodic wave packet frames in a discrete setting. We first establish a general characterization of wave packet systems to be Parseval frames in using discrete Fourier transforms, and provide a sufficient condition for the system to be a first-stage discrete periodic wave packet frame for . And then, we construct a class of -stage discrete periodic wave packet frame by iterating the filter sequence, and establish the associated decomposition and reconstruction algorithms for these wave packet frames, which include the corresponding results of wavelet analysis and Gabor theory as the special cases. Finally, we give an illustrative example to demonstrate the validity of the proposed scheme.