Construction of -stage discrete periodic wave packet frames

Abstract

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.

Keywords:

• Wave packets
• DFT
• Parseval frames
• periodic sequences

AMS Subject Classifications:

• 42C15
• 42C40

Acknowledgements

The authors express their gratitude to the anonymous referees for their kind suggestions and useful comments on the original manuscript, which resulted in this final version.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Science Foundation of China under [grant number 61179039]; the National Key Basic Research Development Program (973 Program) of China under [grant number 2011CB707100]; the National Natural Science Foundation of China under [grant number 61471410].