Abstract
It is a well-known problem in Gabor analysis how to construct explicitly given dual frames associated with a given frame. In this paper we will consider a class of window functions for which approximately dual windows can be calculated explicitly. The method makes it possible to get arbitrarily close to perfect reconstruction by allowing the modulation parameter to vary. Explicit estimates for the deviation from perfect reconstruction are provided for some of the standard functions in Gabor analysis, e.g., the Gaussian and the two-sided exponential function.
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The authors would like to thank the reviewers for several useful suggestions, which improved the presentation of the results.
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Communicated by: Gitta Kutyniok
This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2016R1D1A1B02009954).
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Christensen, O., Janssen, A.J.E.M., Kim, H.O. et al. Approximately dual Gabor frames and almost perfect reconstruction based on a class of window functions. Adv Comput Math 44, 1519–1535 (2018). https://doi.org/10.1007/s10444-018-9595-7
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DOI: https://doi.org/10.1007/s10444-018-9595-7