Approximately dual Gabor frames and almost perfect reconstruction based on a class of window functions |
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| Authors: | Ole Christensen Augustus J E M Janssen Hong Oh Kim Rae Young Kim |
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| Institution: | 1.Department of Applied Mathematics and Computer Science,Technical University of Denmark,Lyngby,Denmark;2.Department of Mathematics and Computer Science,Technische Universiteit Eindhoven,Eindhoven,The Netherlands;3.Department of Mathematical Sciences,UNIST,Ulsan,Republic of Korea;4.Department of Mathematics,Yeungnam University,Gyeongbuk,Republic of Korea |
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| 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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