Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor Transform

The long-periodic/infinite discrete Gabor transform (DGT) is more effective than the periodic/finite one in many applications. In this paper, a fast and effective approach is presented to efficiently compute the Gabor analysis window for arbitrary given synthesis window in DGT of long-periodic/infin...

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Main Authors: Rui Li, Yong Huang, Jia-Bao Liu
Format: Article
Language:English
Published: Wiley 2018-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2018/9039240
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author Rui Li
Yong Huang
Jia-Bao Liu
author_facet Rui Li
Yong Huang
Jia-Bao Liu
author_sort Rui Li
collection DOAJ
description The long-periodic/infinite discrete Gabor transform (DGT) is more effective than the periodic/finite one in many applications. In this paper, a fast and effective approach is presented to efficiently compute the Gabor analysis window for arbitrary given synthesis window in DGT of long-periodic/infinite sequences, in which the new orthogonality constraint between analysis window and synthesis window in DGT for long-periodic/infinite sequences is derived and proved to be equivalent to the completeness condition of the long-periodic/infinite DGT. By using the property of delta function, the original orthogonality can be expressed as a certain number of linear equation sets in both the critical sampling case and the oversampling case, which can be fast and efficiently calculated by fast discrete Fourier transform (FFT). The computational complexity of the proposed approach is analyzed and compared with that of the existing canonical algorithms. The numerical results indicate that the proposed approach is efficient and fast for computing Gabor analysis window in both the critical sampling case and the oversampling case in comparison to existing algorithms.
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spelling doaj-art-c0e5175a50c940ea8208c93d89fdbd222025-08-20T02:19:22ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/90392409039240Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor TransformRui Li0Yong Huang1Jia-Bao Liu2College of Information and Network Engineering, Anhui Science and Technology University, Bengbu 233030, ChinaCollege of Information and Network Engineering, Anhui Science and Technology University, Bengbu 233030, ChinaSchool of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, ChinaThe long-periodic/infinite discrete Gabor transform (DGT) is more effective than the periodic/finite one in many applications. In this paper, a fast and effective approach is presented to efficiently compute the Gabor analysis window for arbitrary given synthesis window in DGT of long-periodic/infinite sequences, in which the new orthogonality constraint between analysis window and synthesis window in DGT for long-periodic/infinite sequences is derived and proved to be equivalent to the completeness condition of the long-periodic/infinite DGT. By using the property of delta function, the original orthogonality can be expressed as a certain number of linear equation sets in both the critical sampling case and the oversampling case, which can be fast and efficiently calculated by fast discrete Fourier transform (FFT). The computational complexity of the proposed approach is analyzed and compared with that of the existing canonical algorithms. The numerical results indicate that the proposed approach is efficient and fast for computing Gabor analysis window in both the critical sampling case and the oversampling case in comparison to existing algorithms.http://dx.doi.org/10.1155/2018/9039240
spellingShingle Rui Li
Yong Huang
Jia-Bao Liu
Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor Transform
Complexity
title Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor Transform
title_full Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor Transform
title_fullStr Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor Transform
title_full_unstemmed Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor Transform
title_short Effective Approach to Calculate Analysis Window in Infinite Discrete Gabor Transform
title_sort effective approach to calculate analysis window in infinite discrete gabor transform
url http://dx.doi.org/10.1155/2018/9039240
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AT yonghuang effectiveapproachtocalculateanalysiswindowininfinitediscretegabortransform
AT jiabaoliu effectiveapproachtocalculateanalysiswindowininfinitediscretegabortransform