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http://hdl.handle.net/10397/90512
| Title: | Performing fractional delay via fractional singular spectrum analysis | Authors: | Zhou, Y Ling, BWK Huang, Z Chan, YL Lin, Y |
Issue Date: | Feb-2022 | Source: | Signal, image and video processing, Feb. 2022, v. 16, no. 1, p. 39-46 | Abstract: | This paper proposes a fractional singular spectrum analysis (SSA)-based method for performing the fractional delay. First, the input sequence is divided into two overlapping sequences with the first sequence being the input sequence without its last point and the second sequence being the input sequence without its first point. Then, the singular value decompositions (SVD) are performed on the trajectory matrices constructed based on these two sequences. Next, the designs of both the right unitary matrix and the left unitary matrix for generating the new trajectory matrix are formulated as the quadratically constrained quadratic programing problems. The analytical solutions of these quadratically constrained quadratic programing problems are derived via the SVD approach. Finally, the fractional SSA components are obtained by performing the diagonal averaging operation, and the fractional delay sequence is obtained by summing up all the fractional SSA components together. Since the fractional SSA operations are nonlinear and adaptive, our proposed method is a kind of nonlinear and adaptive approach for performing the fractional delay. Besides, by discarding some fractional SSA components, the joint fractional delay operation and the denoising operation can be performed simultaneously. | Keywords: | Fractional delay Fractional singular spectrum analysis Quadratically constrained quadratic programing |
Publisher: | Springer | Journal: | Signal, image and video processing | ISSN: | 1863-1703 | DOI: | 10.1007/s11760-021-01954-x | Rights: | © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2021 This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s11760-021-01954-x. |
| Appears in Collections: | Journal/Magazine Article |
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| Zhou_Performing_Fractional_Delay.pdf | Pre-Published version | 4.57 MB | Adobe PDF | View/Open |
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