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      Optimal fractional fourier filtering for graph signals

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      Author(s)
      Öztürk, Cüneyd
      Özaktaş, Haldun M.
      Gezici, Sinan
      Koç, Aykut
      Date
      2021-05-19
      Source Title
      IEEE Transactions on Signal Processing
      Print ISSN
      1053-587X
      Electronic ISSN
      1941-0476
      Publisher
      IEEE
      Volume
      69
      Pages
      2902 - 2912
      Language
      English
      Type
      Article
      Item Usage Stats
      34
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      150
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      Abstract
      Graph signal processing has recently received considerable attention. Several concepts, tools, and applications in signal processing such as filtering, transforming, and sampling have been extended to graph signal processing. One such extension is the optimal filtering problem. The minimum mean-squared error estimate of an original graph signal can be obtained from its distorted and noisy version. However, the best separation of signal and noise, and thus the least error, is not always achieved in the ordinary Fourier domain, but rather a fractional Fourier domain. In this work, the optimal filtering problem for graph signals is extended to fractional Fourier domains, and theoretical analysis and solution of the proposed problem are provided along with computational cost considerations. Numerical results are presented to illustrate the benefits of filtering in fractional Fourier domains.
      Keywords
      Fractional Fourier transform
      Graph signal processing (GSP)
      Optimal filtering
      Wiener filter
      Graph Fourier transform (GFT)
      Signal processing on graphs
      Graphs
      Permalink
      http://hdl.handle.net/11693/76931
      Published Version (Please cite this version)
      https://doi.org/10.1109/TSP.2021.3079804
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      • Department of Electrical and Electronics Engineering 4011
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