Optimal Fractional Fourier Filtering for Graph Signals

Ozturk, Cuneyd; Özaktaş, Haldun M.; Gezici, Sinan; Koç, Aykut

doi:10.1109/tsp.2021.3079804

Cited by 22 publications

(4 citation statements)

References 77 publications

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“…The resulting graph fractional Fourier transform (GFRFT) [35] transforms the graph signal into the intermediate vertex frequency or vertex spectral domain. Furthermore, the windowed fractional Fourier transform and the linear canonical transform have been generalized to GSP [36], [37], and sampling [38], filtering [39], denoising [40] and classification [38] in the fractional domain have been studied.…”

Section: Introductionmentioning

confidence: 99%

Quantum entangled fractional Fourier transform based on the IWOP technique

Zhang¹,

Li²,

Zhao³

et al. 2023

Chinese Phys. B

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In our previous papers, the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics, and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform. The core function of the coordinate–momentum exchange operators in the addition law of fractional Fourier transform was analyzed too. In this paper, the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators (IWOP) are used to establish the entanglement fractional Fourier transform theory to the extent of quantum. A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

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Section: Introductionmentioning

confidence: 99%

Quantum entangled fractional Fourier transform based on the IWOP technique

Zhang¹,

Li²,

Zhao³

et al. 2023

Chinese Phys. B

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“…Furthermore, windowed fractional Fourier transform has been generalized to GSP [86], [87] and sampling in fractional domains is studied [11]. Very recently, the Wiener filtering has also been studied in the GSP domain [90], where the optimal filtering happens in intermediate domains.…”

Section: Introductionmentioning

confidence: 99%

Joint Time-Vertex Fractional Fourier Transform

Kartal¹,

Özgünay²,

Koç³

2022

Preprint

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Graphs signal processing successfully captures highdimensional data on non-Euclidean domains by using graph signals defined on graph vertices. However, data sources on each vertex can also continually provide time-series signals such that graph signals on each vertex are now time-series signals.Joint time-vertex Fourier transform (JFT) and the associated framework of time-vertex signal processing enable us to study such signals defined on joint time-vertex domains by providing spectral analysis. Just as the fractional Fourier transform (FRT) generalizes the ordinary Fourier transform (FT), we propose the joint time-vertex fractional Fourier transform (JFRT) as a generalization to the JFT. JFRT provides an additional fractional analysis tool for joint time-vertex processing by extending both temporal and vertex domain Fourier analysis to fractional orders. We theoretically show that the proposed JFRT generalizes the JFT and satisfies the properties of index additivity, reversibility, reduction to identity, and unitarity (for certain graph topologies). We provide theoretical derivations for JFRT-based denoising as well as computational cost analysis. Results of numerical experiments are also presented to demonstrate the benefits of JFRT.

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“…The main contributions include wavelet and Fourier transforms [5,[7][8][9][10], sam-pling and reconstruction of graph signals [11][12][13][14][15], uncertainty principles [16,17], filtering of graph signals [18,19], etc. Different transforms of graph signal are still the core of GSP.…”

Section: Introductionmentioning

confidence: 99%

Spectral graph fractional Fourier transform for directed graphs and its application

Yan¹,

Li²

2022

Preprint

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In graph signal processing, most studies assume that the underlying network is undirected. Although the digraph model is rarely adopted, it is more appropriate for many applications, especially for real world networks. In this paper, we present a general framework for extending the graph signal processing to directed graphs in graph fractional domain. For this purpose, we consider a new definition for fractional Laplacian matrix on directed graph and generalize the spectral graph fractional Fourier transform to directed graph (DGFRFT).Based on our new transform, we then define filtering.

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Optimal Fractional Fourier Filtering for Graph Signals

Cited by 22 publications

References 77 publications

Quantum entangled fractional Fourier transform based on the IWOP technique

Quantum entangled fractional Fourier transform based on the IWOP technique

Joint Time-Vertex Fractional Fourier Transform

Spectral graph fractional Fourier transform for directed graphs and its application

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