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The graph Fourier transform (GFT) is in general dense and requires O(n^2) time to compute and O(n^2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is…

Numerical Analysis · Computer Science 2017-11-07 Luc LeMagoarou , Nicolas Tremblay , Rémi Gribonval

Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional…

Information Theory · Computer Science 2024-04-30 Václav Pavlíček , Ayush Bhandari

We propose novel two-channel filter banks for signals on graphs. Our designs can be applied to arbitrary graphs, given a positive semi definite variation operator, while using arbitrary vertex partitions for downsampling. The proposed…

Signal Processing · Electrical Eng. & Systems 2023-04-26 Eduardo Pavez , Benjamin Girault , Antonio Ortega , Philip A. Chou

In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…

Signal Processing · Electrical Eng. & Systems 2024-01-23 Darukeesan Pakiyarajah , Eduardo Pavez , Antonio Ortega

In Graph Signal Processing (GSP), data dependencies are represented by a graph whose nodes label the data and the edges capture dependencies among nodes. The graph is represented by a weighted adjacency matrix $A$ that, in GSP, generalizes…

Signal Processing · Electrical Eng. & Systems 2020-12-02 João Domingos , José M. F. Moura

Contemporary data is often supported by an irregular structure, which can be conveniently captured by a graph. Accounting for this graph support is crucial to analyze the data, leading to an area known as graph signal processing (GSP). The…

Information Theory · Computer Science 2017-05-26 Geert Leus , Santiago Segarra , Alejandro Ribeiro , Antonio G. Marques

The analysis of signals defined over a graph is relevant in many applications, such as social and economic networks, big data or biological networks, and so on. A key tool for analyzing these signals is the so called Graph Fourier Transform…

Spectral Theory · Mathematics 2017-10-11 Stefania Sardellitti , Sergio Barbarossa , Paolo Di Lorenzo

The one-dimensional (1D) fractional Fourier transform (FRFT) generalizes the Fourier transform, offering significant advantages in the time-frequency analysis of non-stationary signals. While various 2D extensions exist, such as the 2D…

Signal Processing · Electrical Eng. & Systems 2026-03-03 Daxiang Li , Zhichao Zhang , Wei Yao

We study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs. A frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators…

Information Theory · Computer Science 2016-06-29 Aamir Anis , Akshay Gadde , Antonio Ortega

The Fractional Fourier Transform (FrFT) has widespread applications in areas like signal analysis, Fourier optics, diffraction theory, etc. The Holomorphic Fractional Fourier Transform (HFrFT) proposed in the present paper may be used in…

Mathematical Physics · Physics 2019-05-13 William D. Kirwin , José Mourão , João P. Nunes , Thomas Thiemann

The Fast Fourier Transform(FFT) is a classic signal processing algorithm that is utilized in a wide range of applications. For image processing, FFT computes on every pixel's value of an image, regardless of their properties in frequency…

Signal Processing · Electrical Eng. & Systems 2020-02-25 Sheng Shi , Runkai Yang , Haihang You

Multivariate signals, which are measured simultaneously over time and acquired by sensor networks, are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these…

Signal Processing · Electrical Eng. & Systems 2025-01-10 Stephan Goerttler , Fei He , Min Wu

A unitary shift operator (GSO) for signals on a graph is introduced, which exhibits the desired property of energy preservation over both backward and forward graph shifts. For rigour, the graph differential operator is also derived in an…

Signal Processing · Electrical Eng. & Systems 2019-09-18 Bruno Scalzo Dees , Ljubisa Stankovic , Milos Dakovic , Anthony G. Constantinides , Danilo P. Mandic

An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the…

Machine Learning · Computer Science 2012-07-19 Eric P. Xing , Michael I. Jordan , Stuart Russell

This paper proposes a graph linear canonical transform (GLCT) by decomposing the linear canonical parameter matrix into fractional Fourier transform, scale transform, and chirp modulation for graph signal processing. The GLCT enables…

General Mathematics · Mathematics 2024-07-18 Jian Yi Chen , Bing Zhao Li

Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…

Numerical Analysis · Mathematics 2016-10-05 Anne Gelb , Guohui Song

In many applications, from sensor to social networks, gene regulatory networks or big data, observations can be represented as a signal defined over the vertices of a graph. Building on the recently introduced Graph Fourier Transform, the…

Information Theory · Computer Science 2015-12-03 Mikhail Tsitsvero , Sergio Barbarossa , Paolo Di Lorenzo

The short-time Fourier transform (STFT) is widely used to analyze the spectra of temporal signals that vary through time. Signals defined over graphs, due to their intrinsic complexity, exhibit large variations in their patterns. In this…

Social and Information Networks · Computer Science 2016-01-27 Mariano Tepper , Guillermo Sapiro

To address limitations of the graph fractional Fourier transform (GFRFT) Wiener filtering and the traditional joint time-vertex fractional Fourier transform (JFRFT) Wiener filtering, this study proposes a filtering method based on the…

Signal Processing · Electrical Eng. & Systems 2025-07-30 Ziqi Yan , Zhichao Zhang

The Special Affine Fourier Transformation or the SAFT generalizes a number of well known unitary transformations as well as signal processing and optics related mathematical operations. Shift-invariant spaces also play an important role in…

Information Theory · Computer Science 2016-01-25 Ayush Bhandari , Ahmed I. Zayed