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Related papers: Time-frequency analysis of bivariate signals

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Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…

Numerical Analysis · Mathematics 2023-05-05 Benjamin Kenwright

Fourier transform has become a basic tool for analyzing biological signals 1,2,3. Mostly a fast Fourier transform is computed for a finite sequence of data sample 4. This is the standard way apparatuses and modern computerized technology…

Quantitative Methods · Quantitative Biology 2008-04-01 Silvia Solis Ortiz , Rafael G. Campos , Julian Felix , Octavio Obregon

The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of…

A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…

Numerical Analysis · Mathematics 2008-03-19 Salem Said , Nicolas Le Bihan , Stephen J. Sangwine

The time-frequency content of a signal can be measured by the Gabor transform or windowed Fourier transform. This is a function defined on phase space that is computed by taking the Fourier transform of the product of the signal against a…

funct-an · Mathematics 2008-02-03 Jayakumar Ramanathan , Pankaj Topiwala

Graph signal processing extends spectral analysis to data supported on irregular domains. Existing fractional transforms for two-dimensional graph signals, including the two-dimensional graph fractional Fourier transform (GFRFT), typically…

Signal Processing · Electrical Eng. & Systems 2026-03-03 Mingzhi Wang , Manjun Cui , Feiyue Zhao , Yangfan He , Zhichao Zhang

Source wavelet estimation is the key in seismic signal processing for resolving subsurface structural properties. Homomorphic deconvolution using cepstrum analysis has been an effective method for wavelet estimation for decades. In general,…

Information Theory · Computer Science 2012-06-06 K. H. Miah , R. H. Herrera , M. van der Baan , M. D. Sacchi

The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…

Signal Processing · Electrical Eng. & Systems 2017-11-08 Hani Nejadriahi , David HillerKuss , Jonathan K. George , Volker J. Sorger

In this article, we study the properties of the nonlinear Fourier spectrum in order to gain better control of the temporal support of the signals synthesized using the inverse nonlinear Fourier transform (NFT). In particular, we provide…

Computational Physics · Physics 2018-09-17 Vishal Vaibhav

In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…

Signal Processing · Electrical Eng. & Systems 2025-06-26 Yusuf Yigit Pilavci , Pierre Palud , Julien Flamant , Pierre-Antoine Thouvenin , Jérémie Boulanger , Pierre Chainais

In this paper, we mainly establish the uncertainty principle (UP) for a function and its quaternion Fractional Fourier transform (QFrFT), as well as the UP for two QFrFTs. Using the polar representation of quaternion-valued signals, we give…

Complex Variables · Mathematics 2026-05-26 Ke Cui , Haipan Shi , Xiaomin Tang

Gravitational-wave memory is characterized by a signal component that persists after a transient signal has decayed. Treating such signals in the frequency domain is non-trivial, since discrete Fourier transforms assume periodic signals on…

General Relativity and Quantum Cosmology · Physics 2024-12-17 Jorge Valencia , Rodrigo Tenorio , Maria Rosselló-Sastre , Sascha Husa

The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix…

Signal Processing · Electrical Eng. & Systems 2020-10-29 Daichi Kitahara

This paper presents an experimental study on the application of quaternions in several machine learning algorithms. Quaternion is a mathematical representation of rotation in three-dimensional space, which can be used to represent complex…

Machine Learning · Computer Science 2023-08-07 Tianlei Zhu , Renzhe Zhu

In this paper we obtain the Fourier Transform of a continuous gravitational wave. We have analysed the data set for (i) one year observation time and (ii) arbitrary observation time, for arbitrary location of detector and source taking into…

General Relativity and Quantum Cosmology · Physics 2007-05-23 D. C. Srivastava , S. K. Sahay

This letter extends the concept of graph-frequency to graph signals that evolve with time. Our goal is to generalize and, in fact, unify the familiar concepts from time- and graph-frequency analysis. To this end, we study a joint temporal…

Machine Learning · Computer Science 2016-02-17 Andreas Loukas , Damien Foucard

Inspired by the success of recent data augmentation methods for signals which act on time-frequency representations, we introduce an operator which convolves the short-time Fourier transform of a signal with a specified kernel. Analytical…

Functional Analysis · Mathematics 2025-10-17 Simon Halvdansson

In continuous-time wavelet analysis, most wavelet present some kind of symmetry. Based on the Fourier and Hartley transform kernels, a new wavelet multiresolution analysis is proposed. This approach is based on a pair of orthogonal wavelet…

Classical Analysis and ODEs · Mathematics 2015-02-10 L. R. Soares , H. M. de Oliveira , R. J. Cintra

We study an application of the quantum tomography framework for the time-frequency analysis of modulated signals. In particular, we calculate optical tomographic representations and Wigner-Ville distributions for signals with amplitude and…

Signal Processing · Electrical Eng. & Systems 2020-09-29 A. S. Mastiukova , M. A. Gavreev , E. O. Kiktenko , A. K. Fedorov

The analysis of signals created by a variety of instruments involves calculating the phase of a sinusoidal type signal. One widely used method to extract this information is through the use of Fourier transforms, but it is known that…

Optics · Physics 2018-11-02 Andrew John Henning , Dawei Tang , Xiangqian , Jiang