Related papers: On the frequency variogram and on frequency domain…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…
Standard direct forecasting models typically rely on point-wise objectives such as Mean Squared Error, which fail to capture the complex spatio-temporal dependencies inherent in graph-structured signals. While recent frequency-domain…
Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…
Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…
Fourier analysis has been an instrumental tool in the development of signal processing. This leads us to wonder whether this framework could similarly benefit generative modelling. In this paper, we explore this question through the scope…
It is shown here that precision is gained by analyzing the interferometric spectra directly from the interferograms, with no previous Fourier transformation to put them in the standard frequency domain. The method is based on the…
The synchrosqueezing transform, a kind of reassignment method, aims to sharpen the time-frequency representation and to separate the components of a multicomponent non-stationary signal. In this paper, we consider the short-time Fourier…
The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and…
Time of flight cameras may emerge as the 3-D sensor of choice. Today, time of flight sensors use phase-based sampling, where the phase delay between emitted and received, high-frequency signals encodes distance. In this paper, we present a…
As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
In frequency domain analysis for spatial data, spectral averages based on the periodogram often play an important role in understanding spatial covariance structure, but also have complicated sampling distributions due to complex variances…
The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical…
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,…
Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…
In order to enhance the performance of Transformer models for long-term multivariate forecasting while minimizing computational demands, this paper introduces the Joint Time-Frequency Domain Transformer (JTFT). JTFT combines time and…
In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time…