Related papers: Time-frequency transforms of white noises and Gaus…
Mittag-Leffler analysis is an infinite dimensional analysis with respect to non-Gaussian measures of Mittag-Leffler type which generalizes the powerful theory of Gaussian analysis and in particular white noise analysis. In this paper we…
We present a time-frequency framework adapted to dispersive phase functions via a subdyadic geometry in phase space. On top of this geometry we construct stable Gabor frames with quantitative control of overlap, almost orthogonality, and…
This article presents a convenient approach to Fourier analysis for the investigation of functions and distributions defined in $\mathbb{T}^m \times \mathbb{R}^n$. Our approach involves the utilization of a mixed Fourier transform,…
In this article, we first briefly recall Gabor's communication theory and then Gabor transform and expansion, and also its connection with joint time frequency analysis.
Graph signal processing (GSP) is an effective tool in dealing with data residing in irregular domains. In GSP, the optimal graph filter is one of the essential techniques, owing to its ability to recover the original signal from the…
Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational…
Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…
We present a novel family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales. Similar to classical time-frequency or time-scale representations, the representation coefficients are…
Time series analysis is ubiquitous in many fields of science including gravitational-wave astronomy, where strain time series are analyzed to infer the nature of gravitational-wave sources, e.g., black holes and neutron stars. It is common…
Given a non-quasianalytic subadditive weight function $\omega$ we consider the weighted Schwartz space $\mathcal{S}_\omega$ and the short-time Fourier transform on $\mathcal{S}_\omega$, $\mathcal{S}'_\omega$ and on the related modulation…
Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often…
Seismic attributes calculated by conventional methods are susceptible to noise. Conventional filtering reduces the noise in the cost of losing the spectral bandwidth. The challenge of having a high-resolution and robust signal processing…
Identification of a transient gravitational-wave signal embedded into non-stationary noise requires the analysis of time-dependent spectral components in the resulting time series. The time-frequency distribution of the signal power can be…
The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed…
WiFi-based human action recognition (HAR) has been regarded as a promising solution in applications such as smart living and remote monitoring due to the pervasive and unobtrusive nature of WiFi signals. However, the efficacy of WiFi…
In this paper we review the application of the matched filter (MF) technique and its application to detect weak, deterministic, smooth signals in a stationary, random, Gaussian noise. This is particular suitable in astronomy to detect…
Graphons are infinite-dimensional objects that represent the limit of convergent sequences of graphs as their number of nodes goes to infinity. This paper derives a theory of graphon signal processing centered on the notions of graphon…
Audio domain transfer is the process of modifying audio signals to match characteristics of a different domain, while retaining the original content. This paper investigates the potential of Gaussian Flow Bridges, an emerging approach in…
Morlet or Gabor wavelet transforms as well as Gaussian smoothing, are widely used in signal processing and image processing. However, the computational complexity of their direct calculations is proportional not only to the number of data…
We study functions whose time-frequency content are concentrated in a compact region in phase space using time-frequency localization operators as a main tool. We obtain approximation inequalities for such functions using a finite linear…