相关论文: Time-frequency transforms of white noises and Gaus…

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…

We have presented a new and alternative algorithm for noise reduction using the methods of discrete wavelet transform and numerical differentiation of the data. In our method the threshold for reducing noise comes out automatically. The…

This paper presents a pioneering exploration of the mechanisms underlying large foundation models' (LFMs) weights, aiming to simplify AI research. Through extensive observation and analysis on prevailing LFMs, we find that regardless of…

A Gabor system generated by a window function $\phi$ and a rectangular lattice $a \Z\times \Z/b$ is given by $${\mathcal G}(\phi, a \Z\times \Z/b):=\{e^{-2\pi i n t/b} \phi(t- m a):\ (m, n)\in \Z\times \Z\}.$$ One of fundamental problems in…

In quantum computing, characterizing the full noise profile of qubits can aid in increasing coherence times and fidelities by developing error-mitigating techniques specific to the noise present. This characterization also supports efforts…

Certain signal classes such as audio signals call for signal representations with the ability to adapt to the signal's properties. In this article we introduce the new concept of quilted frames, which aim at adaptivity in time-frequency…

In recent years there has been a growing interest in the fractional Fourier transform driven by its large number of applications. The literature in this field follows two main routes. On the one hand, the areas where the ordinary Fourier…

With the advent of gravitational-wave astronomy and the discovery of more compact binary coalescences, data quality improvement techniques are desired to handle the complex and overwhelming noise in gravitational wave (GW) observational…

We perform Wigner analysis of linear operators. Namely, the standard time-frequency representation \emph{Short-time Fourier Transform} (STFT) is replaced by the $\mathcal{A}$-\emph{Wigner distribution} defined by $W_{\mathcal A}…

2-D complex Gabor filtering has found numerous applications in the fields of computer vision and image processing. Especially, in some applications, it is often needed to compute 2-D complex Gabor filter bank consisting of the 2-D complex…

We obtain a representation theorem for Banach space valued Gaussian random variables as integrals against a white noise. As a corollary we obtain necessary and sufficient conditions for the existence of a white noise representation for a…

Stochastic integration \textit{wrt} Gaussian processes has raised strong interest in recent years, motivated in particular by its applications in Internet traffic modeling, biomedicine and finance. The aim of this work is to define and…

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…

Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of…

Graph signal processing deals with signals which are observed on an irregular graph domain. While many approaches have been developed in classical graph theory to cluster vertices and segment large graphs in a signal independent way, signal…

Studies of sparse representation of deterministic signals have been well developed. Amongst there exists one called adaptive Fourier decomposition (AFD) established through adaptive selections of the parameters defining a Takenaka-Malmquist…

We consider the Bayesian detection statistic for a targeted search for continuous gravitational waves, known as the $\mathcal{B}$-statistic. This is a Bayes factor between signal and noise hypotheses, produced by marginalizing over the four…

Asymptotic energy-distortion performance of zero-delay communication scenarios under additive white Gaussian noise is investigated. Using high-resolution analysis for quantizer design, the higher-order term in the logarithm of the…

This work deals with the ill-posed inverse problem of reconstructing a function $f$ given implicitly as the solution of $g = Af$, where $A$ is a compact linear operator with unknown singular values and known eigenfunctions. We observe the…

We study the fractal uncertainty principle in the joint time-frequency representation, and we prove a version for the Short-Time Fourier transform with Gaussian window on the modulation spaces. This can equivalently be formulated in terms…