Related papers: Refreshing idea on Fourier analysis
The purpose of this paper is to investigate several issues concerning the Dirac equation from a time-frequency analysis perspective. More precisely, we provide estimates in weighted modulation and Wiener amalgam spaces for the solutions of…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
This article introduces an effective generalization of the polar flavor of the Fourier Theorem based on a new method of analysis. Under the premises of the new theory an ample class of functions become viable as bases, with the further…
We study the frequentist properties of confidence intervals for the On-Off problem. The methods include all those in common use today. We derive explicit formulas for the limits and calculate the true coverage and the expected lengths of…
Neural time-series analysis has traditionally focused on modeling data in the time domain, often with some approaches incorporating equivalent Fourier domain representations as auxiliary spectral features. In this work, we shift the main…
A Python package for the calculation of spectrograms with optimized time and frequency resolution for application in the analysis of numerical simulations on ultrashort pulse propagation is presented. Gabor's uncertainty principle prevents…
Energy forecasting is pivotal in energy systems, by providing fundamentals for operation, with different horizons and resolutions. Though energy forecasting has been widely studied for capturing temporal information, very few works…
Traditional resolvent analysis is a powerful framework for identifying the most amplified input-output structures in fluid flows from a stationary base state. Extending this resolvent analysis to periodic base flows poses computational…
To study the dynamical behaviour of the engineering and physical systems, we often need to capture their continuous behaviour, which is modeled using differential equations, and perform the frequency-domain analysis of these systems.…
In this study, we introduce and explore a delay differential equation that lends itself to explicit solutions in the Fourier-transformed space. Through the careful alignment of the initial function, we can construct a highly accurate…
Classical spectral analysis is based on the discrete Fourier transform of the auto-covariances. In this paper we investigate the asymptotic properties of new frequency domain methods where the auto-covariances in the spectral density are…
We consider a particular approach to the regularization of the inverse problem of computerized tomography. This approach is based on notions pertaining to Fourier synthesis. It refines previous contributions, in which the preprocessing of…
In this paper we study the inverse problem of identifying a source or an initial state in a time-fractional diffusion equation from the knowledge of a single boundary measurement. We derive logarithmic stability estimates for both…
The subject of time-band-limiting, originating in signal processing, is dominated by the miracle that a naturally appearing integral operator admits a commuting differential one allowing for a numerically efficient way to compute its…
An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically…
Functions that are smooth but non-periodic on a certain interval possess Fourier series that lack uniform convergence and suffer from the Gibbs phenomenon. However, they can be represented accurately by a Fourier series that is periodic on…
The traditional theory of Laplace transformation in its currently prevalent form is unsatisfactory. Its deficiencies can be traced back to a mismatch of the definition intervals of the original function and of the inverse L-transform. A new…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…
Time-frequency scattering is a mathematical transformation of sound waves. Its core purpose is to mimick the way the human auditory system extracts information from its environment. In the context of improving the artificial intelligence of…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…