Related papers: OptFROG - Analytic signal spectrograms with optimi…
The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…
While frequency-resolved optical gating (FROG) is widely used in characterizing the ultrafast pulse in optics, analytic signals are often considered in time-frequency analysis and signal processing, especially when extracting instantaneous…
The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method…
This article deals with the use of optimal lattice and optimal window in Discrete Gabor Transform computation. In the case of a generalized Gaussian window, extending earlier contributions, we introduce an additional local window adaptation…
The study of X-ray time-lag spectra in active galactic nuclei (AGN) is currently an active research area, since it has the potential to illuminate the physics and geometry of the innermost region (i.e. close to the putative super-massive…
We study the problem of constructing a graph Fourier transform (GFT) for directed graphs (digraphs), which decomposes graph signals into different modes of variation with respect to the underlying network. Accordingly, to capture low,…
Band-limited functions can oscillate locally at an arbitrarily fast rate through an interference phenomenon known as superoscillations. Using an optical pulse with a superoscillatory envelope we experimentally break the temporal…
Periodicity analysis of unevenly collected data is a relevant issue in several scientific fields. In astrophysics, for example, we have to find the fundamental period of light or radial velocity curves which are unevenly sampled…
We use time-frequency methods for the study of Fourier Integral operators (FIOs). In this paper we shall show that Gabor frames provide very efficient representations for a large class of FIOs. Indeed, similarly to the case of shearlets and…
The short-time Fourier transform (STFT) is widely used for analyzing non-stationary signals. However, its performance is highly sensitive to its parameters, and manual or heuristic tuning often yields suboptimal results. To overcome this…
We present a common pulse retrieval algorithm (COPRA) that can be used for a broad category of ultrashort laser pulse measurement schemes including frequency-resolved optical gating (FROG), interferometric FROG, dispersion scan, time domain…
We present an algorithm for sound analysis and resynthesis with local automatic adaptation of time-frequency resolution. There exists several algorithms allowing to adapt the analysis window depending on its time or frequency location; in…
Windowing a Fourier transform is a useful tool, which gives us the similarity between the signal and time frequency signal, and it allows to get sense when/where ceratin frequencies occur in the input signal, this method is introduced by…
We develop a systematic theory for optimising single-photon frequency conversion using optical Bragg scattering. The efficiency and phase-matching conditions for the desired Bragg scattering conversion as well as spurious scattering and…
The temporal dynamics of ultrashort pulses are a fundamental feature in ultrafast optics. These dynamics can often be extracted from a two-dimensional trace consisting of a set of nonlinear spectra, using an iterative algorithm. Typically,…
We introduce a novel uncertainty principle for generalized graph signals that extends classical time-frequency and graph uncertainty principles into a unified framework. By defining joint vertex-time and spectral-frequency spreads, we…
Tuneable ultrafast laser pulses are a powerful tool for measuring difficult-to-access degrees of freedom in materials science. In general these experiments require the ability to address resonances and excitations both above and below the…
Extensions of the split-step Fourier method (SSFM) for Schr\"odinger-type pulse propagation equations for simulating femto-second pulses in single- and two-mode optical communication fibers are developed and tested for Gaussian pulses. The…
Phase retrieval refers to recovering a signal from its Fourier magnitude. This problem arises naturally in many scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. Unfortunately, phase…
Time-resolved electronic spectra can be obtained as the Fourier transform of a special type of time correlation function known as fidelity amplitude, which, in turn, can be evaluated approximately and efficiently with the dephasing…