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When employing non-linear methods to characterise complex systems, it is important to determine to what extent they are capturing genuine non-linear phenomena that could not be assessed by simpler spectral methods. Specifically, we are…
Fourier transform spectroscopy based on incoherent light sources is a well-established tool in research fields from molecular spectroscopy and atmospheric monitoring to material science and biophysics. It provides broadband molecular…
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of…
We describe an approach based on compressive-sampling which allows for a considerable reduction in the acquisition time in Fourier-transform spectroscopy. In this approach, an N-point Fourier spectrum is resolved from much less than N…
Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent…
There has been a growing interest in wideband spectrum sensing due to its applications in cognitive radios and electronic surveillance. To overcome the sampling rate bottleneck for wideband spectrum sensing, in this paper, we study the…
A method for spatial deconvolution of spectra is presented. It follows the same fundamental principles as the ``MCS image deconvolution algorithm'' (Magain, Courbin, Sohy, 1998) and uses information contained in the spectrum of a reference…
In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
The object of this work is to design an adequate regularization for the problem of recovering missing Fourier coefficients, particularly in some non standard situations were low frequency coefficients are lost. In the framework of non-local…
Exploring the noise spectrum impacting a qubit and extending its coherence duration are fundamental components of quantum technologies. In this study, we introduce parametric spectroscopy, a method that merges parametric modulation of a…
Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to…
Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to…
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 classical Fourier analysis of a time signal, in the discrete sense, provides the frequency content of signal under the assumption of periodicity. Although the original signal can be exactly recovered using an inverse transform, the time…
The spectral resolution of broadband Fourier-transform coherent anti-Stokes Raman spectroscopy is limited by the maximum optical path length difference that can be scanned within a short time in an interferometer. However, alternatives to…
We present an experimental approach to detect the saturated absorption spectroscopy different from conventional scheme. Using this approach, crossovers are removed to avoid their overlap with other peaks in the spectrum and sensitivity of…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…