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###### Journal Paper

## Foldings of Periodic Nonuniform Samplings

**IEEE Transactions on Circuits and Systems II, vol. 69, issue 3, pp. 1862-1868, March 2022.**

Periodic Nonuniform Samplings of order N (PNSN) are interleavings of periodic samplings. For a base period T, simple algorithms can be used to reconstruct functions of spectrum included in an union of N intervals δk of length 1/T. In this paper we study the behavior of these algorithms when applied to any function. We prove that they result in N (or less) foldings on , each of δk holding at most one folding.

Signal and image processing / Other

## Random Propagation Times for Ultrasonics through Polethylene

**Ultrasonics, vol. 111, pp. 130-134, March 2021.**

Low power ultrasonics are used for testing high density polyethylene pipe material. Attenuation and velocity give valuable information on the material in situ and without damages. In this paper we revisit recent data in the frequency band (4,10) megahertz. We prove that propagation is equivalent to random delays following stable probability laws. Moreover, the emergence of a companion noise non-detectable by devices is compliant with the law of conservation of energy.

Signal and image processing / Other

## New CO² Concentration Predictions and Spectral Estimation Applied to the Vostok Ice Core

**IEEE Transactions on Geoscience and Remote Sensing, vol. 56, issue 1, pp. 145-151, January, 2018.**

The Vostok ice core provides measurements of the CO 2 concentration during the last 414 × 10 3 years (yr). Estimations of power spectra show peaks, with the strongest one corresponding to a time period of around 100 × 10 3 yr. In this paper, a new reconstruction method from irregular sampling is used, allowing more accurate estimation of spectral peaks. This method intrinsically decomposes the analyzed signal as a sum of sines, providing amplitudes but also phase measurements of periodic tendencies (due to the nature of the studied phenomena). This decomposition can be conducted with noisy and inaccurate measurements of the sampling instants and the concentrations. The widely used Vostok data were chosen as an example, but the method could also be applied to data from other places (e.g., dome C, Antarctica) or to study other phenomena as nitrogen dioxide NO 2 , methane CH 4 , oxygen isotope 18 O (closely linked to temperature), deuterium 2 H, or dust concentrations.

Signal and image processing / Other

## New Indices of Coherence for One and Two-Dimensional Fields

**ArXiv Optics, 1603.02420, September, 2016.**

The modern deﬁnition of optical coherence highlights a frequency dependent function based on a matrix of spectra and cross-spectra. Due to general properties of matrices, such a function is invariant in changes of basis. In this article, we attempttomeasuretheproximityoftwostationaryﬁeldsbya real and positive number between 0 and 1. The extremal values will correspond to uncorrelation and linear dependence, similartoacorrelationcoefﬁcientwhichmeasureslinearlinks between two random variables. We show that these ”indices of coherence” are generally not symmetric, and not unique. We study and we illustrate this problem together for onedimensional and two-dimensional ﬁelds in the framework of stationary processes.

Signal and image processing / Other

## Splitting up an Optical Beam in a Polarized Component Added to an Unpolarized Component

**Journal of Modern Optics, vol. 63, n°15, pp. 1525-1528, March, 2016.**

The decomposition of an optical beam in a polarized part added to an unpolarized part was studied by G.G. Stokes among numerous other works. Today, the problem is no longer a trigonometric manipulation proper to monochromatic waves, but a problem handling stationary processes with band spectra. In literature, the question seems to be: given some spectral properties and some propagation medium, can we obtain a decomposition? Furthermore, in the case of a positive answer, we have to provide devices for exhibiting solutions. In a linear framework, the problem always has a solution (and even an infinity) whatever the chosen polarization direction. In this paper, we study the links which appear most often between the members of the decomposition.

Signal and image processing / Other

## Behavior of ultrasounds crossing perfluorocarbon liquids and random propagation times

**Ultrasonics, vol. 63, pp. 130-134, December, 2015.**

Random propagation times are able to model waves attenuation and velocity. It is true for electromagnetic waves (light, radar, guided propagation) and also for acoustics and ultrasounds (acoustics for high frequencies). About the latter, it can be shown that stable probability laws are well-fitted for frequencies up to dozens of megahertz in numerous cases. Nowadays, medical applications are performed using propagation through perfluorocarbon (PFC). Experiments were done to measure attenuations and phase changes. Using these results, this paper addresses the question to know if stable probability laws can be used to characterize the propagation of ultrasounds through PFC liquids.

Signal and image processing / Other

## The Stokes decomposition theorem for three-dimensional stationary fields

**Optics Communications, vol. 355, pp. 64–73, November, 2015.**

Paraxial approximation defines the electric field of an optical beam at each point as a two-dimensional vector orthogonal to the direction of propagation. The Stokes decomposition theorem asserts that “any light beam is equivalent to the sum of two lights, one of which is polarized and the other unpolarized”. In a modern framework of random stationary processes, the theorem needs more accurate statements. In this paper, we study three-dimensional fields, and we prove that the decomposition problem has at most two solutions (except for an undetermined argument) which are characterized by well determined circuits of LIF (Linear Invariant Filters).

Signal and image processing / Other

## Stable Probability Laws Modeling Random Propagation Times of Waves Crossing Different Media

**ArXiv physics. ins-det, pp. 1411-5249, November, 2014.**

In a communication scheme, there exist points at the transmitter and at the receiver where the wave is reduced to a ﬁnite set of functions of time which describe amplitudes and phases. For instance, the information is summarized in electrical cables which preceed or follow antennas. In many cases, a random propagation time is sufﬁcient to explain changes induced by the medium. In this paper we study models based on stable probability laws which explain power spectra due to propagation of different kinds of waves in different media, for instance, acoustics in quiet or turbulent atmosphere, ultrasonics in liquids or tissues, or electromagnetic waves in free space or in cables. Physical examples show that a sub-class of probability laws appears in accordance with the causality property of linear ﬁlters.

Signal and image processing / Other

## Errors due to Demodulation in Measurements of Laser Beam Envelope and Phase

**Optics Communications, vol 322, pp 82–89, July, 2014.**

The propagation of a laser beam through the atmosphere leads to spectral widening, which has a detrimental effect on information transmission. In literature the study of laser beam envelope and phase was achieved through demodulation. In this paper we explain that amplitude demodulation in the baseband leads to changes in analytic signals. We give a formula which allows this drawback to be overcome, achieving two demodulations with same frequency and different phases. Examples are given in the Gaussian framework and in the case of random propagation times.

Signal and image processing / Other

## Characteristics of the DC/AC Ratio of Radar Backscatter from Trees

**IEEE Transactions on Aerospace and Electronic Systems, vol. 50, Issue 1, pp. 364-370, January, 2014. **

In the analysis of fluctuating clutter in radar systems, the dc/ac ratio, defined as the ratio of power contained in the dc component at zero Doppler to the power contained in the clutter spectrum, is an important parameter which impacts the detection of slowly-moving targets. Thus, proper characterization of the dc/ac ratio is important for a meaningful assessment of system performance. We explain why the dc component can be hidden due to shortness of the data set or due to apodization. We show that a random propagation time can explain any form of dc/ac ratio and many shapes of the broadband Doppler spectra. Examples are based on a paper by Narayanan et al. about backscatter from trees of a radar at 8 GHz.

Signal and image processing / Other

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