Acoustic and ultrasonic propagation results in a Linear Invariant Filter (LIF). Its complex gain is most often described by a ‘frequency power law’. Equivalently, the complex gain is the characteristic function (c.f.) of a ‘stable probability law’. This strong property justifies a modelization by ‘random propagation times’, which together predict the measured attenuations and obey the principle of energy balance. Except for a Gaussian component, propagation through the atmosphere has no connection with ‘frequency power laws’. In this paper, we show that other components are c.f. of probability laws linked to Poisson and exponential random variables (r.v). Consequently, random propagation times are able to explain propagation losses in the atmosphere.

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.

Two parallel Analog-to-Digital Converters (ADC) are the components of 2-Channel TI-ADC (for Time-Interleaved ADC). They are addressed at times nT and is the clock period). ”Timing skews” are biases of these sampling times. They vary slowly, and they have to be estimated and corrected. In this article, we give a method of estimation which utilizes results about Periodic Nonuniform Sampling of order 2.

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.

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.

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.

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.

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.

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).

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.