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Connection between atomic functions and Thue-Morse sequence and more general self-similar sequences is discussed. This connection improves the atomic functions theory and study of properties of Thue-Morse-like sequences and makes advantages in numerical methods, digital signal processing and many other applications of atomic functions and Thue-Morse sequences.

New constructions of 1D and 2D generalized Kravchenko-Kotel’nikov sampling theorems based on atomic function up(t) are proposed and justified. The theorems are rigorously proved for both 2D and 1D cases. A simulation performed to analyze the construction and improvement of new series estimates shows their advantage over the classical Whittaker-Kotel’nikov-Shannon series.

In this study the problem of statistical synthesis of chopper radiometric systems with unstable predetection section of receiver is solved for the first time. A new technique of estimating the fluctuation sensitivity is proposed.

It is a classical fact that the exponential function is a solution of the integral equation . If we slightly modify this equation to source with , it seems that no classical techniques apply to yield solutions. In this article, we consider the parameter . We will show the existence of a solution which takes the values of the Thue–Morse sequence on the odd integers.

Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. In 1D signals, is usual to compute the phase and the magnitude of a signal using the analytic signal (the signal and its Hilbert transform using complex numbers). However, for high dimensional signals the monogenic signal (the signal and its Riesz transform) has been used to obtain the local phase and orientation with good results. The main aim of this work is to present a new way to make the computation of the Hilbert transform using the atomic function. The computation of the Hilbert transform take relevance when the phase computation is required.

The 2D to 3D conversion is currently a hot topic for several applications because of the 3D content lack in a new era of different hardware. The proposed algorithm in 3D reconstruction is based on the wavelets, especially on the wavelet atomic functions (WAF), which are used in the computation of the disparity maps employing multilevel decomposition, and technique of 3D visualization via color anaglyphs synthesis. Novel approach performs better in depth and spatial perception than do existing techniques, both in terms of objective SSIM criterion and based on the more subjective measure of human vision that has been confirmed in numerous simulation results obtained in synthetic images, in synthetic video sequences and in real-life video sequences.

The risk characterization resulting from the introduction of toxic chemicals in a subsurface flow field is presented. The concept of concentration threshold is used to quantify the risk associated with non-carcinogenic chemicals introduced to the population by ingestion of groundwater as the exposure pathway. The risk assessment methodology presented uses the expected mass fraction (EMF) concept with exposure duration to identify the distribution of dosage over different concentrations during the plume migration over the well location. The numerical simulation of the subsurface transport by advection and local diffusion is used to produce the concentration plume that passes different locations of interest. The EMF obtained presents the probability of the expected mass above some concentration threshold found at the location of interest. The risk formulation is defined with the risk reliability (safety) and its complement, the risk exceedance (failure) value. The risk characterization is obtained as a probability for exceeding the human reference dose which is considered uncertain due to the necessary extrapolation between concentration used in toxicological studies and the concentration to which humans could be exposed in nature. The final risk assessment expression is derived in a closed form by coupling the expected mass fraction with the safe human threshold concentration probability density function (pdf) inferred from the toxicological studies. The results indicate the importance of estimating the probability of a concentration mass found at locations of interest together with its exposure duration. The exposure duration was revealed to be an important parameter that needs to be estimated depending on the human concentration threshold selected and the distance from the source. The results in terms of the risk safety and risk failure also indicate the dilution effect on the passing concentration plume in the subsurface as a function of the distance and orientation from the source. Inclusion of uncertainty in the selection of the human concentration threshold shows the important effect on the risk quantification.

Most computer vision applications base their operation on the interest point detection. Therefore accurate interest point detection is essential for them. The detected interest points must be invariant to rotation, zoom, blur, illumination, changes of viewpoints, etc. This paper presents a novel image interest point detector, called Harris Atomic detector, which is based on the conventional Harris detector, but the Gaussian Function used in was replaced by an Atomic Function (AF) to improve the detection accuracy. In order to know which Atomic Function provides better results under different imaging conditions, a performance evaluation was done using several AFs. The main criterion used for the comparison was the invariance, in position and number, among the interest points detected in the first and the subsequent frames of a known image sequence. Evaluation results show that, although in general any atomic function improves the performance of conventional Harris detector, the up(x) AF provides best performance, with an improvement of about 10% on the interest point detection accuracy under rotation, blur, zoom and view point changes.

Continuous Phase Modulation Signal has the advantages of continuous phase, faster decay speed of power spectrum, constant envelope and so on, which is widely used in Communication Systems. The phase smoothing degree is one of main factors that affect the decay speed of CPM signal power spectrum. One method of smoothing CPM signal phase based on Atomic function is proposed. The expressions of frequency modulation function and phase modulation function are given as well as the method of CPM signal modulating by orthogonal method. This paper analyses the time-frequency characteristics and realizes the Process of CPM signal orthogonal modulation by MATLAB. The spectrum characteristics of the signal generated has great improvement compared with MSK signal.

Atomic Functions are widely used in different applications in image processing, pattern recognition, computational physics and also in the digital interpretation of signal measurements. The main contribution of this work is to develop a Quaternionic Atomic Function Wavelet as a new quaternionic image wavelet transform. This filter have a real part and three imaginary parts (i,j,k) of the Quaternion Atomic Function, as a result we can extract more information from the image by the three phases (φ,θ, ϕ) of the quaternion representation. The experimental part shows clearly that the phase information of the image is not afected by illumination changes.