Problem Of Spectral Analysis Research Articles

Jade Identification Using Ultraviolet Spectroscopy Based on the SpectraViT Model Incorporating CNN and Transformer

Jade is a highly valuable and diverse gemstone, and its spectral characteristics can be used to identify its quality and type. We propose a jade ultraviolet (UV) spectrum recognition model based on deep learning, called SpectraViT, aiming to improve the accuracy and efficiency of jade identification. The algorithm combines residual modules to extract local features and transformers to capture global dependencies of jade’s UV spectrum, and finally classifying jade using fully connected layers. Experiments were conducted on a UV spectrum dataset containing four types of jade (natural diamond, cultivated diamond (CVD/HPHT), and moissanite). The results show that the algorithm can effectively identify different types of jade, achieving an accuracy of 99.24%, surpassing traditional algorithms based on Support Vector Machines (SVM) and Partial Least Squares Discriminant Analysis (PLS_DA), as well as other deep learning methods. This paper also provides a reference solution for other spectral analysis problems.

Direct and Inverse Problems of Spectral Analysis for Arbitrary-Order Differential Operators with Nonintegrable Regular Singularities

Direct and Inverse Problems of Spectral Analysis for Arbitrary-Order Differential Operators with Nonintegrable Regular Singularities

Ratiometric room-temperature phosphorescence platform for visual and spectral analysis of naphthalene

Host-guest doping room-temperature phosphorescence (RTP) materials have showed excellent potential for ultra-sensitive detection due to its bright luminescence in presence of trace guests. However, the inherent signal fluctuation of solid-state sensors restricts their widespread applications. Herein we constructed a simple internal standard method to overcome the signal fluctuation problem in RTP spectral analysis. Ultralong organic RTP can be obtained by using 1,4-dichlorobenzene (DCB) as a host and trace gaseous NL as a guest through the host-guest doping strategy. In this study, a dual-emission ratiometric phosphorescent probe pyrene (Py)/pentachloropyridine (PCP)-DCB was constructed by using the Py/PCP system fabricated via melt-casting as the reference afterglow and using the DCB as the stimuli-responsive unit of gaseous NL. This probe can be used for visual identification and content detection of NL in commercial mothballs. The ratio of phosphorescence intensity (I485/I595) was linearly related to the mass of added NL (mNL) within the range of 0.05–1.45 mg in this ratiometric RTP platform, and had a low detection limit of 0.012 mg. Furthermore, the NL content of five commercially available mothballs with different NL content was detected by this Py/PCP-DCB platform, and it had good performance compared to the gas chromatography (GC) analysis results.

Methods for Calculating the Shape of the Spectral Transmission Window of an Acousto-Optic Filter

The problem of calculation of acousto-optic filter characteristics with control of the number of volumetric diffraction gratings and their structure is taken into consideration. Special-case calculation methods are described including those in collinear geometry. It is demonstrated that there is an approach allowing to perform detailed calculation of spectral characteristics in wide-aperture diffraction geometry used for problems of spectral analysis of object images. It allows to divide the entire luminous flux into separate beams with the partial transmission function of each of them being described by a simple path integral. This method allows for determining the impact of acoustic wave modulation on the filter spectral transmission function.

Algorithm for Calculating Primary Spectral Density Estimates Using FFT and Analysis of its Accuracy

Introduction. Fast algorithms for solving problems of spectral and correlation analysis of random processes began to appear mainly after 1965, when the algorithm of fast Fourier transform (FFT) entered computational practice. With its appearance, a number of computational algorithms for the accelerated solution of some problems of digital signal processing were developed, speed-efficient algorithms for calculating such estimates of probabilistic characteristics of control objects as estimates of convolutions, correlation functions, spectral densities of stationary and some types of non-stationary random processes were built. The purpose of the article is to study a speed-efficient algorithm for calculating the primary estimate of the spectral density of stationary ergodic random processes with zero mean. Most often, the direct Fourier transform method using the FFT algorithm, is used to calculate it. The article continues the research and substantiation of this method in the direction of obtaining better estimates of rounding errors. Results. The research and substantiation of the method in the direction of obtaining more qualitative estimates of rounding errors, taking into account the errors of the input information specification, has been continued. The main characteristics of the given algorithm for calculating the primary estimate of the spectral density are accuracy and computational complexity. The main attention is paid to obtaining error estimates accompanying the process of calculating the primary estimate of the spectral density. The estimates of the rounding error and ineradicable error of the given algorithm for calculating the primary estimate of the spectral density, which appear during the implementation of the algorithm for the classical rounding rule for calculation in floating-point mode with τ digits in the mantissa of the number, taking into account the input error, are obtained. Conclusions. The obtained results make it possible to diagnose the quality of the solution to the problem of calculating the primary estimate of the spectral density of stationary ergodic random processes with a zero mean value by the described method and to choose the parameters of the algorithm that will ensure the required accuracy of the approximate solution of the problem. Keywords: primary estimation of spectral density, fast Fourier transform, discrete Fourier transform, rounding error, input error.

Единственность восстановления оператора Штурма-Лиувилля со спектральным параметром, квадратично входящим в граничное условие

The work is devoted to the study of the inverse problem for the Sturm-Liouville operator with a real square-integrable potential. The boundary conditions are non-separated. One of these boundary conditions includes a quadratic function of the spectral parameter. A uniqueness theorem is proved and an algorithm for solving the inverse problem is constructed. As spectral data, we use the spectrum of the considered boundary value problem, the constant term of the quadratic function of the spectral parameter included in the boundary condition, and some special sequence of signs. From these spectral data, the characteristic function of the boundary value problem is first reconstructed in the form of an infinite product and the parameters of the boundary conditions, and then the problem is reduced to the inverse problem of reconstructing the potential of the Sturm-Liouville operator from the spectra of two boundary value problems with separated boundary conditions. The results of the article can be used for solving various versions of inverse problems of spectral analysis for differential operators, as well as for integrating some nonlinear equations of mathematical physics.

Direct and Inverse Problems of Spectral Analysis for Arbitrary-Order Differential Operators with Nonintegrable Regular Singularities

A short review is presented of results on the spectral theory of arbitrary order ordinary differential operators with non-integrable regular singularities. We establish properties of spectral characteristics, prove theorems on completeness of root functions in the corresponding spaces, prove expansion and equiconvergence theorems, and provide a solution of the inverse spectral problem for this class of operators.

Алгоритм оцінювання частоти комплексного гармонічного сигналу з сегментацією даних спостережень

The article deals with the technology of estimating the frequency of harmonic components in the presence of additive normal interferences for solving applied problems of spectral analysis. Objective: to develop a methodology for the synthesis of algorithms for determining the frequency of a complex harmonic signal in discrete sections of the process, this is observed when using data segmentation. Objective: to develop the optimal technology for determining the frequency of the hormonal component of the process, provided by a finite number of discrete compartments, according to model representations and requirements that meet the problems of the current state of spectral analysis practice. These results were obtained. The problem of estimating the harmonic frequency from segmented data in the presence of additive Gaussian interference in observations based on the method of maximum likelihood is solved. The processing algorithm and the consequences of digital modeling of the synthesized evaluation technology for a given number of discrete process samples are given. The analysis of both the practical capacity of the technology for determining the assessment and certain qualitative indicators of assessment is performed. Conclusions. The scientific novelty of the obtained results is as follows: further development as a method for solving problems of estimating the frequency of the harmonic signal from a few sample values of the process under conditions of additive normal interference and methods for optimizing the structure of digital processing of observations in data segmentation. The synthesized technology uses one sample of observations to determine the estimates, which ensure the efficiency of information processing in a simple software implementation. The use of segmentation in the technological process of digital processing of observations allows obtaining estimates, the quality of which corresponds to the indicators of maximum likelihood. For unambiguous assessment, there is a need to eliminate ambiguity. Under these conditions, the technology with a given number of samples can significantly solve the range of signal-to-noise ratios at which can be obtained unbiased estimates.

Hyperspectral Camera – Attachment for Microscopy

The paper presents a microscope equipped with a hyperspectral ocular nozzle with a phase diffraction grating, which is used as a dispersing element. The spectral range of the device is 400–1000 nm, with the spectral resolution of 5 nm. The paper describes a microscope software that is used to solve problems of spectral analysis.

Vibration Parameters Study of Ship Structures Using Wavelet Analysis of Vibrogram

The study of the vibration parameters of ship structures is important for developing measures to ensure their reliable operation on ships. The commonly used analysis of vibrograms using the Continuous Fourier Transform (CFT) to accurately represent non-stationary functions in general and noise source signals in particular is unsuitable due to a number of drawbacks. The problems of spectral analysis and time-limited signal synthesis can be partially solved by switching to the Window Fourier Transform (WFT). The disadvantage of the WFT is that its calculation uses a fixed window, which cannot be adapted to the local properties of the signal. In order to get rid of this shortcoming for the analysis of vibrogram you can use wavelet transform. It also solves a number of other problems related to the processing of a noise signal. The word “wavelet” means small waves following each other (some sources have introduced the concept of “splash”). In a narrow sense, wavelets are a family of functions obtained by scaling and shifting a single, parent function. In a broad sense, wavelets are functions with frequency localization, whose average value is zero. The article shows the signs of a wavelet. Examples of the most common wavelet functions are given. The use of wavelet functions is proposed not only on the basis of time, but also frequency transformations. The implementation of the algorithm for analyzing vibration measurement data is proposed. An example of vibration measurement data and the results of their processing based on frequency wavelet analysis are given

Vibration Parameters Study of Ship Structures Using Wavelet Analysis of Vibrogram

The study of the vibration parameters of ship structures is important for developing measures to ensure their reliable operation on ships. The commonly used analysis of vibrograms using the Continuous Fourier Transform (CFT) to accurately represent non-stationary functions in general and noise source signals in particular is unsuitable due to a number of drawbacks. The problems of spectral analysis and time-limited signal synthesis can be partially solved by switching to the Window Fourier Transform (WFT). The disadvantage of the WFT is that its calculation uses a fixed window, which cannot be adapted to the local properties of the signal. In order to get rid of this shortcoming for the analysis of vibrogram you can use wavelet transform. It also solves a number of other problems related to the processing of a noise signal. The word “wavelet” means small waves following each other (some sources have introduced the concept of “splash”). In a narrow sense, wavelets are a family of functions obtained by scaling and shifting a single, parent function. In a broad sense, wavelets are functions with frequency localization, whose average value is zero. The article shows the signs of a wavelet. Examples of the most common wavelet functions are given. The use of wavelet functions is proposed not only on the basis of time, but also frequency transformations. The implementation of the algorithm for analyzing vibration measurement data is proposed. An example of vibration measurement data and the results of their processing based on frequency wavelet analysis are given

Quantile spectral analysis of long-memory processes

This study examines the problem of robust spectral analysis of long-memory processes. We investigate the possibility of using Laplace and quantile periodograms for a non-Gaussian distribution structure. The Laplace periodogram, derived by the least absolute deviations in the harmonic regression procedure, demonstrates its superiority in handling heavy-tailed noise and nonlinear distortion. In this study, we discuss an asymptotic distribution of the Laplace periodogram for long-memory processes. We also derive an asymptotic distribution of the quantile periodogram. Through numerical experiments, we demonstrate the robustness of the Laplace periodogram and the usefulness of the quantile periodogram in detecting the hidden frequency for the spectral analysis of the long-memory process under non-Gaussian distribution. Moreover, as an application of robust periodograms under the long-memory process, we discuss the long-memory parameter estimation based on a log periodogram regression approach.

Quantitative Spectral Data Analysis Using Extreme Learning Machines Algorithm Incorporated with PCA

Extreme learning machine (ELM) is a popular randomization-based learning algorithm that provides a fast solution for many regression and classification problems. In this article, we present a method based on ELM for solving the spectral data analysis problem, which essentially is a class of inverse problems. It requires determining the structural parameters of a physical sample from the given spectroscopic curves. We proposed that the unknown target inverse function is approximated by an ELM through adding a linear neuron to correct the localized effect aroused by Gaussian basis functions. Unlike the conventional methods involving intensive numerical computations, under the new conceptual framework, the task of performing spectral data analysis becomes a learning task from data. As spectral data are typical high-dimensional data, the dimensionality reduction technique of principal component analysis (PCA) is applied to reduce the dimension of the dataset to ensure convergence. The proposed conceptual framework is illustrated using a set of simulated Rutherford backscattering spectra. The results have shown the proposed method can achieve prediction inaccuracies of less than 1%, which outperform the predictions from the multi-layer perceptron and numerical-based techniques. The presented method could be implemented as application software for real-time spectral data analysis by integrating it into a spectroscopic data collection system.

On mesh geometries of root Coxeter orbits and mesh algorithms for corank two edge-bipartite signed graphs

Following a Coxeter spectral analysis problems for positive edge-bipartite graphs (signed multigraphs with a separation property) introduced in Simson (2013) [41] and Simson (2013) [42], we study analogous problems for loop-free corank two edge-bipartite graphs Δ=(Δ0,Δ1), i.e., for edge-bipartite graphs Δ, with n+2=|Δ0|≥3 vertices such that its rational symmetric Gram matrix GΔ:=12(GˇΔ+GˇΔtr)∈Mn+2(Q) is positive semi-definite of rank n. We study such connected edge-bipartite signed graphs (bigraphs, for short), up to the strong Gram congruence Δ≈ZΔ′, by means of the non-symmetric Gram matrix GˇΔ∈Mn+2(Z), the Coxeter matrix CoxΔ:=−GˇΔ⋅GˇΔ−tr∈Mn+2(Z), its complex spectrum speccΔ⊆C, and an associated simply laced Dynkin diagram DynΔ∈{An,Dn,E6,E7,E8}, with n≥1 vertices. It is known that if the congruence holds Δ≈ZΔ′ (i.e., there exists B∈Mn+2(Z) such that det⁡B=±1 and GˇΔ′=Btr⋅GˇΔ⋅B) then (speccΔ,DynΔ)=(speccΔ′,DynΔ′).The inverse implication is proved in [Fund. Inform. 152 (2017) 185–222] for all pairs of non-negative corank two bigraphs Δ, Δ′ without loops with n+2≤6 vertices. One of the main aims of the paper is to find algorithms that construct the set Cong(Δ,Δ′) of all Z-invertible matrices B∈Mn+2(Z) defining the congruence Δ≈ZΔ′, for any pair of corank two bigraphs Δ and Δ′ such that (speccΔ,DynΔ)=(speccΔ′,DynΔ′). We do it in case when Δ and Δ′ have at most six vertices in three steps: (i) to any such Δ, we associate algorithmically a ΦΔ-mesh translation quiver ΓΔ•=Γ(RˆΔ,ΦΔ) in Zn+2 (called ΦΔ-mesh geometry of roots of Δ, in the sense of Simson (2013) [42]), where ΦΔ:Zn+2→Zn+2, v↦v⋅CoxΔ, is the Coxeter transformation of Δ; (ii) we define an injective contravariant map h˜•:Cong(Δ,Δ′)→Iso(ΓΔ′•,ΓΔ•), where Iso(ΓΔ′•,ΓΔ•) is the set of all mesh translation quiver isomorphisms h˜B:ΓΔ′•→ΓΔ•, and (iii) a numerical algorithm computing a required matrix B∈Cong(Δ,Δ′) is constructed by means of the shape of the ΦΔ-mesh translation quiver ΓΔ•, its toroidal-tubular structure, and an analysis of admissible isomorphisms h˜B:ΓΔ′•→ΓΔ•.

Spectral analysis and consensus problems for a class of fractal network models

Because of the application of fractal networks and their spectral properties in various fields of science and engineering, they have become a hot topic in network science. In this paper, a class of fractal network models Gm(t) based on the fractal cactus model is studied whose structure is controlled by the positive integer coefficient m and the number of iterations t. After analyzing the structure and construction of network model Gm(t), the iterative relation of spectrum of Laplacian matrix corresponding to the network is obtained by using the decimation procedure. Then, due to the important role of consensus problems in network and system science, we use the spectrum of Laplacian matrix to analysis the convergence speed, delay robustness and noise robustness of the system built according to the network model Gm(t). Since the spectrum of the Laplacian matrix of the network model Gm(t) is completely determined by the number of iterations t and the coefficient m, and the convergence speed, delay robustness and noise robustness of the system are determined by the second smallest eigenvalue, the largest eigenvalue and all non-zero eigenvalues, respectively, we can finally obtain the analytical expressions and approximate expressions between the variables t, m and the above three characteristic quantity. The above results not only help to analyze the topology and dynamic properties of the network model, but also can accurately regulate the performance of the system, so it has potential application prospects.

Numerical solution and stability of the inverse spectral problem for a convolution integro-differential operator

In recent years, there has been growing interest in nonlinear inverse problems of spectral analysis for integro-differential operators. However, in spite of permanently increasing number of works, there are still no numerical results in this direction. The first aim of this paper is to fill this gap by developing an effective numerical approach to this class of inverse problems. The second aim is to prove the stability theorem, which theoretically justifies our numerical method. As a model situation, we consider one important and illustrative class of integro-differential operators, while the presented method can be extended to more complicated inverse problems. Our approach is based on reducing an inverse problem to some nonlinear integral equation and involves approximation of its solution by entire functions of exponential type. Concrete results of the numerical simulation are provided and discussed.

Coherent Integration Method Based on Radon-NUFFT for Moving Target Detection Using Frequency Agile Radar.

This paper considers the coherent integration problem for moving target detection using frequency agile (FA) radar, involving range cell migration (RCM) and the nonuniform phase fluctuations among different pulses caused by range-agile frequency (R-AF) coupling and velocity-time-agile frequency (V-T-AF) coupling. After the analysis of the term corresponding to the phase fluctuation caused by V-T-AF coupling, the term can be regarded as related to an equivalent non-uniform slow time, and nonuniform fast Fourier transform (NUFFT) could be the solution. So a fast coherent integration method combining Radon Fourier transform (RFT) and NUFFT based on low-rank approximation, i.e., Radon-NUFFT, is proposed. In this method, the RCM is solved by Radon algorithm via target trajectory searching, the non-uniform phase fluctuation caused by R-AF coupling is compensated by constructing a compensation item corresponding to the range and agile frequency. In addition, the compensation of the non-uniform phase fluctuation caused by V-T-AF coupling is converted into a problem of spectral analysis of non-uniform sampling complex-valued signal, which is solved by the NUFFT based on low rank approximation. Compared with the existing methods, the proposed method can realize the coherent integration for FA radar accurately and quickly. The effectiveness of the proposed method is verified by simulation experiments.

Frequency analysis of light field sampling for texture information.

Light field sampling (LFS) theory can properly reduce minimum sampling rate while ensuring that novel views are not distorted for image-based rendering (IBR). The minimum sampling rate is determined by spectral support of light field. The spectral support of light field has studied the influence of the following factors: the minimum depth and the maximum depth, non-Lambertian reflections, whether the scene surfaces are flat, maximum frequency of painted signals. In this paper, we further perfect the light field spectrum analysis from the quantitative description of scene texture information based on the existing spectrum analysis theory. The quantification of texture information can be interactively refined via detected regional entropy. Thus, we can derive a spectral analytical function of light field with respect to texture information. The new function allows the spectral support of light field to be analyzed and estimated for different texture information associated with scene objects. In this way, we limit the spectral analysis problems of light field to those of a simpler signal. We show that this spectral analysis approach can be easily extended to arbitrary scene complexity levels, as we simplify the LFS of complex scenes to a plane. Additionally, the spectral support of light field broadens as the plane texture information becomes more complex. We present experimental results to demonstrate the performance of LFS with texture information, verify our theoretical analysis, and extend our conclusions on the optimal minimum sampling rate.

Feasibility study for applying the lower-order derivative fast Pad\xe9 transform to measured time signals

Magnetic resonance spectroscopy (MRS), as a powerful and versatile diagnostic modality in physics, chemistry, medicine and other basic and applied sciences, depends critically upon reliable signal processing. It provides time signals by encoding, but cannot quantify on its own. Mathematical methods do so. The signal processor of choice for MRS is the fast Padé transform (FPT). The spectrum in the FPT is the unique polynomial quotient for the given Maclaurin expansion. The parametric FPT (parameter estimator) performs quantification of time signals encoded with MRS by explicitly solving the spectral analysis problem. Thus far, the non-parametric FPT (shape estimator) could not quantify. However, the non-parametric derivative fast Padé transform (dFPT) can quantify despite performing shape estimation alone. The dFPT was successfully benchmarked on synthesized MRS time signals for derivative orders ranging from 1 to 50. It simultaneously improved resolution (by splitting apart tightly overlapped peaks) and enhanced signal-to-noise ratio (by suppressing the background baseline). The same advantageous features of improving both resolution and signal-to-noise ratio are presently found to be upheld with encoded MRS time signals. Moreover, it is demonstrated that the dFPT hugely outperforms the derivative fast Fourier transform even for derivatives of orders as low as four. The clinical implications are discussed.

On the numerical solution of an inverse spectral problem with a singular potential

This paper deals with the unique solvability of the inverse problem for second-order differential operators having a singular potential. It is shown that the coefficients of the differential operator can be determined from the spectral data. Then, we construct the theoretical bases and provide a numerical algorithm for solving the inverse problem of spectral analysis and finding the potential function. Finally, some numerical examples are considered to demonstrate the applicability of the algorithm.