Sinc Interpolation Research Articles

Frequency Response Enhancement of Φ-OTDR Using Interval-Sweeping Pulse Equivalent Sampling Based on Compressed Sensing

An interval-sweeping pulse equivalent sampling (ISPES) method based on compressed sensing technique is proposed to enhance the frequency response of phase-sensitive optical time-domain reflectometry (Φ-OTDR). The proposed method achieves an equivalent high-sampling-rate acquisition of Rayleigh backscattered signals along each sensing point of the fiber by the interval-sweeping pulse sampling and compressed sensing reconstruction. Meanwhile, based on the Whittaker-Shannon interpolation formula, the observation matrix corresponding to the interval-sweeping pulse sampling is successfully constructed and proved, which is easy to implement in hardware. In experiments, an ultrasonic signal with a frequency up to 28 kHz at the end of a 4.4-km sensing fiber is accurately identified by using this method, which outperforms other compressed-sensing-based methods. And multi-frequency vibration signals are also accurately detected. Besides, this method performs signal compression while sampling. The number of samples is only 13.3% of the reconstructed data, significantly reducing the amount of data acquisition/transmission/storage. Therefore, the proposed method can effectively enhance the frequency response of Φ-OTDR to sparse-wideband vibration signals without any hardware modification. It also has great advantages in reducing the hardware burden and improving the response speed.

Two-dimensional image zooming by adaptive Sinc-based technique

This article reports a novel adaptive Sinc-based zooming technique. The theoretical basis of the zooming technique is the Whittaker–Shannon interpolation formula and the Nyquist–Shannon sampling theorem. The technique can be used to zoom out, zoom in, and reconstruct two-dimensional images with no zoom. The technique introduces a novel concept called pixel-local-scaled k-space, which is calculated as follows. The k-space magnitude and the bandwidth of the image to zoom are calculated. The bandwidth of the frequency components of the image to zoom is estimated by the difference between the maximum and the minimum numerical value of the k-space magnitude. The ratio between the standardised k-space magnitude of the image and the bandwidth is calculated pixel-by-pixel, and is called pixel-local-scaled k-space. The signal is reconstructed using a finite convolution between image pixel intensities and Sinc functions. The zooming factor is consequential to the numerical difference between the pixel-local-scaled k-space and the sampling rate. The novelty of this zooming technique is to be adaptive because the pixel-local-scaled k-space is a pixel-by-pixel map, that is, an image with the same number of pixels as the departing image. Adaptive Sinc-based zooming is validated through the comparison with non-adaptive Sinc-based zooming, and its smoothing effect is compared to the smoothing of a variety of image space and z-space filters. The adaptive Sinc-based zooming technique achieves image zooming reconstruction using sampling rates within an extended range versus the range allowed by non-adaptive Sinc-based zooming.

On a new higher order kernel for density estimation

Higher order kernels have been widely implemented for nonparametric function estimation, mainly due to their faster asymptotic rates of convergence and interpretability. This article constructs a novel higher order kernel of any pre‐specified even order by using Shannon's formula. The proposed kernels have a closed form expression and are easy to implement. We compare the constructed kernel with several popular higher order kernels in the context of density estimation. Further, we observe that the mean integrated squared error (MISE) of the density estimator corresponding to the proposed kernel is comparable with that of the popular kernels. The constructed kernel performs somewhat better for the Fejér‐de la Vallée Poussin and the ‐symmetric densities. The MISE of the corresponding kernel density estimator and a few related theoretical results are also presented.

Dynamic Synchrophasor Estimation Based on Weighted Real-Valued Sinc Interpolation Method

Phasor measurement units (PMUs) are the cornerstone of intelligent sensing and monitoring of power systems. The superiority of the sinc interpolation function-based least squares (SLS) method, a signal processing algorithm for PMUs, has been proven in harmonic phasor estimation. However, the SLS-based estimators suffer from spectral interferences and heavy computational burden. To this end, a real-valued sinc weighted least squares (SWLS-R) method is proposed to track the dynamic synchrophasor accurately and quickly. First, the weighted vector, i.e., window function, is introduced to enhance the SLS estimator’s behavior by mitigating the impact of spectral interference. Then, the complex-valued system matrix is transformed into the real-valued system matrix to lower the computational burden by avoiding complex matrix multiplication. Finally, an explicit and fast solution is designed to calculate the pseudoinverse matrix of the SWLS-R, which aims to further improve computational efficiency. The accuracy and effectiveness of the proposed method are validated by simulations. These are designed, under steady and dynamic conditions, according to the M-class requirements of the Standard IEC/IEEE 60255-118-1.

Sinc Interpolation for Further Improvement in Frequency Estimation Using Three DFT Samples

This study presents three different sinc estimators and a method to estimate complex-valued exponential tone signal frequency using three DFT samples. The proposed method suggests using sinc interpolation together with the well-known Jacobsen estimator. According to simulation results, the root mean square error (RMSE) of the proposed algorithm is lower than those of the Jacobsen estimator and its improved version suggested by Candan. The price paid for improvements in the RMSE is a slight increase in computation time.

Construction and Analysis of Public Management System Indicators Based on AHP (Analytic Hierarchy Process)

In the era of intelligent network, my country’s public management services are in a transition period, and many problems have gradually occurred, which have a certain impact on public management. In the previous management mode, the latest management requirements could not be met, and there were many problems in the actual management process. With the rapid development of social economy, public management is the key to promote social development. Only by constructing a reasonable index system of public management can public management play its due role in the era of rapid development. Therefore, this paper uses Bohr formula, Shannon formula, and entropy weight method to construct the public management system index based on AHP. The research results of this paper are in the stage of model checking, and the accuracy of this method is the highest in different data sets. The accuracy of big data analysis method and the original method decreases with the increase of data sets, which reflects the obvious advantages of this method. The response time of big data analysis methods increases gradually due to the increase of data sets, but the method in this paper grows slowly. All indicators show that the constructed public management index system has high reliability and validity.

Interpolation Methods with Phase Control for Backprojection of Complex-Valued SAR Data.

Time-domain backprojection algorithms are widely used in state-of-the-art synthetic aperture radar (SAR) imaging systems that are designed for applications where motion error compensation is required. These algorithms include an interpolation procedure, under which an unknown SAR range-compressed data parameter is estimated based on complex-valued SAR data samples and backprojected into a defined image plane. However, the phase of complex-valued SAR parameters estimated based on existing interpolators does not contain correct information about the range distance between the SAR imaging system and the given point of space in a defined image plane, which affects the quality of reconstructed SAR scenes. Thus, a phase-control procedure is required. This paper introduces extensions of existing linear, cubic, and sinc interpolation algorithms to interpolate complex-valued SAR data, where the phase of the interpolated SAR data value is controlled through the assigned a priori known range time that is needed for a signal to reach the given point of the defined image plane and return back. The efficiency of the extended algorithms is tested at the Nyquist rate on simulated and real data at THz frequencies and compared with existing algorithms. In comparison to the widely used nearest-neighbor interpolation algorithm, the proposed extended algorithms are beneficial from the lower computational complexity perspective, which is directly related to the offering of smaller memory requirements for SAR image reconstruction at THz frequencies.

Existence of solution of functional Volterra-Fredholm integral equations in space L∞(ℝ+) and sinc interpolation to find solution

A new measure of noncompactness (Mnc) and Darbo fixed point theorem are utilized on the space L∞(ℝ+) to prove the existence of solution for functional Volterra–Fredholm integral equations. An example is given to confirm the validity of results. Furthermore, we propound an iterative algorithm by sinc interpolation to find the solution with an acceptable accuracy. In this algorithm, it is not necessary for the problem to be discretized to an algebraic system with unknown coefficients. We also use an iterative process to approximate a solution with exponential convergence.

QUANTIFICATION OF INFORMATION AS A BASIS FOR DATABASE CONSTRUCTION (ON THE EXAMPLE OF STANDARDS FOR METAL PRODUCTS)

Determining the amount of information contained in standards is the key issue in the application of digital technologies in the field of practical standardization. Since the practice of developing standards is based on the use of reference standards, the process of updating standards is largely difficult. Digitalization as an activity to present information in the form of numerical data or mathematical models should take into account the specifics of the construction and presentation of the documentation text. Since the structure of standards can contain not only a text part, but also a graphic part, therefore, for their digitalization, it is necessary to use an alphabetical approach using the Shannon formula. Using the alphabetical approach it is possible to calculate the size of the information contained in the standards of various types and categories. In the article, on the example of the GOST 21073.1‒75 standard “Non-ferrous metals. Determination of the grain size by comparison with the scale of microstructures”, the application of the Shannon formula for calculating the amount of information is shown. For calculation the following was taken into account: Russian and Latin letters, digits and numbers, spaces and other characters available in the standard. An analysis was made about the amount of information contained in the current standards of subgroup 77.120.01 “Non-ferrous metals in general” of various periods of their approval. This line of research can be used as basics to adapt the known techniques for building databases and electronic libraries of standards as well as a direction for the digitalization of regulatory and technical documents, taking into account the specifics of presenting information about the requirements regulated in them.

Distributed memory of neural networks and the problem of the intelligence`s essence

The question of the nature of the distributed memory of neural networks is considered. Since the memory capacity of a neural network depends on the presence of feedback in its structure this question requires further study. It is shown that the neural networks without feedbacks can be exhaustively described based on analogy with the algorithms of noiseproof coding. For such networks the use of the term "memory" is not justified at all. Moreover, functioning of such networks obeys the analog of Shannon formula, first obtained in this paper. This formula allows to specify in advance the number of images that a neural network can recognize for a given code distance between them. It is shown that in the case of artificial neural networks with negative feedback it is really justified to talk about a distributed memory network. It is also shown that in this case the boundary between distributed memory of a neural network and information storage mechanisms in such elements as RS-triggers is diffuse. For the given example a specific formula is obtained, which connects the number of possible states of outputs of the network (and, hence, the capacity of its memory) with the number of its elements.

Existence of solution of functional integral equations by measure of noncompactness and sinc interpolation to find solution

Existence of solution of functional integral equations by measure of noncompactness and sinc interpolation to find solution

Content analysis of spiritual intelligence in Persian books

Background and Aim: One of the most important curricula in our country is the Persian curriculum, which is directly part of the subjects of all students from the first grade to the end of high school. The purpose of the current research was to analyze the content of the fourth-grade Persian book with the revelation of spiritual intelligence and to provide information and offer suggestions to the planners to improve and correct this book. Methods: The current research is descriptive in terms of practical purpose, in terms of data collection, and is specifically based on qualitative content analysis. The statistical population of this research consists of the fourth-grade Persian books. Descriptive statistics and entropy coefficient calculations based on Shannon's formula were used to check the data and information. Results: The results of data analysis showed that the highest weight was related to the feeling of giving meaning to life, respect and kindness, creating value, positivity and excellence. Conclusion: The effective components in strengthening spiritual intelligence including giving meaning to life, perception of creative excellence, creative value and strengthening of positive thinking have been obtained. Therefore, spiritual intelligence should be one of the functions that education curriculum planning experts should develop in textbooks.

A fixed point theorem using condensing operators and its applications to Erdelyi--Kober bivariate fractional integral equations

The primary aim of this article is to discuss and prove fixed point results using the operator type condensing map, and to obtain the existence of solution of Erdelyi-Kober bivariate fractional integral equation in a Banach space. An instance is given to explain the results obtained, and we construct an iterative algorithm by sinc interpolation to find an approximate solution of the problem with acceptable accuracy.

Maneuvering Target Coherent Integration and Detection in PRI-Staggered Radar Systems

As for a new-style radar, the random pulse repetition interval (PRI) pulse waveform may be transmitted, and then the target Doppler parameter estimation precision and detection ability by using the conventional techniques may be invalid due to the irregular signal sampling. To solve these problems, this letter proposes a simple, yet effective and quasi-optimal coherent integration method with random pulse resampling. The proposed method first reconstructs the nonuniformly sampled signal into a uniform grid in the range frequency domain based on the modified sinc interpolation theory. Then, a matched filtering function related to the target chirp parameter is constructed in order to eliminate the residual coupling between range and azimuth. Finally, a moving target can be well imaged after performing the target motion compensation.

Signal power and energy-per-bit optimization problems in systems mMTC

Introduction: Currently, the issues of Internet of Things technology are being actively studied. The operation of a large number of various self-powered sensors is within the framework of a massive machine-type communication scenario, using random access methods. Topical issues in this type of communication are how to reduce the transmission signal power and to increase the device lifetime by reducing the consumed energy per bit. Purpose: Formulation and analysis of the problems of minimizing the transmission power and consumed energy per bit in systems with or without retransmissions in order to obtain the achievability bounds. Results: A model of the system is described, within which four problems are formulated and described, concerning the signal power minimization and energy consumption for given parameters (the number of information bits, the spectral efficiency of the system, and the Packet Delivery Ratio). The numerical results of solving these optimization problems are presented. They make it possible to obtain the achievability bounds for the considered characteristics in systems with or without losses. The lower bounds obtained by the Shannon formula are also presented, assuming that the message length is not limited. The obtained results showed that solving the minimization problem with respect to one of the parameters (signal power or consumed energy per bit) does not minimize the second parameter. This difference is most significant for information messages of a small length, which is common in IoT scenarios. Practical relevance: The results obtained allow you to assess the potential for minimizing the transmission signal power and consumed energy per bit in random multiple access systems with massive machine-type communication scenarios. Discussion: The presented problems were solved without taking into account the average delay of message transmission; the introduction of such a limitation should increase the transmitted signal power and consumed energy per bit.

Fast Time-Domain Solution of Dynamic Electromagnetic Problems Based on Sinc Interpolation

In time-domain electromagnetic field problems that have a fast time response with sharp field change or need a long time transient process to get the steady-state solution, a large number of time step iterations are required using the classical time-stepping method. A reduced model based on Sinc interpolation is proposed in this work. The accuracy of the proposed method does not depend on the traditional time-domain discretization step but only the number of sampling points. Two numerical examples, namely an electro-quasistatic (EQS) problem and a field-circuit coupled problem, are considered to illustrate the accuracy and performance of the proposed method. It is shown that only a few pre-computed samplings are sufficient to obtain a good performance while comparing with the traditional time-stepping method.

Measuring complexity in organisms and organizations.

While there is no consensus about the definition of complexity, it is widely accepted that the ability to produce uncertainty is the most prominent characteristic of complex systems. We introduce new metrics that purport to quantify the complexity of living organisms and social organizations based on their levels of uncertainty. We consider three major dimensions regarding complexity: diversity based on the number of system elements and the number of categories of these elements; flexibility which bears upon variations in the elements; and combinability which refers to the patterns of connection between elements. These three dimensions are quantified using Shannon's uncertainty formula, and they can be integrated to provide a tripartite complexity index. We provide a calculation example that illustrates the use of these indices for comparing the complexity of different social systems. These indices distinguish themselves by a theoretical basis grounded on the amount of uncertainty, and the requirement that several aspects of the systems be accounted for to compare their degree of complexity. We expect that these new complexity indices will encourage research programmes aiming to compare the complexity levels of systems belonging to different realms.

Checking the adequacy of the method for generating a random process of disturbance of oscillations of rail carriages according to the impulse response of the forming filter

Usually, to study the vibrations of rail carriages, the equivalent geometric unevenness of the track obtained as a result of processing the records of the track measuring car is taken as a disturbance. Such a record contains a certain set of irregularity wavelengths, for example, 50, 25 and 12.5 m. However, when it is used to simulate disturbances at different operation speeds, these wavelengths will correspond to frequencies depending on the given speed of motion, which is not permissible, since a stable frequency range from 0.2 to 10 Hz is required to excite the vibrations of all the bodies included in the carriage. To eliminate this drawback, in the previously performed works it was proposed to generate a random process of geometric irregularities for a given operation speed by changing the set of wavelengths included in the irregularities. In this paper, based on the study of random oscillations of a simplified model of a rail carriage, as a system with one degree of freedom, the adequacy of the method for generating a random disturbance process is verified in two ways. In the first method, it was found that the characteristics of random oscillations of such a model, obtained in the time domain on the basis of numerical integration of the equation of motion when specifying the generated disturbance, have satisfactory convergence with similar characteristics found by the frequency method using Shannon's formula. In the second verification method, the cross-correlation function and the mutual spectral density between the disturbance and the bouncing oscillations were determined from the generated disturbance realization and obtained by numerical integration of the vibration process realization. Then, using the method of identifying the dynamic system, experimental amplitude and phase frequency characteristics were found, which showed satisfactory convergence with the corresponding calculated characteristics obtained by numerically solving the equation of oscillations of the model under study. On the basis of the results obtained, it was concluded that the considered method of generating a random process of disturbance is sufficiently adequate and that it can be applied to solve problems of the dynamics of rail carriages.

Research of antenna complexes using chiral metamaterials and fractal geometry of radiators for MIMO systems

This article is devoted to the study of the possibilities of increasing spectral efficiency in MIMO systems by using antennas with substrates of biisotropic and bianisotropic chiral metamaterials and various types of fractal emitters, in particular, fractal structures in the form of a Sierpinski triangle, Koch and Gilbert curves, as well as a dipole triangular antenna of complex configuration FRM. The spectral efficiency was calculated by using one of the variations of the Shannon formula, which includes a complete matrix of Z-parameters. In turn, this matrix was determined using the software package of electrodynamic modeling. It is shown that the use of such antennas with the fractal geometry of the emitters located on chiral substrates reduces the mutual influence between the emitters, and, in turn, increases the spectral efficiency in several frequency ranges compared to traditional solutions.

Sinc and B-Spline scaling functions for time-fractional convection-diffusion equations

We study combination of Sinc and B-Spline scaling functions to develop numerical method for the time-fractional convection-diffusion equations. Dou to exponential convergence of Sinc interpolation, the shifted Sinc functions based on double exponential transformation have been used for the spatial discretization, and the B-Spline scaling functions have been used for the temporal discretization. We consider two examples to test the proposed method, and we have compared the presented method to verify the effectiveness of the proposed method in comparison with recent existing methods.