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Small signal stability in electrical systems refers to the ability of the system to maintain stable operation in the face of low-amplitude disturbances, such as fluctuations in electrical demand or the off and on switching of generators. This type of analysis is essential because it provides insight into how the system responds to minor disturbances, such as variations in generation or unplanned load. Significant disturbances can induce unstable conditions with potentially serious consequences, such as widespread power outages. Advanced mathematical techniques address these issues, such as the Fourier transform and the Prony method. In this study, a method was developed using MATLAB, and flow runs were performed in Digsilent software to analyze the oscillations of small signals in a 138 kV substation with low penetration of renewable energy. This research is relevant because it allows us to assess the impact of small disturbances in the electricity system during the transition toward greater integration of renewable technologies. The goal is to improve the efficiency and safety of electrical infrastructure in the Dominican Republic, ensuring a more reliable and stable energy supply for residents and businesses. The analysis shows that the current system can absorb anomalies of small signals due to the low penetration of renewables. In addition, the tool developed allows the evaluation of scenarios with greater penetration of renewable energy, providing a solid basis for implementing preventive or corrective measures.

Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e., a sequence of sampling vectors constructed by the repeated action of an operator. The loss of the phase here turns the well-posed dynamical sampling into a severe ill-posed inverse problem. In the existing literature, the involved operator is usually completely known. In this paper, we combine phase retrieval in dynamical sampling with the identification of the system. For instance, if the dynamical frame is based on a repeated convolution, then we want to recover the unknown convolution kernel in advance. Using Prony’s method, we establish several recovery guarantees for signal and system, whose proofs are constructive and yield algebraic recovery methods. The required assumptions are satisfied by almost all signals, operators, and sampling vectors. Studying the sensitivity of the recovery procedures, we establish error bounds for the approximate Prony method with respect to complex exponential sums. [ABSTRACT FROM AUTHOR]

Complex natural resonances (CNRs) extraction methods such as matrix pencil method (MPM), Cauchy, vector-fitting Cauchy method (VCM), or Prony's method decompose a signal in terms of frequency components and damping factors based on Baum's singularity expansion method (SEM) either in the time or frequency domain. The validation of these CNRs is accomplished through a reconstruction of the signal based on these complex poles and residues and a comparison with the input signal. Here, we perform quantitative performance metrics in order to have an evaluation of each method's hardware suitability factor before selecting a hardware platform using benchmark signals, simulations of backscattering scenarios, and experiments. [ABSTRACT FROM AUTHOR]

In high-speed relay-protection applications, decisions are made based on signal processing over a short observation window. Classical adaptive signal models, which are prone to increasing their order so as to increase their resolution, do not cope with the task of recognition in a short window. The article proposes a new approach to constructing a signal model based on the use of an adaptive filter with a distributed structure. The proposed model is perfected by means of excluding canonical filters of controlled components from the competitive environment that arises in the classical adaptive filter. The filter-tuning scheme with a distributed structure is a multichannel system, in each channel of which a canonical filter is tuned to block of its component; the more accurately each individual canonical filter is tuned, the better the conditions are that are created for tuning the remaining canonical filters and the residual signal filter. The results of the computational experiment confirm the high performance of an adaptive filter with a distributed structure in terms of accuracy and speed when recognizing input signals of relay protection. [ABSTRACT FROM AUTHOR]

Oscillations occurring in the power system are one of the biggest threats to its secure operation. Although they occur rarely, these oscillations can cause severe damage to the power system if they are not detected at the earliest. Hence, this work focuses on identifying the parameters of oscillations in the power system using a combination of Empirical Wavelet Transform and Yoshida-Bertecco algorithm. As these oscillations occur rarely, a preprocessing method based on Teager Kaiser Energy Operator is used to check whether the signal under consideration contains any oscillation modes. The effectiveness of the proposed method is tested using a test signal, simulated power system signal, and PMU data from an actual power system under various levels of noise contamination. Further, the performance of the proposed method is compared with a VMD-Hilbert transform-based, Prony-based, and SSI-based methods in the literature. Results reveal the superiority of the proposed method irrespective of the parameters of the signal under consideration.

Recovery of multivariate exponential polynomials, i.e., the multivariate version of Prony's problem, can be stabilized by using more than the minimally needed multiinteger samples of the function. We present an algorithm that takes into account this extra information and prove a backward error estimate for the algebraic recovery method SMILE. In addition, we give a method to approximate data by an exponential polynomial sequence of a given structure as a step in the direction of multivariate model reduction. [ABSTRACT FROM AUTHOR]

In this paper we establish accuracy bounds of Prony's method (PM) for recovery of sparse measures from incomplete and noisy frequency measurements, or the so-called problem of super-resolution, when the minimal separation between the points in the support of the measure may be much smaller than the Rayleigh limit. In particular, we show that PM is optimal with respect to the previously established min-max bound for the problem, in the setting when the measurement bandwidth is constant, with the minimal separation going to zero. Our main technical contribution is an accurate analysis of the inter-relations between the different errors in each step of PM, resulting in previously unnoticed cancellations. We also prove that PM is numerically stable in finite-precision arithmetic. We believe our analysis will pave the way to providing accurate analysis of known algorithms for the super-resolution problem in full generality. [ABSTRACT FROM AUTHOR]

This note proposes an algorithm for identifying the poles and residues of a meromorphic function from its noisy values on the imaginary axis. The algorithm uses Möbius transform and Prony’s method in the frequency domain. Numerical results are provided to demonstrate the performance of the algorithm. [ABSTRACT FROM AUTHOR]

Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively, they form a framework for fitting trigonometric rational models to data that is robust to various forms of corruption, including additive Gaussian noise, perturbed sampling grids, and missing data. Our approach combines a variant of Prony's method with a modified version of the adaptive Antoulas-Anderson algorithm. Using representations in both frequency and time space, a collection of algorithms is described for adaptively computing with trigonometric rationals. This includes procedures for differentiation, filtering, convolution, and more. A new MATLAB software system based on these algorithms is introduced. Its effectiveness is illustrated with synthetic and practical examples drawn from applications including biomedical monitoring, acoustic denoising, and feature detection. [ABSTRACT FROM AUTHOR]

As technology advances, the utilization of lighting systems based on light-emitting diode (LED) technology is becoming increasingly essential, given its benefits in terms of efficiency, reliability, and lifespan. Unfortunately, the power electronic components required to drive LEDs are unable to compete with LED devices in terms of lifetime. Aluminum electrolytic capacitor (AEC) failures represent the root cause of power electronic equipment breakdown, mainly through both aging and temperature effects. This highlights the importance of designing robust power converter architectures and control methods that allow the evaluation of the condition of electrolytic capacitors while maintaining the performance of converter controllers, even in the presence of capacitor failure. On this basis, this work proposes a novel condition-monitoring system for the diagnosis of capacitor faults on a fault-tolerant LED driver, which is able to deal with the specific architecture and low ratings of the most recent LED lighting systems. The fault-detection task applies the short time least square Prony's (STLSP) approach to perform an online estimation of the ESR and C parameters, allowing the continuous evaluation of the electrolytic capacitor's condition and, as a result, the prevention of total system failure. With regard to capacitor failure, the experimental results suggest that the condition-monitoring task is extremely effective, even when considering a limited number of data samples. [ABSTRACT FROM AUTHOR]

The Unlimited Sensing Framework (USF) is a digital acquisition protocol that allows for sampling and reconstruction of high dynamic range signals. By acquiring modulo samples, the USF circumvents the clipping or saturation problem that is a fundamental bottleneck in conventional analog-to-digital converters (ADCs). In the context of the USF, several works have focused on bandlimited function classes and recently, a hardware validation of the modulo sampling approach has been presented. In a different direction, in this paper we focus on non-bandlimited function classes and consider the well-known super-resolution problem; we study the recovery of sparse signals (Dirac impulses) from low-pass filtered, modulo samples. Taking an end-to-end approach to USF based super-resolution, we present a novel recovery algorithm (US-SR) that leverages a doubly sparse structure of the modulo samples. We derive a sampling criterion for the US-SR method. A hardware experiment with the modulo ADC demonstrates the empirical robustness of our method in a realistic, noisy setting, thus validating its practical utility. [ABSTRACT FROM AUTHOR]

Following the Unlimited Sampling strategy to alleviate the omnipresent dynamic range barrier, we study the problem of recovering a bandlimited signal from point-wise modulo samples, aiming to connect theoretical guarantees with hardware implementation considerations. Our starting point is a class of non-idealities that we observe in prototyping an unlimited sampling based analog-to-digital converter. To address these non-idealities, we provide a new Fourier domain recovery algorithm. Our approach is validated both in theory and via extensive experiments on our prototype analog-to-digital converter, providing the first demonstration of unlimited sampling for data arising from real hardware, both for the current and previous approaches. Advantages of our algorithm include that it is agnostic to the modulo threshold and it can handle arbitrary folding times. We expect that the end-to-end realization studied in this paper will pave the path for exploring the unlimited sampling methodology in a number of real world applications. [ABSTRACT FROM AUTHOR]

This note considers the unstructured sparse recovery problems in a general form. Examples include rational approximation, spectral function estimation, Fourier inversion, Laplace inversion, and sparse deconvolution. The main challenges are the noise in the sample values and the unstructured nature of the sample locations. This note proposes the eigenmatrix, a data-driven construction with desired approximate eigenvalues and eigenvectors. The eigenmatrix offers a new way for these sparse recovery problems. Numerical results are provided to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This paper describes the implementation of a technique to improve the accuracy of spectral evaluation of periodic changes in the brightness of multi-frequency reflections from space objects under conditions of a smooth change in their intensity. A comparative analysis is carried out to determine the relative deviation of the estimate of the rotational speed ΔF by the classical method of the smallest squares of the Proni and weighing observations.

In frequency analysis an often appearing problem is the reconstruction of a signal from given samples. Since the samples are usually noised, pure interpolating approaches are not recommended and appropriate approximation methods are more suitable as they can be interpreted as a kind of denoising. Two approaches are widely used. One uses the reflection coefficients of a finite sequence of Szegő polynomials and the other one the zeros of the so called Prony polynomial. We show that both approaches are closely related. As a kind of inverse problem, it’s not surprising that they have in common that both methods depend very sensitive on sampling errors. We use known properties of the signal to estimate the positions of the zeros of the corresponding Szegő- or Prony-like polynomials and construct adaptive algorithms to calculate these ones. Hereby, we get the corresponding parameters in the exponential parts of the signal, too. Then, the coefficients of the signal (as a linear combination of such exponential functions) can be obtained from a system of linear equations by minimizing the residuals with respect to a suitable norm as a kind of denoising. [ABSTRACT FROM AUTHOR]

Prior Artificial Magnetic Conductor (AMC) designs using Genetic Programming (GP) showed that GP-based designs are competitive and often exceed those based on human expertise. However, the resultant typologies are of wild shapes and beyond intuitive explanation. To gain better physical insight into GP-designed AMCs, we develop equivalent circuit models for them and use Prony's method to reveal their deep physical characteristics. Ansys Q3D Extractor is employed to help determine the RLC component values of the equivalent circuits. The natural resonant frequencies extracted by Prony's method provide further explanation of the bandwidth of the structures. The equivalent circuit models and related natural frequencies of the GP designs can also provide guidance for human experts to reduce the optimization time and improve the performance of the designs. [ABSTRACT FROM AUTHOR]

Accurate grounding parameters calculation ensures the safe and stable operation of the power equipment, and the Green's function calculation of layered soil is the basis of the grounding parameters calculation. The conventional complex image method for Green's function of layered soil mainly include the global equal interval sampling method and the Prony's fitting method, which often have 2 disadvantages: 1. The complex exponential terms of Prony's method are usually twice the number of soil layers, and the amount of calculation increases linearly with the number of soil layers; 2. The global equal interval sampling method cannot guarantee to accurately approximate the integral kernel function, causing the failure to solve Green's function of some complex layered soils. To accurately and efficiently solve the Green's function of arbitrary layered soil, this paper, taking Green's function of horizontally layered soil where the field points and source points are both on the soil surface as an example, summarizes 3 key features of the integral kernel function. Segmented sampling method based on the extreme points of the integral kernel function and the 3-order least squares method are combined to innovatively propose the segmented sampling least squares algorithm (SSLSA) for solving Green's function of layered soil. Only 6 sampling points are required for SSLSA in each sampling segment. The results show that the SSLSA can approximate the integral kernel function more accurately, solve some complicated cases that the conventional complex image method cannot, and has the advantages of good accuracy and efficiency. [ABSTRACT FROM AUTHOR]

Prony's method is a standard tool exploited for solving many imaging and data analysis problems that result in parameter identification in sparse exponential sum sf(k) where the parameters are pairwise different subset [0,1)d, and subset Bbb setminus are nonzero. The focus of our investigation is on a Prony's method variant based on a multivariate matrix pencil approach. The method constructs matrices from the sampling values, and their simultaneous diagonalization yields the parameters The parameters are computed as the solution of an linear least squares problem, where the matrix of the problem is determined by Since the method involves independent generation and manipulation of a certain number of matrices, there is an intrinsic capacity for parallelization of the whole computational process on several levels. Hence, we propose a parallel version of the Prony's method in order to increase its efficiency. The tasks concerning the generation of matrices are divided among the block of threads of the graphics processing unit (GPU) and the central processing unit (CPU),where heavier load is put on the GPU. From the algorithmic point of view, the CPU is dedicated to the more complex tasks of computing the singular value decomposition, the eigen decomposition, and the solution of the least squares problem, while the GPU is performing matrix--matrix multiplications and summations. With careful choice of algorithms solving the sub tasks, the load between CPU and GPU is balanced. Besides the parallelization techniques, we are also concerned with some numerical issues, and we provide detailed numerical analysis of the method in case of noisy input data. Finally,we performed a set of numerical tests which confirm superior efficiency of the parallel algorithm and consistency of the forward error with the results of numerical analysis. [ABSTRACT FROM AUTHOR]

Abstract Background The response of many biomedical systems can be modelled using a linear combination of damped exponential functions. The approximation parameters, based on equally spaced samples, can be obtained using Prony’s method and its variants (e.g. the matrix pencil method). This paper provides a tutorial on the main polynomial Prony and matrix pencil methods and their implementation in MATLAB and analyses how they perform with synthetic and multifocal visual-evoked potential (mfVEP) signals. This paper briefly describes the theoretical basis of four polynomial Prony approximation methods: classic, least squares (LS), total least squares (TLS) and matrix pencil method (MPM). In each of these cases, implementation uses general MATLAB functions. The features of the various options are tested by approximating a set of synthetic mathematical functions and evaluating filtering performance in the Prony domain when applied to mfVEP signals to improve diagnosis of patients with multiple sclerosis (MS). Results The code implemented does not achieve 100%-correct signal approximation and, of the methods tested, LS and MPM perform best. When filtering mfVEP records in the Prony domain, the value of the area under the receiver-operating-characteristic (ROC) curve is 0.7055 compared with 0.6538 obtained with the usual filtering method used for this type of signal (discrete Fourier transform low-pass filter with a cut-off frequency of 35 Hz). Conclusions This paper reviews Prony’s method in relation to signal filtering and approximation, provides the MATLAB code needed to implement the classic, LS, TLS and MPM methods, and tests their performance in biomedical signal filtering and function approximation. It emphasizes the importance of improving the computational methods used to implement the various methods described above.

Summary: The diagnosis of electrical motor for broken rotor bars faults through frequency signatures of the stator current method has been widely explored. In fact, a high‐resolution spectrum analysis based on the multiple signal classification (MUSIC) method has been widely applied to detect induction machine faults for that purpose. Moreover, MUSIC is a powerful tool that extracts significant frequencies from the signal, but cannot give precise amplitude information of the fault indicator frequency. Nevertheless, the MUSIC algorithm takes a long‐time acquisition to find many frequencies. To solve these problems, the short‐time least square Prony's technique is developed. The technique is based on a modified Prony's method for the estimation of amplitudes certain harmonics and frequencies of broken rotor bar fault. The main objective in this context is the reduction in the samples of measurement data with shorter time to allow a clearer view of the fault harmonics components when the motor turns at low load. It allows determining the characteristic frequencies and amplitudes of the lateral bands around the fundamental frequency component with great precision. Additionally, using this proposed method for the magnitude modulation of stator current envelope spectrum is produced and induces current harmonics by the rotor fault at frequency. It is based on tracking the amplitude of harmonics of the stator current envelope. The effectiveness of the proposed method is tested in simulation and a real‐time implementation on experimental validation. [ABSTRACT FROM AUTHOR]

Massive MIMO is widely touted as an enabling technology for 5th generation (5G) mobile communications and beyond. On paper, the large excess of base station (BS) antennas promises unprecedented spectral efficiency gains. Unfortunately, during the initial phase of industrial testing, a practical challenge arose which threatens to undermine the actual deployment of massive MIMO: user mobility-induced channel Doppler. In fact, testing teams reported that in moderate-mobility scenarios, e.g., 30 km/h of user equipment (UE) speed, the performance drops up to 50% compared to the low-mobility scenario, a problem rooted in the acute sensitivity of massive MIMO to this channel Doppler, and not foreseen by many theoretical papers on the subject. In order to deal with this “curse of mobility”, we propose a novel form of channel prediction method, named Prony-based angular-delay domain (PAD) prediction, which is built on exploiting the specific angle-delay-Doppler structure of the multipath. In particular, our method relies on the high angular-delay resolution which arises in the context of 5G. Our theoretical analysis shows that when the number of base station antennas and the bandwidth are large, the prediction error of our PAD algorithm converges to zero for any UE velocity level, provided that only two accurate enough previous channel samples are available. Moreover, when the channel samples are inaccurate, we propose to combine the PAD algorithm with a denoising method for channel estimation phase based on the subspace structure and the long-term statistics of the channel observations. Simulation results show that under a realistic channel model of 3GPP in rich scattering environment, our proposed method is able to overcome this challenge and even approaches the performance of stationary scenarios where the channels do not vary at all. [ABSTRACT FROM AUTHOR]

The initial transient of an organ pipe is known to be of great influence to the perceived sound quality. At the same time, the unsteady process of the tone onset is essentially nonlinear and lacks exact repeatability, so the search for a robust descriptor is in place. Initial transients were recorded using an adjustable flue organ pipe. The blowing pressure and cut-up height were varied. Prony's method was employed to analyze the results. Utilizing the Principal Component Analysis (PCA) on the standardized exponential model coefficients, it was shown that the transients are well described by just one scalar parameter. Its value is predominantly dependent on the number of important Prony's components taking part in the transient process (i.e., the overall complexity of the transient signal). A strong correlation was found between the PCA component and the Strouhal number inverse. [ABSTRACT FROM AUTHOR]

Sampling a signal below the Shannon–Nyquist rate causes aliasing, meaning different frequencies to become indistinguishable. It is also well-known that recovering spectral information from a signal using a parametric method can be ill-posed or ill-conditioned and therefore should be done with caution. We present an exponential analysis method to retrieve high-resolution information from coarse-scale measurements, using uniform downsampling. We exploit rather than avoid aliasing. While we loose the unicity of the solution by the downsampling, it allows to recondition the problem statement and increase the resolution. Our technique can be combined with different existing implementations of multi-exponential analysis (matrix pencil, MUSIC, ESPRIT, APM, generalized overdetermined eigenvalue solver, simultaneous QR factorization, ...) and so is very versatile. It seems to be especially useful in the presence of clusters of frequencies that are difficult to distinguish from one another. [ABSTRACT FROM AUTHOR]

The paper presents a method of adaptation of the original second order Prony’s method for applications in lowcost digital measurement systems with low computing performance. The presented method can be used in measuring systems where it is important to obtain in real time the values of amplitude, frequency, initial phase and damping coefficient of a single sinusoidal component of an analysed signal. The paper presents optimized, in terms of the number of mathematical operations, implementation of the method in selected embedded devices as well as the calculation times of the method for each platform.

Professor C R Rao has made significant contributions in different areas of statistics and in related fields particularly in inference, biometrics, design of experiments, linear models, variance components, econometrics, and most of his contributions are well known to the statistical community. But it may not be known to many statisticians that Professor Rao has worked quite extensively, for about six to seven years, on statistical signal processing and has made some fundamental contributions which has generated significant interest along that direction. He along with his collaborators have worked mainly on three classical signal processing problems, and provided theoretical foundations and efficient estimation procedures. In my opinion, the main contribution of Professor Rao is that he has provided new insights in all these problems, which has helped to bring new way of solving these and some related problems. He has guided two Ph.D. students in the area of Statistical Signal Processing. The main aim of this article is two-fold. First, we would like to introduce to the statistical community the contribution of Professor Rao in this area and our second aim is to provide a class of different related open problems which are of interest and which require sophisticated statistical tools to provide efficient solutions. [ABSTRACT FROM AUTHOR]

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This note deals with transmission lines equation. The frequency dependent parameters which are often considered constants to ease the numerical implementation, are actually taken for their real physical state. We aim to obtain a physical solution of the equation by a high order scheme. The proposed scheme is an enhanced version of FDTD methods known to be powerful tools for solving equations of this alike. In particular, the scheme is built to deal with oscillations of the load voltage. The oscillations that are a result of the taking-over of the hyperbolic characteristic of the equation are corrected by a high order relaxed FDTD method and a regularizing effect of Runge Kutta. We validate our theoretical results by few numerical simulations. [ABSTRACT FROM AUTHOR]

A novel finite-difference time-domain (FDTD) approach is proposed for the analysis of wave propagation in a general frequency-dependent medium. In the proposed method, formulation of the fractional derivatives in the time-domain representation is circumvented by using the fast inverse Laplace transform (FILT) and Prony’s method. The FILT is used to transform the dispersion expressed in a frequency-domain response into a time-domain response, and Prony’s method is utilized to extract the parameters and transform the time-domain responses into those in the z-domain so that they can be incorporated into the FDTD method directly. The update equation of the electric field in the FDTD method is then formulated by using the z-transformation. Stability analysis of the proposed scheme is also investigated by means of the root-locus method. Reflection coefficients of dispersive media, such as Debye, Cole–Cole, Davidson–Cole, and Havriliak–Negami media simulated in a 1-D domain and a three-layered biological medium of skin, fat, and muscle tissues inside a waveguide with a TE10 fundamental mode in a 2-D domain, are found to be in good agreement with those obtained by an analytical method over a broad frequency range, demonstrating the validity of the proposed FDTD scheme. [ABSTRACT FROM AUTHOR]

We show that the sparse polynomial interpolation problem reduces to a discrete super-resolution problem on the n-dimensional torus. Therefore, the semidefinite programming approach initiated by Candès and Fernandez-Granda (Commun. Pure Appl. Math. 67(6) 906–956, 2014) in the univariate case can be applied. We extend their result to the multivariate case, i.e., we show that exact recovery is guaranteed provided that a geometric spacing condition on the supports holds and evaluations are sufficiently many (but not many). It also turns out that the sparse recovery LP-formulation of ℓ1-norm minimization is also guaranteed to provide exact recovery provided that the evaluations are made in a certain manner and even though the restricted isometry property for exact recovery is not satisfied. (A naive sparse recovery LP approach does not offer such a guarantee.) Finally, we also describe the algebraic Prony method for sparse interpolation, which also recovers the exact decomposition but from less point evaluations and with no geometric spacing condition. We provide two sets of numerical experiments, one in which the super-resolution technique and Prony's method seem to cope equally well with noise, and another in which the super-resolution technique seems to cope with noise better than Prony's method, at the cost of an extra computational burden (i.e., a semidefinite optimization). [ABSTRACT FROM AUTHOR]

Nowadays, there are two leading sea sounding technologies: the multibeam echo sounder and the multiphase echo sounder (also known as phase-difference side scan sonar or bathymetric side scan sonar). Both solutions have their advantages and disadvantages, and they can be perceived as complementary to each other. The article reviews the development of interferometric echo sounding array configurations and the various methods applied to determine the direction-of-arrival. “Interferometric echo sounder” is a broad term, applied to various devices that primarily utilize phase difference measurements to estimate the direction-of-arrival. The article focuses on modifications to the interferometric sonar array that have led to the state-of-the-art multiphase echo sounder. The main algorithms for classical and modern interferometric echo sounder direction-of-arrival estimation are also outlined. The accuracy of direction-of-arrival estimation methods is dependent on the configuration of the array and external and internal noise sources. The main sources of errors, which influence the accuracy of the phase difference measurements, are also briefly characterized. The article ends with a review of the current research into improvements in the accuracy of interferometric echo sounding and the application of the principle of interferometric in other devices.

Background: The response of many biomedical systems can be modelled using a linear combination of damped exponential functions. The approximation parameters, based on equally spaced samples, can be obtained using Prony's method and its variants (e.g. the matrix pencil method). This paper provides a tutorial on the main polynomial Prony and matrix pencil methods and their implementation in MATLAB and analyses how they perform with synthetic and multifocal visual-evoked potential (mfVEP) signals. This paper briefly describes the theoretical basis of four polynomial Prony approximation methods: classic, least squares (LS), total least squares (TLS) and matrix pencil method (MPM). In each of these cases, implementation uses general MATLAB functions. The features of the various options are tested by approximating a set of synthetic mathematical functions and evaluating filtering performance in the Prony domain when applied to mfVEP signals to improve diagnosis of patients with multiple sclerosis (MS). Results: The code implemented does not achieve 100%-correct signal approximation and, of the methods tested, LS and MPM perform best. When filtering mfVEP records in the Prony domain, the value of the area under the receiver-operating-characteristic (ROC) curve is 0.7055 compared with 0.6538 obtained with the usual filtering method used for this type of signal (discrete Fourier transform low-pass filter with a cut-off frequency of 35 Hz). Conclusions: This paper reviews Prony's method in relation to signal filtering and approximation, provides the MATLAB code needed to implement the classic, LS, TLS and MPM methods, and tests their performance in biomedical signal filtering and function approximation. It emphasizes the importance of improving the computational methods used to implement the various methods described above. [ABSTRACT FROM AUTHOR]

A novel frequency-dependent finite-difference time-domain (FDTD) method, previously proposed by the author, is applied to numerical dosimetry of exposures by an electromagnetic (EM) pulse incident to biological bodies, which are characterized by four Cole–Cole relaxation terms. The proposed method applies the fast inverse Laplace transform to determine the time-domain impulse responses of the complex permittivity function and utilizes Prony’s method to determine the infinite impulse response representation in the $z$ -domain. The FDTD formulation for the update of the electric field is then directly derived by using the $z$ -transformation. The validity of the method is demonstrated by the 3-D analyses of a homogeneous dielectric sphere and a multilayer sphere illuminated by an EM pulse. It is demonstrated that the numerical results of induced electric field distributions inside the spheres are in good agreement with those derived from Mie’s theory over a broad frequency range, proving the validity of the proposed method. Finally, numerical dosimetry of a heterogeneous human head excited by an EM pulse is performed and specific energy absorption due to the pulse illumination is calculated by using the proposed method. [ABSTRACT FROM AUTHOR]

Aluminum electrolytic capacitors (AECs) are the most common capacitors used in power electronics. They are frequently used for filtering and storage functions because of their small size, large capacitance, and low price. However, AECs also represent the major cause for power electronics equipment breakdown, mainly due to their wear out through the vaporization of the electrolyte, as a result of both aging and temperature effects. The aging of AECs is expressed by the increase of their equivalent series resistance (ESR) and the decrease of their capacitance (C). Therefore, estimating these two parameters can provide a good indicator for a potential capacitor failure. Additionally, these changes in C and ESR parameters strongly influence the ratio between the capacitors voltage ripple and their current ripple. This ratio is dominated by C at low frequencies and by the ESR in the high-frequency range. Hence, this paper suggests a method for online estimating and tracking of both C and ESR using that ratio, which is computed starting from some always existing harmonics at low and high frequencies. The proposed method uses the short time least square Prony's (STLSP) technique to determine and track the amplitudes of the target harmonics. It is shown that compared with the discrete Fourier transform method, the STLSP technique is well suitable for such application, since it has the ability to determine and track the amplitude and frequency of any spectral component, even for noisy and nonstationary signals, using a small number of data samples. This reduces a lot the data storage requirements. Consequently, the proposed method is appropriate for online implementation. The method's effectiveness is proved by simulation and experimental tests using a boost dc–dc converter. [ABSTRACT FROM AUTHOR]

The problem of multivariate exponential analysis or sparse interpolation has received a lot of attention, especially with respect to the number of samples required to solve it unambiguously. In this paper we show how to bring the number of samples down to the absolute minimum of (d + 1)n where d is the dimension of the problem and n is the number of exponential terms. To this end we present a fundamentally different approach for the multivariate problem statement. We combine a one-dimensional exponential analysis method such as ESPRIT, MUSIC, the matrix pencil or any Prony-like method, with some linear systems of equations because the multivariate exponents are inner products and thus linear expressions in the parameters. [ABSTRACT FROM AUTHOR]

There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices. [ABSTRACT FROM AUTHOR]

In this letter, we propose new sub-Nyquist sampling schemes for multiple sinusoids, which require fewer number of samples than previous works. Since it is impossible to resolve the frequency ambiguity using a single sub-Nyquist sample sequence, an additional sampling channel is used to determine the correct frequencies. First, a time-staggered sampling system, with the staggered time less than or equal to the Nyquist sampling interval, is proposed. This approach requires only 3K samples to estimate the K frequency components in the signal. However, aliasing can occur when the differences between some frequencies are integer multiples of the sampling rate. Then, another sampling strategy that makes use of feedback is proposed to prevent aliasing. We demonstrate that using two sampling channels and with feedback, 4K samples suffice to resolve both frequency ambiguity and image frequency aliasing. Simulation results are provided to demonstrate the effectiveness of the proposed systems. [ABSTRACT FROM AUTHOR]

The paper considers a symbolic approach to Prony's method in several variables and its close connection to multivariate polynomial interpolation. Based on the concept of universal interpolation that can be seen as a weak generalization of univariate Chebychev systems, we can give estimates on the minimal number of evaluations needed to solve Prony's problem. [ABSTRACT FROM AUTHOR]

Partial differential equations are central to describing many physical phenomena. In many applications, these phenomena are observed through a sensor network, with the aim of inferring their underlying properties. Leveraging from certain results in sampling and approximation theory, we present a new framework for solving a class of inverse source problems for physical fields governed by linear partial differential equations. Specifically, we demonstrate that the unknown field sources can be recovered from a sequence of, so called, generalized measurements by using multidimensional frequency estimation techniques. Next we show that-for physics-driven fields-this sequence of generalized measurements can be estimated by computing a linear weighted sum of the sensor measurements; whereby the exact weights (of the sums) correspond to those that reproduce multidimensional exponentials, when used to linearly combine translates of a particular prototype function related to the Green's function of our underlying field. Explicit formulas are then derived for the sequence of weights, which map sensor samples to the exact sequence of generalized measurements when the Green's function satisfies the generalized Strang-Fix condition. Otherwise, the same mapping yields a close approximation of the generalized measurements. Based on this new framework, we develop practical, noise robust, sensor network strategies for solving the inverse source problem, and then present numerical simulation results to verify their performance. [ABSTRACT FROM AUTHOR]

We introduce an algorithm which combines ideas of Prony’s approach to recover signals from given samples with approximation methods. We solve two overdetermined systems of linear equations with linear programming methods and calculate the zeros of a suitable ‘Prony-like’ polynomial. We get the bandwidth m , the frequencies as well as the amplitudes and some other characteristics of the signal. Especially, it is reconstructed if sufficient many (at least 2 m ) samples are given. If we have too few samples or if they are too much noised, we get an approximation of the original noiseless signal. Even if we have sufficient many but possible erroneous samples the obtained signal interpolates at least m of them (usually the low-noised or noiseless ones) and, of course, all samples if the signal is recovered. The described method behaves well to moderate sampling errors and is resistant to outliers in the samples which can be detected, filtered off or corrected during the calculations to improve the quality of the computed signal. [ABSTRACT FROM AUTHOR]

Prony's method is a widely used method for modelling signals using a finite sum of exponential terms. It has innumerable applications in weather modelling, finance, medical signal analysis, image compression, time series analysis, power grids, etc. Prony's method has, however, the reputation of being unstable with respect to noise perturbations. The goal of the present paper is to assess the potential improvements of a nuclear-norm-penalized regularization of Prony's method. The nuclear norm regularization is a standard technique for improving the performance when processing noisy signals with low-rank underlying structure such as in matrix completion, matrix compressed sensing, hidden variable models. We consider both the standard setting and the case of missing data. We provide a fast estimation algorithm for the nuclear-norm-penalized least-squares minimization. Monte Carlo experiments show that regularization can significantly enhance the performance of Prony's method with and without missing data. [ABSTRACT FROM AUTHOR]