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We propose a new algorithm based on the Fourier transform with matched non-linear frequency modulation for processing femtosecond laser ranging data. The algorithm allows us to compensate for both the influence of the third-order dispersion in the fiber-based dispersive Fourier spectrometer and the influence of imbalanced second- and third-order dispersions in the interferometer. Computer simulations and experimental results show that the proposed algorithm significantly increases the accuracy of measuring the position of an object at larger displacements than the well-established non-linear time stretching. [ABSTRACT FROM AUTHOR]

In an effort to estimate the number of true nulls in large scale multiplicity problems (the normal means problem), we generalize the current Fourier transform based oracle estimator with a Laplace transform based estimator. Our interest in this problem stems from the application of r-power which requires knowledge of the number of nulls (Dasgupta et al. in Sankhya B 78(1):96–118, 2016). We analytically show that our method is consistent and theoretically has lower mean squared error than the existing competitor (Jin in J R Stat Soc Ser B (Stat Methodol) 70(3):461–493, 2008). We follow up by a numerical example and a simulation study that ratifies our theoretical results. [ABSTRACT FROM AUTHOR]

The conventional approach to phase reconstruction in Reflective Ghost Imaging (RGI) typically involves the introduction of three reference screens into the reference path, deeming the Fourier transform step indispensable. However, this method introduces complexity to the system and raises concerns regarding potential errors in phase retrieval. In response to these challenges, we advocate for adopting the Five-Step Phase-Shifting (FSPS) method in the RGI system. This method presents two key advantages over traditional approaches: (1) It streamlines the phase reconstruction process by eliminating the requirement for a Fourier inverse transform. (2) It avoids the need to insert objects into the reference optical path, simplifying the computation of reference optical path intensity and enabling seamless application to Computational Ghost Imaging (CGI), overcoming the constraints of Dual-Arm Ghost Imaging (DAGI). We substantiate the theoretical proposition through numerical simulations involving two intricate objects. Furthermore, our discussion delves into exploring the influence of varying reflective angles on the phase reconstruction performance. [ABSTRACT FROM AUTHOR]

In this paper, the security strength of a phase-only asymmetric cryptosystem based on interference and phase-truncated Fourier transforms (PTFTs) has been evaluated. Compared to the conventional PTFTs-based scheme where the plaintext is directly encoded into two phase masks (PMs) and the ciphertext, here the plaintext is firstly converted to the phase-only distribution by PTFTs-based encryption process I, and then modulated by the encryption process II with the aid of two masks generated by a carrier image. The security strength of this cryptosystem has been enhanced by an additional secure layer for the output of PTFTs-based structure. Moreover, the four masks generated in the encryption processes I and II are required for the decryption also, it enlarges the key space which further ensures the security strength of the improved cryptosystem. However, we noticed that the carrier image used to generate one of private keys is same as the ciphertext when the input of the encryption is the zero matrix. Thus, the amplitude mask (AM) as the private key could be recovered by the designed chosen-plaintext attack, and then it can be used as the known parameter in the iterative attacks. Employing the recovered mask, two specific attacks with different constraints are designed to break the cryptosystem based on interference and PTFTs successfully. Based on our cryptoanalysis, it is found that most information of the plaintexts were encoded into the AM and the PM in the encryption process I, and silhouette problem would be caused when one of these keys is known. Numerical simulations have been carried out to validate the feasibility and effectiveness of proposed hybrid attacks. [ABSTRACT FROM AUTHOR]

This research focuses on the analysis of the free propagation of Hermite-Gaussian beams diffracted by a symmetrical annular aperture placed at the beam waist plane. The propagation is studied analytically and numerically using the angular spectrum method and the 2D fast Fourier transformation. Numerical simulation examples illustrate the propagation characteristics of the Hermite-Gaussian beams diffracted by an annular aperture. The beam truncation parameters and obscuration ratio influence Hermite-Gaussian beam diffraction properties. [ABSTRACT FROM AUTHOR]

We propose a double image encryption approach based on a hybrid phase-truncation scheme. This approach is realized by spatial and Fresnel encoding, where two plaintexts are encrypted by a random amplitude mask into two private key masks and one ciphertext mask. The random amplitude mask is introduced to break the functional relation of the plaintexts to the ciphertext. Compared with other reported phase-truncation-based techniques, the proposed hybrid scheme is not only free from information leakage but also resistant to several different types of attacks. In addition, the parameters of the Fresnel transform and discrete multiple parameter fractional Fourier transform serve as additional keys to strengthen security significantly. Numerical simulations and a performance analysis are conducted to demonstrate the reliability and validity of the proposed approach. [ABSTRACT FROM AUTHOR]

In this study, the behavior of parabolic, Jacobsen, bias-corrected Jacobsen, and Quinn estimators, which are used in frequency estimation and based on three samples of discrete Fourier transform, are examined on real signals comparatively. As an alternative to these estimators, a sine function-based frequency estimator is proposed, and the root means square errors (RMSE) of the estimator are compared by performing computer simulations. It has been observed that the proposed sine-based estimator gives lower RMS errors in a wide part of the frequency range compared to other estimators. [ABSTRACT FROM AUTHOR]

The paper describes how the calculation of diffuse scattering from atomistic model crystals has developed over the last approximately 50 years. Not only has the quality of observed diffuse X‐ray scattering data improved immensely with the advent of electronic area detectors and synchrotron radiation but the enormous increase in computer power has enabled patterns, of comparable quality to the observations, to be calculated from a Monte Carlo model. [ABSTRACT FROM AUTHOR]

In this study, we propose an edge detection scheme based on Fourier single-pixel imaging, which extracts edges directly from the Fourier spectrum of the target object. The numerical simulations and experimental results show that the edges extracted by the proposed scheme have a better signal-to-noise ratio (SNR) than those extracted by the phase-shift sinusoidal pattern scheme. Furthermore, we investigate the effect of edge extraction in the case of undersampling and propose a plug-and-play edge detection algorithm to enhance the image. Our work combines Fourier single-pixel imaging with edge detection to extract the edges of a target object without imaging, providing a new idea for edge detection techniques. • Long extraction time and poor image quality using phase-shifted sinusoidal scattering schemes. • In the Fourier spectrum, the edge detection operator-object multiplication extracts edges effectively. • Compressive sensing helps to extract edges in extreme cases. • Plug-and-play algorithms can be used to improve image quality in Fourier transform-based imaging work. [ABSTRACT FROM AUTHOR]

The Doppler signature of a man walking in a forested area analysed at L-band is presented here. The aim is twofold: to assess the best time-frequency distribution to characterise the activity; to highlight the similarity of the simulated data to the measured ones to validate the simulation tool. Indeed, the Doppler-Time (DT) signal variation represents the main characteristic of Artificial Neural Networks (ANNs) for classification. The more accurately the DT characterises the activity, the higher the machine's accuracy in classifying it. Besides, in the training data frame, reliable simulated models may supply the amount of data needed by ANN applications. Thus, a short-time Fourier transform (STFT), a reassigned spectrogram (RE-Spect), and a pseudo-Wigner-Ville distribution have been applied to the measured and simulated data. The measurements have been performed using a bistatic radar working at 1 GHz. Then, the measurement setup has been replicated in simulation, and 3-D human bodies walking in free space have been computed using physical optics. The results show that the STFT is the most suitable time-frequency method for recognising and classifying the walk. Moreover, the simulated data are in agreement with the measured data, regardless of the chosen Cohen's technique. [ABSTRACT FROM AUTHOR]

In this paper, an asymmetric cryptosystem with unequal modulus decomposition in the Fourier domain is presented. The input-colour image is decomposed into its red, green, and blue components. Each component is bounded with random phase mask and undergoes Fourier Transform followed by unequal modulus decomposition. One of resulting masks acts as first private key and other one is again Fourier Transformed and undergoes unequal modulus decomposition. Further two masks are obtained, where one acts as second private key and other is phase truncated to obtain encrypted image. Encrypted image is attenuated by a factor and appended with host image to obtain watermarked image. Numerical simulations on MATLAB are performed for authenticating and validating proposed scheme. Statistical, correlation distribution, information entropy and histogram analyses are performed to demonstrate scheme efficacy. The results illustrate that the scheme resists classical cryptographic, special and occlusion attacks. The proposed scheme is also highly sensitive to its private keys and attenuation factor. [ABSTRACT FROM AUTHOR]

This paper proposes a new measurement method based on a single probe scanning to measure the roundness error of the artifact. The presented method simplifies the mathematical processing. There is no need for complex forward and inverse Fourier transforms. The probe is installed on a micro-stage platform, and a voice coil motor drives the micro-stage platform. In this paper, a precise mathematical model of the proposed measurement method is carried out and a detailed introduction process. Computer simulation analysis proves the feasibility and repeatability of the method. The related factors affecting the accuracy of the measurement system are analyzed, and the corresponding suppression methods are proposed. Finally, a comparative experiment verifies that this method dramatically improves the measurement accuracy compared to direct measurement. [ABSTRACT FROM AUTHOR]

This paper aims at introducing the concept of time-dependent polarization tensors (TDPTs) for the wave equation associated to a diametrically small acoustic inclusion, with constitutive parameters different from those of the background and size smaller than the operating wavelength. Firstly, the solution to the Helmholtz equation is considered, and a rigourous systematic derivation of a complete asymptotic expansion of the scattered field due to the presence of the inclusion is presented. Then, by applying the Fourier transform, the corresponding time-domain expansion is readily obtained after truncating the high frequencies. The new concept of TDPTs is shown to be promising for performing imaging. In particular, the optimization approach proposed by Ammari et al. (Ammari, H. Kang, H. Kim, & E. Lee, J.-Y. (2012)The generalized polarization tensors for resolved imaging. Part II: shape and electromagnetic parameters reconstruction of an electromagnetic inclusion from multistatic measurements. Math. Comp. , 81, 839–860.) is extended to TDPTs. Numerical simulations are presented, showing that the TDPTs reconstructed from noisy measurements allow to image fine shape details of the inclusion. [ABSTRACT FROM AUTHOR]

Detection of cyclostationary (CS) signals has been addressed by means of generalized likelihood ratio test criteria. However, an accurate maximum likelihood estimator requires the estimation of cycle period (CP) as a priori information, which has not yet been correctly addressed in the literature. In this correspondence, an estimator of CP is devised under the information theoretic criterion(ITC) framework for long observation regime. In particular, we formulate asymptotic log-likelihood function in discrete frequency domain. From the evidence that direct implementation of ITC leads to a high probability of CP overestimation, we reformulate ITC by Bayesian information criterion (BIC), and derive an accurate penalty function. The proposed BIC variant appears to be consistent as signal-to-noise ratio increases. Numerical simulations corroborate the feasibility of the proposed estimator and show its superiority over state-of-the-art schemes. [ABSTRACT FROM AUTHOR]

We have assembled together our ejecta measurements from explosively shocked tin acquired over a period of about ten years. The tin was cast at 0.99995 purity, and all of the tin targets or samples were shocked to loading pressures of about 27 GPa, allowing meaningful comparisons. The collected data are markedly consistent, and because the total ejected mass scales linearly with the perturbations amplitudes they can be used to estimate how much total Sn mass will be ejected from explosively shocked Sn, at similar loading pressures, based on the surface perturbation parameters of wavelength and amplitude. Most of the data were collected from periodic isosceles shapes that approximate sinusoidal perturbations. Importantly, however, we find that not all periodic perturbations behave similarly. For example, we observed that sawtooth (right triangular) perturbations eject more mass than an isosceles perturbation of similar depth and wavelength, demonstrating that masses ejected from irregular shaped perturbations cannot be normalized to the cross-sectional areas of the perturbations. [ABSTRACT FROM AUTHOR]

The short-time fractional Fourier transform (STFrFT) is beneficial for addressing non-stationary signals in many application settings. However, the STFrFT algorithm fails to obtain a high time–frequency (TF) concentration because of the uncertainty principle. To resolve these problems, we introduce a new algorithm that is referred to as the SSTFrFT, which is a combination of the synchroextracting transform and STFrFT. The main principle of this algorithm is to establish a synchroextracting operator based on the STFrFT and then to extract the TF coefficient of the ridgeline position in the TF distribution to improve the concentration. Using numerical simulations with two examples (linear frequency modulation signal and nonlinear frequency modulation signal), we illustrate how the algorithm can be useful in improving concentration. The instantaneous frequency estimation and energy distribution description are more accurate than traditional methods, such as the short-time Fourier transform, Wigner Ville distribution, synchrosqueezed transform, and STFrFT. Furthermore, we apply the algorithm to identify the frequency curve generated by the target's motion from Ice Multiparameter Imaging X-Band radar echo data from the sea clutter background. The test results of the SSTFrFT method that we developed can accurately distinguish moving targets and sea clutter, which suggest the possible utility of this approach for detection and motion characteristics of marine moving targets. [ABSTRACT FROM AUTHOR]

The Rayleigh–Taylor instability at the weakly nonlinear (WN) stage in spherical geometry is studied by numerical simulation. The mode coupling processes are revealed. The results are consistent with the WN model based on parameter expansion, while higher order effects are found to be non-negligible. For Legendre mode perturbation Pn(cosθ), the nonlinear saturation amplitude (NSA) of the fundamental mode decreases with the mode number n. When n is large, the spherical NSA is lower than the corresponding planar one. However, for large n, the planar NSA can be recovered by applying Fourier transformation to the bubble/spike near the equator and calculating the NSA of the converted trigonometric harmonic. [ABSTRACT FROM AUTHOR]

We present an optical encryption scheme for hyperspectral images using an improved binary tree structure (IBTS) and phase-truncated discrete multiple-parameter fractional Fourier transform (PTdmpFrFT). In the IBTS, the encryption modules based on the phase-truncated fractional Fourier transform represented the branch nodes, while the hyperspectral bands of the plain images were considered as leaf nodes. All pairs of bands were encoded into intermediate data using the IBTS, with subsequent encryption into asymmetric ciphertexts using the PTdmpFrFT. The proposed approach generated different pairs of bands with different secret keys, and encryption and decryption paths. Compared with state-of-the-art optical hyperspectral encryption methods, our approach not only achieved superior encryption security but also reduced the computation and storage requirements of the encrypted data. The original hyperspectral image information could be successfully decrypted only when using all the correct keys. Numerical simulations were performed to verify the performance of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, a double image encryption mechanism for iris template protection using 3D Lorenz chaotic system with modified equal modulus decomposition in the hybrid transform domain is proposed. The hybrid transform is produced by the combination of Walsh transform, Kekre transform and fractional Fourier transform of various orders. Here the fractional orders of the fractional Fourier transform enlarge the key-space of the proposed scheme and improve robustness against brute-force attack. The proposed scheme is asymmetric and non-linear in nature. To validate and authenticate the proposed cryptosystem, the numerical simulations have been performed on grayscale images. Results demonstrate that the proposed cryptosystem has higher robustness against noise and special attacks. [ABSTRACT FROM AUTHOR]

By adding one-step memory to enrich the model of discrete-time quantum walk on the Caylay graph of the dihedral group, the model of quantum walk with memory on the Cayley graph of the dihedral group is constructed. The Fourier Transform is used to analyze the walk, and a formula for probability distribution and time-average probability distribution is given. According to the one-to-one correspondence between quantum walk with memory on a regular graph and quantum walk without memory on the corresponding line digraph, the diagrammatic counterpart of quantum walk with one-step memory on the Cayley graph of the dihedral group is presented. Moreover, basic probabilistic properties of the proposed model are further studied using numerical simulation method. Furthermore, the similarities and differences are discussed in comparison to the memoryless model. [ABSTRACT FROM AUTHOR]

Large net structures used in engineering can easily get into vibration under external excitations; however, the corresponding vibration control strategy still remains challenging. In this paper, a wave boundary control (WBC) strategy is proposed for the vibration suppression of large net structures. The stability of the controlled structures is confirmed by using inverse Fourier transform, transfer function analysis, and numerical simulation. When WBC controllers are set at all boundaries and excitations come from the boundaries, dynamic responses for all the strings of the net structures can quickly reduce to zero without any residual vibration. The effects of different observations, controls, and distributions of sensors on the control laws are discussed. As an application, a method for reducing the number of controllers for large net structures is finally proposed. The research provides theoretical guidance for vibration control of large net structures. [ABSTRACT FROM AUTHOR]

Time-frequency (TF) analysis (TFA) method is an important tool in industrial engineering fields. However, restricted to Heisenberg uncertainty principle or unexpected cross terms, the classical TFA methods often generate blurry TF representation, which heavily hinder its engineering applications. How to generate the concentrated TF representation for a strongly time-varying signal is a challenging task. In this paper, we propose a new TFA method to study the nonstationary features of strongly time-varying signals. The proposed method is based on synchrosqueezing transform and employs an iterative reassignment procedure to concentrate the blurry TF energy in a stepwise manner, meanwhile retaining the signal reconstruction ability. Two implementations of the discrete algorithm are provided, which show that the proposed method has limited computational burden and has potential in real-time application. Moreover, we introduce an effective algorithm to detect the instantaneous frequency trajectory, which can be used to decompose monocomponent modes. Numerical and real-world signals are employed to validate the effectiveness of the proposed method by comparing with some advanced methods. By comparisons, it is shown that the proposed method has the better performance in addressing strongly time-varying signals and noisy signals. [ABSTRACT FROM AUTHOR]

In this paper, we review the main problem concerning the calculation of x-ray scattering of simulated model systems, namely, their finite size. A novel method based on the Rayleigh-Debye-Gans approximation was derived, which allows sidestepping this issue by complementing the missing surroundings of each particle with an average image of the system. The method was designed to operate directly on particle configurations without an intermediate step (e.g., calculation of pair distribution functions): in this way, all information contained in the configurations was preserved. A comparison of the results against those of other known methods showed that the new method combined several favorable properties: an arbitrary q-scale, scattering curves free of truncation artifacts, and good behavior down to the theoretical lower limit of the q-scale. A test of computational efficiency was also performed to establish a relative scale between the speeds of all known methods: the reciprocal lattice approach, the brute force method, the Fourier transform approach, and the newly presented complemented system approach. [ABSTRACT FROM AUTHOR]

It is shown that particles undergoing discrete-time jumps in three dimensions, starting at a distance r0 from the center of an adsorbing sphere of radius R, are captured with probability (R-cσ)/r0 for r0>R, where c is related to the Fourier transform of the scaled jump distribution and σ is the distribution’s root-mean square jump length. For particles starting on the surface of the sphere, the asymptotic survival probability is nonzero (in contrast to the case of Brownian diffusion) and has a universal behavior σ/(R6) depending only upon σ/R. These results have applications to computer simulations of reaction and aggregation. [ABSTRACT FROM AUTHOR]

The structure factor for hard hyperspheres in two to eight dimensions is computed by Fourier transforming the pair correlation function obtained by computer simulation at a variety of densities. The resulting structure factors are compared to the known Percus-Yevick equations for odd dimensions and to the model proposed by Leutheusser [J. Chem. Phys. 84, 1050 (1986)] and Rosenfeld [J. Chem. Phys. 87, 4865 (1987)] in even dimensions. It is found that there is fine agreement among all these approaches at low to moderate densities but that the accuracy of the analytical models breaks down as the freezing transition is approached. The structure factor gives another insight into the decrease in the ordering of the hyperspheres as the dimension is increased. [ABSTRACT FROM AUTHOR]

Transient simulation is indispensable for capturing the periodic disturbance between the rotor and stator for turbomachine applications. In order to avoid resonance risk, the turbomachine systems generally have prime number of components between the rotor and stator, which makes the periodic boundary conditions failed and the transient simulation must be carried out including all the passages. However, prohibitive computing resources and too much time cost are required to obtain detailed accurate simulations for the conventional methods of modeling all the passage. In this paper, 3 numerical approaches, the full passages simulation, the PT(Profile Transform) method with only 1 passage, the FT(fourier transform) method with double-passage, were respectively used to numerically predict the hydraulic performance and loading for the Francis99 turbine based on the k-ω SST turbulent model. The PT method overcame the unequal pitch problem by scaling the flow profile across the blade row interfaces. In the Fourier Transformation method, a phase-shifted boundary condition with Fourier data compression was used to account for the unequal pitch between the blade rows passages, and the solution history of circumferential boundary and rotational boundary was reasonably reconstructed. During the transient numerical simulations, the inlet and outlet boundary were given by the method of Profile Boundary Conditions. The mass flow with the velocity vector direction was prescribed on the inlet section, and the outlet was treated as a static pressure outlet where a static gauge pressure was specified. Compared with the experimental tests, the 3 simulation methods could accurately predict the hydraulic efficiency and the average pressure at different locations, and the static pressure distribution on the mid-span plane and pressure loading on runner blade were comparable. The hydraulic efficiency extracted by FT and PT methods were both higher than the result of the full passages simulation, which was attributed to the fact that the 2 simulation methods only included part of the flow passages and didn’t consider the hydraulic loss of volute, fixed guide vane and draft tube. The temporal variation of blade force and torque generated by the FT method showed in good agreement with the full passages method, expect for small deviation in pulsating amplitude. However, the PT method showed larger discrepancy with the full passages results for both of pulsating frequency and amplitude. In term of spectrum characteristics of pressure fluctuation, the numerical results extracted by the FT method yielded to a very good validation with the full passages and the experimental obtainment. Due to variable scaling or stretching at the Rotor-Stator interface, the passing frequency of the blade was captured in both the static domain and the rotating domain, and the pressure amplitude of PT method was lower than that of the full passages and the experimental. In addition, the time cost ratio among the full passages, the FT method and the PT method was about 1:0.375:0.23. We concluded that the FT method was capable of predicting the hydraulic performance and pressure fluctuation well with less computing resources and was a good alternative compared to the conventional full passage method. [ABSTRACT FROM AUTHOR]

Highlights • The problems of quadratic range migration and Doppler frequency migration for the maneuvering target are addressed. • A method based on TSS-FrFT is proposed to achieve the coherent integration and it has superior detection performance and low computational complexity. • The acceleration matched filter is presented to remove the DFRC caused by the sudden change of targets acceleration. Abstract This paper considers the detection problem of radar maneuvering target with the range migration (RM) and Doppler frequency migration (DFM) and proposes an coherent integration method based on two steps scaling and fractional Fourier transform, i.e., TSS-FrFT. To be specific, this method corrects the quadratic RM (QRM) and DFM based on FrFT and a scaling processing of the rotation angle firstly. Then, it eliminates the coupling between the range frequency variable and FrFT domain (FrFD) variable via a second scaling processing. In the end, the coherent integration is achieved by the inverse Fourier transform (IFT) with respect to the range frequency variable. Compared with the existing methods, the proposed TSS-FrFT method has superior detection performance and low computational complexity. Moreover, considering the sudden change of the target acceleration within the coherent integration interval, this paper also presents an acceleration matched filter (AMF) to remove the Doppler frequency rate change (DFRC) caused by this acceleration change. Computer simulation results are also given to demonstrate the effectiveness of the proposed method from different aspects, i.e., computational complexity, coherent integration for a single target and multiple targets and detection performance for a uniform acceleration and non-uniform accelerations. [ABSTRACT FROM AUTHOR]

We demonstrate using theoretical analysis and full-wave numerical simulations nondiffracting circular Airy beams modulated with different orbital angular momenta (OAM) at millimeter wavelengths. It is shown that applying an azimuthal spiral phase component to the circular Airy beam results in a circular Airy OAM beam. These beams are radially symmetric with a null at the center and experience an inward radial shift within a certain propagation distance. Such propagation dynamics are contrary to that of a conventional OAM beam where the vortex radius increases, and the beam intensity decreases as the beam propagates due to diffraction effects. Thus, the circular Airy OAM beam can be nondiffracting over an appreciable distance of few tens of meters (i.e., few thousand wavelengths) and open the door for high data-rate communications. Phase only spatial wave modulators of aperture 20 cm $\times20$ cm with $40 \times 40$ pixels are designed for generating the circular Airy OAM beams with OAM of order 0, 1, and 2. These spatial wave modulators when illuminated with Gaussian beams generate the corresponding circular Airy OAM beam. Full-wave numerical simulation results showing the generation and propagation of circular Airy OAM beams at millimeter wavelengths that are nondiffracting up to 50 m are presented. [ABSTRACT FROM AUTHOR]

Abstract In this study, the dynamic response of a periodic viaduct to a moving mass is investigated. In view of the periodicity of the viaduct, the mass-viaduct interaction force is expanded into a Fourier series first, each term of which represents one component of the interaction force. By using the Fourier transform method and finite element method (FEM), the frequency domain response of the periodic viaduct to each interaction force component is obtained. The time domain response of the periodic viaduct to the force component can be recovered by applying the inverse Fourier transform to the corresponding frequency domain response. With the mass-viaduct coupling condition and the time domain response of the viaduct to the force component, the Fourier coefficients of the mass-viaduct interaction force are obtained. Superposing the responses of the periodic viaduct due to all the interaction force components yields the response of the periodic viaduct to the moving mass. Numerical results show that the force-weight ratio increases with increasing mass and speed of the mass, suggesting that the inertial effect of the moving mass should be taken into account for the large mass with high speeds. Also, it is found that for the case of the large moving mass with high speeds, the mass-viaduct interaction force may become negative, indicating that the mass has a tendency to separate from the viaduct in this case. Highlights • A model is developed for the dynamic response of a periodic viaduct to a moving mass. • The convergence of the proposed model is confirmed by numerical simulations and some numerical results are presented. • The occurrence of the negative mass-viaduct interaction force is found by numerical simulations. [ABSTRACT FROM AUTHOR]

We reinterpret the shear estimator developed by Zhang & Komatsu within the framework of shapelets and propose the Fourier Power Function Shapelets (FPFS) shear estimator. Four shapelet modes are calculated from the power function of every galaxy's Fourier transform after deconvolving the point-spread function (PSF) in Fourier space. We propose a novel normalization scheme to construct dimensionless ellipticity and its corresponding shear responsivity using these shapelet modes. Shear is measured in a conventional way by averaging the ellipticities and responsivities over a large ensemble of galaxies. With the introduction and tuning of a weighting parameter, noise bias is reduced below one per cent of the shear signal. We also provide an iterative method to reduce selection bias. The FPFS estimator is developed without any assumptions regarding galaxy morphology or any approximations for PSF correction. Moreover, our method does not rely on heavy image manipulations or complicated statistical procedures. We test the FPFS shear estimator using several Subaru Hyper Suprime-Cam (HSC)-like image simulations and the main results are as follows. (i) For simulations that only contain isolated galaxies, the amplitude of the multiplicative bias is below 1 × 10−2. (ii) For more realistic simulations, which also contain blended galaxies, the blended galaxies are deblended by the first-generation HSC deblender before shear measurement. A multiplicative bias of (−5.71 ± 0.31) × 10−2is found. The blending bias is calibrated by image simulations. Finally, we test the consistency and stability of this calibration. [ABSTRACT FROM AUTHOR]

In this paper, the security of a nonlinear optical cryptosystem is evaluated. Compared with traditional cryptosystems based on phase-truncated Fourier transform (PTFT), nonlinear operations are introduced to amplify the error between the estimated and actual ciphertexts during the iterative attack process to improve the security level of the cryptosystem. To figure out the principle of error generation during the iterative process, the error analysis on the classical PTFT-based cryptosystem and the cryptosystem with nonlinear operations is conducted However, from the error analysis, it is found that the amplification effect of error by those nonlinear operations is affected by the initial value of the plaintexts and can be reduced by a normalization operation. Hence, a specific phase-retrieval attack with normalization and a bilateral filter is proposed to break the cryptosystem. The bilateral filter is introduced to improve the convergence rate and quality of the retrieved images. To the best of our knowledge, it is the first time that the cryptosystem based on PTFT and nonlinear operations is cracked successfully. Numerical simulation is carried out to show the feasibility and effectiveness of the proposed attack. [ABSTRACT FROM AUTHOR]

An asymmetric image encryption scheme is proposed using a phase-truncated discrete multiple-parameter fractional Fourier transform (DMPFRFT). After applying a pixel-scrambling operation and random-phase mask, an asymmetric ciphertext with stationary white noise can be obtained using phase truncation in the DMPFRFT domain. Using the phase key, an inverse pixel-scrambling operation, and the parameters of the DMPFRFT, the original image can be successfully retrieved. Numerical simulations were conducted to demonstrate the validity and the security of the proposed method, and electro-optical hybrid setups are suggested for encryption and decryption. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the fractional transient thermal mixed boundary value problem of distributed order. We employ the Cagniard‐de Hoop and the Wiener‐Hopf techniques to solve this problem. The Laplace and Fourier transforms are used to present the formal solution of this problem in terms of some special functions. The numerical simulation of a model example is also given for the heat flow through the foundation of building. [ABSTRACT FROM AUTHOR]

Symbol timing offset (STO) estimation constitutes an important part in orthogonal frequency-division multiplexing (OFDM) signal synchronization, and many blind methods based on the maximum likelihood (ML) principle have been proposed. A theoretical analysis of the estimation performance, however, is very difficult, due in part to the discrete nature of the STO. As a result, most studies on OFDM STO estimation have relied only on computer simulation for performance evaluation. This paper presents a theoretical performance analysis for ML-based blind OFDM STO estimation. We start with a review of the formulation of ML blind STO estimation problem and its solution. We then conduct the said performance analysis. The analysis turns out to involve a study of the eigenvalues of some matrix functions of the autocorrelation of the received signal. As the general case leads to highly complicated mathematics, we treat the case of full-band OFDM in additive white Gaussian noise in more detail. In this case, we are able to obtain mathematically tractable bounds and approximation to the estimation error probability and the corresponding mean-square error. In high signal-to-noise ratio (SNR), these bounds and approximation show inverse power-law dependence on the SNR. We also compare the bounds with simulation results and with an existing approximation in the literature. [ABSTRACT FROM AUTHOR]

In recent years, passive vision-based methods in the weld seam tracking system are becoming more and more popular due to their higher accuracy and robustness to various interferences. In this paper, we present a novel robust weld seam tracking system based on passive vision. A robust discriminative correlation filter is proposed to locate the seam accurately by using weld seam images and background images as positive and negative samples,respectively. Additionally, a new online updating filter strategy is proposed to reduce the effect of varying illumination or changing structure and appearance. The two-scale searching window mode and the fast Fourier transform are combined to increase the speed and precision of the weld seam tracking. The extensive experimental results indicate that the proposed method is simple and fast, and also, its accuracy is high in tracking weld seams. The proposed system has been applied successfully to industrial production lines. [ABSTRACT FROM AUTHOR]

Cavitation is a challenging flow abnormality that leads to undesirable effects on the energy performance of the centrifugal pump and the reliable operation of the pump system. The onset and mechanism of a phenomenon that results in unsteady cavitation must be realised to ensure a reliable operation of pumps under the cavitation state. This study focuses on cavitation instability at normal flow rate, at which point the unsteady cavitation occurs as the available net positive suction head (NPSHa) falls below 5.61 m for the researched pump. An ameliorative algorithm-united algorithm for cavitation vibration analysis is proposed on the basis of short time Fourier transform (STFT) and Wigner-Ville distribution (WVD). The STFT-WVD method is then tested using vibration data measured from the centrifugal pump. The relationship between vibration and suction performance indicates that the inception and development of cavitation can be effectively detected by the distribution and intensity of the united algorithm at the testing points. Intermediate frequency components at approximately 6 kHz fluctuate initially with the development of cavitation. A time-frequency characteristic is found to be conducive to monitoring the cavitation performance of centrifugal pumps. [ABSTRACT FROM AUTHOR]

Finding a balance between observation duration and detection rates is the ultimate goal of the detection of ultrahigh speed targets. However, short observation durations, both across range unit, and Doppler frequency migration, may severely limit the detection performance of ultrahigh speed targets. Although, traditional coherent integration methods can efficiently accumulate signal energy to produce a high signal-to-noise-ratio measurement, they often need to search for unknown motion parameters. This search is time consuming and unacceptable for the real-time detection of ultrahigh speed targets. In this paper, a coherent-like detection method is designed based on the finite-dimension theory of Wigner matrices along with velocity identification. The proposed method can efficiently integrate signal energy without rendering motion parameters. We use the distribution and mean of the eigenvalues of the constructed matrix, i.e., an additive Wigner matrix, to identify velocities and detect ultrahigh speed targets, respectively. Simulation results validate the theoretical derivation, superiority and operability of the proposed method. [ABSTRACT FROM AUTHOR]

We study the possibilities of integral representation for the two-frequency mutual coherence function of the wave field in a randomly inhomogeneous ionosphere. The integral representation was obtained using the Double Weighted Fourier Transform (DWFT) method. We point out that the conditions of validity of the geometrical-optics approximation for frequency coherence are weaker than the same condition for individual samples. Examples of calculation of the frequency coherence functions for waves in the ionospheric plasma with the irregularities described by the Gaussian spectrum and Shkarofsky's model are given. Simulation results show that diffraction effects reduce the width of the frequency coherence function. The capabilities of the methods for spatial processing of the wave field and its two-frequency mutual coherence function, which eliminate these effects through the Fresnel and DWFT inversions, are examined. [ABSTRACT FROM AUTHOR]

Modulation measurement profilometry applies coaxial and coimage plane optical systems to reconstruct the surface shape of the measured object, in which, the direction of the grating projection is the same as that of CCD to capture the images. This technology completes the reconstruction by the extraction of modulation values instead of phase information. It can effectively avoid the shadows, shutoff and calculation of phase unwrapping and accomplish the shape measurement for object with complex surface. However, in the practical application, the measurement precision is usually affected by the nonlinearity of CCD’s photoelectric response. In order to avoid the influence of high-order harmonics on fundamental spectrum, Wavelet Transform is introduced into fringe analysis and modulation extraction. With the merits of local analysis and multi-resolution, this method can obtain higher measurement precision by comparing with the Fourier transform method. Both computer simulation and practical experiment testified the validity of the proposed method. [ABSTRACT FROM AUTHOR]

The conventional impact-echo analysis applies the Fourier transform to the surface response of the target structure due to an impact of a steel ball. Then, the amplitude spectrum is used to determine the frequency of the echo signals. Although the amplitude spectrum may disclose the existence of an interface in the structure, it contains no information about the type of interface. This research group has proposed using the phase spectrum to differentiate reflections from cracks and reinforcing bars. Through numerical and physical tests, it was found that the phase of reflections at an air interface and reflections at steel interface fall within two distinct ranges, - π , π / 4 and π / 4 , π , respectively. This study aims at examining the influence of the impact duration, the inclusion size/depth ratio, the sampling rate, and the sampling duration on the effectiveness of the impact-echo phase method. Numerical simulations and physical tests were conducted considering various combinations of impact sizes, inclusion sizes and depths, sampling rates, and sampling durations. The results suggest that the phase offset is an effective indicator of the inclusion type under the following conditions: (1) the product of the impact duration and depth frequency falls in the range 0.25 , 0.8 ; (2) the length-depth ratio of the crack exceeds 0.33; (3) the radius-depth ratio of the reinforcing bar exceeds 0.4; (4) the sampling rate exceeds 6 times of the depth frequency; (5) the product of sampling duration and depth frequency exceeds 33.3. [ABSTRACT FROM AUTHOR]

We consider the numerical solution of the multivariate aggregation population balance equation on a uniform tensor grid. We introduce a multidimensional fast Fourier transformation for the efficient evaluation of the aggregation integrals leading to a reduction in the complexity order of the algorithm compared to the direct evaluation approach. We illustrate the new evaluation algorithm for two discretizations, an FEM approach as well as the sectional method. We discuss the conservation of moments for these methods and provide numerical comparisons illustrating the superior performance of FFT-based algorithms. We also discuss and numerically illustrate their potential for parallelization. [ABSTRACT FROM AUTHOR]

This paper studies characteristics of deformation failure and fracture growth of fractured coal-rock combination with RFPA2D numerical analysis software. Peak strength of the combination increases with increase of the dip of fracture and the peak strength when dip of fracture is 90° approaches to the peak strength without fracture. Under the same dip of fracture, peak strength of the combination when fracture is in the rock is higher than that in the coal, and fracture in the coal has more significant effect on the strength of the combination than in the rock. If fracture locations in combination are different, the characteristics of fracture growth are different. If dips of fracture in the same location are different, the fracture growth characteristics are different, too. However, fracture growth connection in coal is the main cause of overall failure of the combination body. During the loading, sound emission appears in two ends of fracture and the new fracture in the rock in upper end of the fracture, which mainly is caused by tensile failure. While in the coal, the new fracture in the end of fracture is caused by tensile failure; failures in other part are caused by both tensile failure and shear failure. [ABSTRACT FROM AUTHOR]

The use of active sound profiling (ASP) in the automobile industry has been under investigation for several years, and the applications have taken advantage of such techniques, balancing amplitudes instead of simply minimizing the sound pressure level (SPL). This paper presents a novel adaptive algorithm to profile nonstationary disturbances such as the noise generated by a gasoline engine. The new algorithm provides profiling capabilities for nonstationary disturbances and stability properties of the system, whilst expending minimum control effort. Mainly assisted through the use of a reshaping signal, necessary phase information is extracted from nonstationary disturbance signals. To deal with changes in sound as the operating conditions of the engine change, the short-time Fourier transform (STFT) filtered-x least mean square (FXLMS) scheme is introduced to improve the convergence rate. The stability properties are based on the command FXLMS approach, which prevents instabilities caused by magnitude errors in the estimated plant model. Moreover, modification of the STFT-FXLMS scheme improves stability and performance when phase error does exist. In this paper, the performance of the proposed algorithm is demonstrated through a series of simulations configured with either simulated noises or noises from a real engine. The results revealed the effectiveness of the proposed algorithm in profiling nonstationary harmonic noise, and enhancement of stability and performance due to the modification of the STFT-FXLMS scheme. [ABSTRACT FROM AUTHOR]

With proliferation of power electronics devices in the distribution system, harmonic distortion has become one of the major power quality (PQ) problems. In evolving the liberalized electricity market, it becomes necessary to develop suitable methods to allocate the responsibilities for the harmonic distortion to improve the PQ. This paper presents a new technique for harmonic source identification, which is based on total harmonic power (THP) method using estimation of signal parameters via rotational invariance technique (ESPRIT). Traditionally, harmonic powers for THP method is computed using Fourier transform, which inherits serious drawbacks of the discrete and fast Fourier transform, namely, inaccuracy owing to poor spectral resolution, spectral leakage, and so forth. Simulation results have been presented for different distribution system configurations and conditions, which confirms the improved capabilities of the proposed method in harmonic source identification. [ABSTRACT FROM AUTHOR]

Radiative lifetimes of vibrationally excited H2O+ and D2O+ ions in their ground electronic state (X 2B1) have been determined using the monitor ion technique in a triple cell ion cyclotron resonance spectrometer with Fourier transform detection. The monitor reactions are proton or deuteron transfer from H(D)2O+ to CO2 and N2O. The lifetimes are corrected for collisional deactivation and reactions with the background gases occurring during the relaxation time of the ions. N2O probes all the excited vibrational levels of H2O+ and D2O+. For H2O+ only the bending modes (0,v≥1,0) contribute to the decay curve. The corresponding overall lifetime, 26.8±3 ms, is in very good agreement with the computer simulated overall lifetime including the theoretical lifetimes of Weis et al. [J. Chem. Phys. 91, 2818 (1989)] and estimated populations of the bending vibrational levels. For D2O+, the overall lifetime of the (0,v≥1,0) bending modes, 99.5±15 ms, and the lifetime of the (1,0,0) stretching mode, 27.5±4.5 ms, are observed, also in good agreement with the computer simulated and theoretical values, respectively. For both ions the overall lifetime of the (0,v≥1,0) levels may be considered as a good approximation for the radiative lifetime of the (0,1,0) level. The overall lifetimes determined with CO2 as a monitor may be attributed to the (0,v≥4,0) bending modes: 8.1±1 ms for H2O+ and 44±12 ms for D2O+. In this case, several levels having similar populations and lifetimes contribute to the decay curve, therefore the lifetimes of the individual levels cannot be determined. The agreement with computer simulated lifetimes is an indication for the validity of the theoretical lifetimes. [ABSTRACT FROM AUTHOR]

This paper provides the essential mathematical basis for computational studies of space fractional reaction–diffusion systems, from biological and numerical analysis perspectives. We adopt linear stability analysis to derive conditions on the choice of parameters that lead to biologically meaningful equilibria. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. For the solution of the full reaction–diffusion system modelled by the fractional partial differential equations, we introduced the Fourier transform method to discretize in space and advance the resulting system of ordinary differential equation in time with the fourth-order exponential time differencing scheme. Results of numerical experiments are presented. [ABSTRACT FROM AUTHOR]

‘De-Dopplerisation’ is one aspect of a problem frequently encountered in experimental acoustics: deducing an emitted source signal from received data. It is necessary when source and receiver are in relative motion, and requires interpolation of the measured signal. This introduces error. In acoustics, typical current practice is to employ linear interpolation and reduce error by over-sampling. In other applications, more advanced approaches with better performance have been developed. Associated with this work is a large body of theoretical analysis, much of which is highly specialised. Nonetheless, a simple and compact performance metric is available: the Fourier transform of the ‘kernel’ function underlying the interpolation method. Furthermore, in the acoustics context, it is a more appropriate indicator than other, more abstract, candidates. On this basis, interpolators from three families previously identified as promising — — piecewise-polynomial, windowed-sinc, and B-spline-based — — are compared. The results show that significant improvements over linear interpolation can straightforwardly be obtained. The recommended approach is B-spline-based interpolation, which performs best irrespective of accuracy specification. Its only drawback is a pre-filtering requirement, which represents an additional implementation cost compared to other methods. If this cost is unacceptable, and aliasing errors (on re-sampling) up to approximately 1% can be tolerated, a family of piecewise-cubic interpolators provides the best alternative. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to detect the milling chatter based on Variational Mode Decomposition (VMD) and energy entropy. VMD has already been employed in feature extraction from non-stationary signals. The parameters like number of modes (K) and the quadratic penalty (α) need to be selected empirically when raw signal is decomposed by VMD. Aimed at solving the problem how to select K and α, the automatic selection method of VMD’s based on kurtosis is proposed in this paper. When chatter occurs in the milling process, energy will be absorbed to chatter frequency bands. To detect the chatter frequency bands automatically, the chatter detection method based on energy entropy is presented. The vibration signal containing chatter frequency is simulated and three groups of experiments which represent three cutting conditions are conducted. To verify the effectiveness of method presented by this paper, chatter feather extraction has been successfully employed on simulation signals and experimental signals. The simulation and experimental results show that the proposed method can effectively detect the chatter. [ABSTRACT FROM AUTHOR]

Frequency response function (FRF) identification is often used as a basis for control systems design and as a starting point for subsequent parametric system identification. The aim of this paper is to develop a multiple-input multiple-output (MIMO) local parametric modeling approach for FRF identification of lightly damped mechanical systems with improved speed and accuracy. The proposed method is based on local rational models, which can efficiently handle the lightly-damped resonant dynamics. A key aspect herein is the freedom in the multivariable rational model parametrizations. Several choices for such multivariable rational model parametrizations are proposed and investigated. For systems with many inputs and outputs the required number of model parameters can rapidly increase, adversely affecting the performance of the local modeling approach. Therefore, low-order model structures are investigated. The structure of these low-order parametrizations leads to an undesired directionality in the identification problem. To address this, an iterative local rational modeling algorithm is proposed. As a special case recently developed SISO algorithms are recovered. The proposed approach is successfully demonstrated on simulations and on an active vibration isolation system benchmark, confirming good performance of the method using significantly less parameters compared with alternative approaches. [ABSTRACT FROM AUTHOR]