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A model of Synthetic Aperture Radar (SAR) signal and Single Look Complex (SLC) image obtained by satellite Synthetic Aperture Radar (SAR) system are considered. Geometry and kinematics of SAR scenario, including a SAR satellite and a complicated surface are described. SAR signal model based on linear frequency modulated emitted waveform is derived. Standard Fourier transformation is applied to extract an SLC SAR image of high quality. To verify the SAR signal model and image extraction procedure a numerical experiment is carried out. [ABSTRACT FROM AUTHOR]

Abstract: We present a simulation method for the dynamics of dislocation arrays. In this numerical method, dislocation arrays are considered as continuous surfaces in three dimensions, and the level set representation is used for these dislocation array surfaces. The level set representation of the surfaces has the advantage of automatically handling the topological changes occurring during the evolution, and simple implementation using standard accurate finite difference schemes on a uniform grid. The driving force of the evolution of the dislocation array surfaces comes from both the long-range interaction of the constituent dislocations and their local curvature effect. The long-range interaction, which is expressed by a complicated integral over the whole dislocation array surface, is calculated efficiently using the fast Fourier transform (FFT) method. Simulations are performed for dislocation arrays bypassing different particles under applied stress and are compared with those of a single dislocation. The long-range nature of the stress fields of nonplanar infinite dislocation arrays is discussed, and is shown to be essentially different from that by a single dislocation. Examples also show that such long-range stress fields may contribute to the formation of inhomogeneities of dislocation distributions. [Copyright &y& Elsevier]

Abstract: We present an optical encryption method based on the Baker mapping in one-dimensional fractional Fourier transform (1D FrFT) domains. A thin cylinder lens is controlled by computer for implementing 1D FrFT at horizontal direction or vertical direction. The Baker mapping is introduced to scramble the amplitude distribution of complex function. The amplitude and phase of the output of encryption system are regarded as encrypted image and key. Numerical simulation has been performed for testing the validity of this encryption scheme. [Copyright &y& Elsevier]

In this paper, a peak-to-average-ratio (PAPR) reduction scheme based on a weighted orthogonal frequency-division multiplexing (OFDM) signal is proposed to reduce the PAPR without distortion in removing the weight at the receiver side. In the proposed scheme, a weight is imposed on each discrete OFDM signal via a certain kind of a bandlimited signal, and an OFDM signal formed with the weighted discrete data is then considered before a high power amplifier (HPA), whereas the original signal can be recovered completely at the receiver side. Meanwhile, the time duration needed to transmit the weighted OFDM signal is the same as the time duration for the original OFDM signal. The effectiveness of the proposed scheme is evaluated with computer simulations. According to numerical results, the PAPR of the weighted OFDM signal is smaller than that of the clipping and filtering (C&F) method, and the bit-error-rate (BER) performance of the weighted OFDM system is improved compared with the C&F method. Here, the proposed method is simpler than the C&F method. [ABSTRACT FROM PUBLISHER]

Engineers and educators find in computer simulations a powerful substitute for inability of calculus to produce closed form solutions to modern problems. But the validity of quasi-closed-form solutions produced by computers remains suspect. While no magic test exists, pieces of algorithms can individually be examined by the Z-transform [E. I. Jury, Sampled-data control systems, John Wiley & Sons, 1958]. Two examples from engineering and three from education are presented. © 2010 Wiley Periodicals, Inc. Comput Appl Eng Educ 21: 75-88, 2013 [ABSTRACT FROM AUTHOR]

Abstract: The ENUF method, i.e., Ewald summation based on the non-uniform FFT technique (NFFT), is implemented in dissipative particle dynamics (DPD) simulation scheme to fast and accurately calculate the electrostatic interactions at mesoscopic level. In a simple model electrolyte system, the suitable ENUF–DPD parameters, including the convergence parameter α, the NFFT approximation parameter p, and the cut-offs for real and reciprocal space contributions, are carefully determined. With these optimized parameters, the ENUF–DPD method shows excellent efficiency and scales as . The ENUF–DPD method is further validated by investigating the effects of charge fraction of polyelectrolyte, ionic strength and counterion valency of added salts on polyelectrolyte conformations. The simulations in this paper, together with a separately published work of dendrimer–membrane complexes, show that the ENUF–DPD method is very robust and can be used to study charged complex systems at mesoscopic level. [Copyright &y& Elsevier]

By using Fractional Fourier Transform (FRFT) for detecting multicomponent linear frequency-modulated (LFM) signals, weak signal components are usually shadowed by the sidelobes of strong ones and cannot be detected effectively. The CLEAN technique is widely used to improve such a situation via subtracting the detected strong signal component from the multicomponent signals iteratively and applying detection algorithm to the remainder signals. Thus the adverse effect of strong components can be eliminated and weak signal components may be detected. However, since only the strongest LFM component is detected and subtracted in each iteration, the number of detection iteration will be directly proportional to the number of LFM components. Using concept of shading coefficient, a novel threshold setting method for rapid detection of multicomponent LFM signals has been proposed by analyzing the shading relation among the fourth-order origin moment of fractional spectrum (OMFrS) of different LFM components. By employing the proposed method, several LFM components whose fourth-order OMFrS at their own optimal rotation angles are not shadowed by strong components can be detected at the same time in one iteration. Consequently, the number of detection iteration and the computational complexity are reduced dramatically. Simulation results are given to verify that this new approach is valid. [ABSTRACT FROM AUTHOR]

superbox-10 is the successor of superbox, a particle-mesh code where additional grids and sub-grids are applied to regions of high particle density. Previous limitations have been solved. For instance, the vertical resolution is improved considerably when flattened grids are used. Since the computationally most intensive part is the Fast Fourier Transform, we introduce a parallelized version using the library fftw, resulting in a speed-up of a few. The new features are tested using a galaxy model consisting of an exponential disc, a bulge and a dark matter halo. We demonstrate that the use of flattened grids efficiently reduces numerical heating. We simulate the merging of disc–bulge–halo galaxies with small spherical satellites. As a result, satellites on orbits with both low eccentricity and inclination heat the disc most efficiently. Moreover, we find that most of the satellite's energy and angular momentum is transferred to the halo. [ABSTRACT FROM PUBLISHER]

Abstract: To enhance the security of double random phase encoding, a kind of amplitude scrambling operation is designed and introduced into an image encryption process. The random data of the second phase mask in double random phase encoding is also employed for scrambling amplitude distribution in order to save the space of storage and transmission of the key information. The scrambling operator is changeable for generating the key. Some numerical simulations have been provided for testing the validity of the image encryption scheme. [Copyright &y& Elsevier]

In previous experimental observations, Hyun and Wilhelm [Macromolecules 42, 411-422 (2009)] proposed a nonlinear coefficient Q (≡ I3/1/γ02) that was determined from Fourier transform rheology experiments under dynamic oscillatory shear flow. Additionally an intrinsic zero-strain nonlinearity, Q0 (≡ limγ0→0Q), was defined. It was found that this nonlinear coefficient Q(ω,γ0), also given as Q0(ω), is a very promising parameter to quantify nonlinear mechanical properties that are highly affected by polymer topology, e.g., branched structures. In this study, we systematically investigated the effect of polymer topology on the nonlinear parameters Q(ω,γ0) and Q0(ω) with a single mode differential pom-pom model. A number of parameters are affecting the topology of a pom-pom polymer, such as the number of dangling arms (q) and the dimensionless molecular weight of both the backbone (sb) and the arms (sa). In the here presented work, the linear viscoelastic properties G′(ω) and G″(ω) were compared with the nonlinear viscoelastic property Q0(ω) for variety of molecular parameters. The intrinsic nonlinearity Q0(ω) displayed two distinct relaxation processes for pom-pom architectures even though G′(ω) and G″(ω) could not distinguish two relaxation processes. Furthermore, the behavior of Q(γ0) as a function of strain amplitude was also investigated in detail. From the results of these numerical simulations, it was concluded that polymer topology had a stronger influence on the nonlinear viscoelastic properties Q and Q0 than on the linear viscoelastic properties. [ABSTRACT FROM AUTHOR]

Abstract: The normalized frequency of a sine-wave can be estimated by the average of the two estimates achieved using the Interpolated Discrete Fourier Transform (IpDFT) method. This approach is called average-based IpDFT method. The paper investigates the effect of the spectral interference from the image component and additive wideband noise on the accuracy of the normalized frequency estimator provided by the average-based IpDFT method with maximum sidelobe decay windows in the case of a discrete-time sine-wave. The expressions of the maximum of the normalized frequency estimator error due to the spectral interference and variance of the normalized frequency estimator due to the wideband noise are derived. Also, the expression of the combined standard uncertainty of the normalized frequency estimator is derived. The accuracies of all derived expressions are confirmed by means of computer simulations. Moreover, the performance of the average-based IpDFT method is compared with those of a state-of-the-art three-point IpDFT method and IpDFT method through both computer simulations and experimental results. [Copyright &y& Elsevier]

Abstract: Interference-based optical image encryption has triggered much current attention due to its marked advantages, such as non-iterative operation. Although interference-based optical image encryption is an effective approach, cryptosystem security is still a great concern from a cryptanalysis point of view and higher security is always desirable. In this paper, we propose a novel method to enhance the security for conventional interference-based optical image encryption in the fractional Fourier transform (FrFT) domain. A series of random and fixed phase-only masks is used in the optical paths, and subsequently interference principle is applied to extract two phase-only masks (i.e., ciphertexts) during image encryption. Feasibility and effectiveness of the proposed method are demonstrated by computer simulations. [Copyright &y& Elsevier]

Power converters produce a vast range of harmonics, subharmonics and interharmonics. Harmonics analyzing tools based on the Fast Fourier Transform (FFT) assume that only harmonics are present and the periodicity intervals are fixed, while these periodicity intervals are variable and long in the presence of interharmonics. Using FFT may lead to invalid and undesired results due to the above mentioned issues. They can also lead to problems such as frequency blending, spectral leakage and the picket-fence effect. In this paper, the group-harmonic weighting (GHW) approach has been presented to identify the interharmonics in a power system. Afterwards, a modified GHW has been introduced to calculate the proper bandwidth for analyzing the various values of interharmonics. Modifying this method leads to more precise results in the FFT of a waveform containing inter harmonics especially in power systems with a fundamental frequency drift or frequency interference. Numerical simulations have been performed to prove the efficiency of the presented algorithm in interharmonics detection and to increase the accuracy of the FFT and the GWH methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a modified widely linear selective mapping (MWL-SLM) scheme is proposed to reduce the peak-to-average power ratio (PAPR) of the orthogonal frequency-division multiplexing (OFDM) systems. In the proposed MWL-SLM scheme, through partition one complex signals into two real signals and combining the linear properties of the Fourier Transform, at most 4M 2 candidate signals can be obtained but only require M inverse fast Fourier transform (IFFT) operations. As a result, the proposed SLM scheme has the ability to generate more candidates when compared with conventional SLM (C-SLM) and widely linear SLM (WL-SLM). Therefore, MWL-SLM outperforms C-SLM and WL-SLM for the same computational cost of IFFT operations. Alternatively, for a given number of candidates, MWL-SLM has slightly inferior PAPR reduction performance to C-SLM and WL-SLM but requires less IFFT operations to be implemented, thus resulting in a lower computational complexity. Simulation results demonstrate the effectiveness of the proposed scheme. [Copyright &y& Elsevier]

Abstract: This paper presents a time–frequency-domain filtered-x LMS (FXLMS) algorithm for active noise control (ANC) based on the short-time Fourier transform (STFT). We show that proposed algorithm has much reduced computational complexity and better convergence performance, as compared with the time-domain FXLMS algorithm. Additionally, computer simulations show that a time–frequency-domain FXLMS algorithm for ANC is effective in canceling non-stationary noise while a frequency-domain FXLMS algorithm remains inadequate at this task. [Copyright &y& Elsevier]

SUMMARY A framework for a computationally efficient single-carrier frequency-division multiple access (SC-FDMA) transmitter is proposed in this paper. Compared with a wide system bandwidth, the uplink allocation for each user is supposed to be relatively small because of multiple user access, which makes each user's signal vector to be sparse. When the localized subcarrier allocation is used for SC-FDMA, the inverse fast fourier transform can take advantage of the sparse user input vector to reduce its complexity. The analytical and simulation results show that the proposed framework can provide a significant complexity reduction compared with the conventional SC-FDMA transmitter. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In homogeneous and isotropic nonlinear left-handed materials (LHMs), using the split step Fourier transform method, we demonstrate that two dark electromagnetic solitons which are the solutions of coupled nonlinear Schrödinger equations (CNLS) move along a line toward each other, when the distance between them down to a certain value, the interaction of the two dark solitons can produce a stable bright electromagnetic pulse that behaves like a bright soliton. Although our mathematical analysis shows that the new generated stable bright pulse is not an exact solution of the CNLS, it can propagate steadily in the nonlinear LHMs. And this unusual phenomenon can also be observed in our numerical simulation results by another method. [ABSTRACT FROM AUTHOR]

Abstract: A thin gaseous disk has often been investigated in the context of various phenomena in galaxies, which point to the existence of starburst rings and dense circumnuclear molecular disks. The effect of self-gravity of the gas in the disk can be important in confronting observations and numerical simulations in detail. For use in such applications, a new method for the calculation of the gravitational force of a disk is presented. Instead of solving the complete potential function problem, we calculate the force in infinite planes in Cartesian and polar coordinates by a reproducing kernel method. Under the limitation of a disk, we specifically represent the force as a double summation of a convolution of the surface density and a fundamental kernel and employ a fast Fourier transform technique. In this method, the entire computational complexity can be reduced from to , where N is the number of zones in one dimension. This approach does not require softening. The proposed method is similar to a spectral method, but without the necessity of imposing a periodic boundary condition. We further show this approach is of near second order accuracy for a smooth surface density in a Cartesian coordinate system. [Copyright &y& Elsevier]

Abstract: A kind of image encryption scheme is presented by using a rotation operation being regarded as the scrambling scheme of the pixels. The rotation operation is composed of rotation center, radii and angle. For the data of phase and amplitude of complex number, the rotation operation is performed with random controlling parameters iteratively. The parameters are random and serve as the key of this encryption method. Subsequently, the fractional Fourier transform is introduced to alter the values of image pixel. The process mentioned above will be achieved many times for enhancing the security of the proposed algorithm. Numerical simulation is given to demonstrate the validity and performance of the image hiding procedure. [Copyright &y& Elsevier]

A pattern synthesis technique for the flat-top pattern with an arbitrary footprint is proposed in this paper. This technique is based on an iterative fast Fourier transform (FFT) method and the Elliott-Stern method. Due to the Fourier transformation-pair relationship between the array excitations and the array factor, the iterative FFT method is used to adjust the array factor iteratively to obtain the desired pattern. To accelerate this method and to make this method more robust, the initial element excitations are obtained by applying Fourier transform to a pattern designed by the Elliott-Stern method. Several numerical simulations are applied to validate the effectiveness of this technique. [ABSTRACT FROM AUTHOR]

In this article, a fast and accurate method is presented for analyzing the interaction between arbitrary oriented finite beams over planar multilayer structures.The method is based on Transfer Matrix algorithm and optical fast-Fourier-transform based angular spectrum method. Full vectorial near-fields of electromagnetic beam refracted and reflected by the multilayer can be calculated within several seconds. A numerical simulation in FEKO and an experiment are respectively implemented, and good agreement compared with the hybrid method is obtained. The method can be used in the design process of the multilayer with big amount of parameter adjustment, and then full-wave simulation can be adopted to get exact results. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2185-2190, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27014 [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we first review some representative and recent filtering methods for electronic speckle pattern interferometry (ESPI) fringe or wrapped phase patterns, mainly including the second-order oriented partial differential equations (PDEs) filtering methods (SOOPDE), the oriented, regularized quadratic cost function (ORQCF) method, the oriented spatial filter masks (OSFM), the windowed Fourier transform method (WFF), and the localized Fourier transform filter (LFF). Then we compare the performance of these representative and recent filtering methods via application to two computer-simulated ESPI fringe images, a computer-simulated ESPI wrapped phase pattern and one experimentally obtained ESPI wrapped phase pattern which are either high fringe density or variable fringe density. Lastly, we present the summary of the performance for these filtering methods. [Copyright &y& Elsevier]

The aliased polyphase sampling in the linear canonical transform (LCT) domain has been proposed in this study. The result shows that the sampling theorem can be achieved by using parallel samplers to obtain a higher sampling rate in the LCT domain. Further analysis shows that the LCT spectrum of x(nM+m) replicates |X(a, b, c, d)(u)| with a period bMFs along with linear phase modulation in the LCT domain, where b is one parameter of the LCT, M is the number of samplers and Fs is the sampling frequency at which these samplers are operated in the Fourier transform domain. Finally, the simulations are also proposed to verify the correctness of the derived results. [ABSTRACT FROM AUTHOR]

The ambiguity function (AF) as an important tool for time-frequency analysis, has widely been used in radar signal processing, sonar technology and so on. It does well in analysing chirp signals. However, it fails in estimating the cubic phase (CP) signal, which is required in many applications. As the generalisation of the Fourier transform (FT), the linear canonical transform (LCT) has received much attention, and has found many applications in filter design, pattern recognition, optics and so on. In this study, the authors define a new kind of AF - the AF based on the LCT (LCTAF), which is proposed to estimate the CP signal. Some important properties of LCTAF are discussed, such as symmetry and conjugation property, shifting property and Moyal formula. The relationships between the LCTAF and other time-frequency analysis distributions are derived, including the classical AF, the Wigner distribution function (WDF) based on LCT, the short-FT and the wavelet transform. The linear canonical AF (LCAF) is another kind of AF. The authors also discuss its relation with AF and WDF and give some new properties of the LCAF. At last, the LCTAF is applied for estimating the CP signal. The simulation indicates that the LCTAF is useful and effective. [ABSTRACT FROM AUTHOR]

Measurements of two-dimensional (2D) temperature fields are performed by an interferometric method during density fingering of the autocatalytic chlorite-tetrathionate reaction in a Hele-Shaw cell. These measures confirm that, because of heat losses through the glass walls of the reactor, the temperature profile across the front is a pulse rather than a front. Moreover, the full 2D temperature field shows the presence in the reactive zone of hot spots where the temperature exceeds the maximum temperature measured in a stable planar front. We investigate here experimentally the increase of temperature in the hot spots when the composition of the reactants is varied to increase the exothermicity of the reaction. We back up these experimental observations by nonlinear simulations of a reaction-diffusion-convection model which show that the maximum temperature reached in the system depends on the intensity of convection. [ABSTRACT FROM AUTHOR]

Abstract: Three frames of deformed patterns are needed at least in conventional Phase Measuring Profilometry (PMP). It is generally applied to the profile measurement of a static object. For on-line measurement, because of the moving object, it is difficult to capture three or more frames of deformed patterns that satisfy the requirement of PMP. A new method of on-line 3-D shape measurement through only one frame deformed pattern in PMP is presented. A static sinusoidal fringe is projected and any one frame of real-time deformed patterns is captured by CCD. N frames of sub-images are extracted from the captured deformed pattern. Improved Stoilov algorithm is proposed to get phase. Computer simulation and experimental results show its feasibility and affectivity to reconstruct a 3-D shape and the accuracy is higher than Fourier Transform Profilemetry (FTP) which is also a method that only needs one frame of deformed pattern. [Copyright &y& Elsevier]

As the ever-shrinking transistor approaches atomic proportions, Moore's law must confront the small-scale granularity of the world: We cannot build wires thinner than atoms. Worse still, at atomic dimensions, we must contend with the laws of quantum mechanics. This pressure of fundamental limits on classical computation and the promise of exponential speedups from quantum effects have recently brought quantum circuits to the attention of the electronic design automation community. However, the near-term limits are not truly fundamental, and may be avoided by making radical changes to the physical and logical architecture of computers. In particular, certain assumed limits to the energy efficiency of computers have never been rigorously proven, and may be circumvented using physical mechanisms that recover and reuse signal energies with efficiency approaching 100%. However, this concept, called reversible computing, imposes tight constraints on the design of the machine at all levels from physics to algorithms. This research work comprehends the advantages of proposed reversible gate in terms of various device parameters like device utilization, delay and power consumption as compared to existing reversible logic. The proposed design as compared to conventional approach shows 80% reduced unit delay and 27% reduction in delay and 40% reduced complexity in respect to available reversible logic. Also, the quantum simulation is successfully performed for the reversible gates, which proves that reversible gates can be used for quantum computation and are suitable for the next generation designs with all advantages of power and reduced device size. The proposed gate is proved to exhibit the fault detection property also. In this research work fourier tansform simulation using reversible gates as quantum gates(5-bits) is performed and compared with the existing fourier transform algorithm, which comprehends its speed up feature. [ABSTRACT FROM AUTHOR]

A matrix-theoretic approach for studying quasi-cyclic codes based on matrix transformations via Fourier transforms and row and column permutations is developed. These transformations put a parity-check matrix in the form of an array of circulant matrices into a diagonal array of matrices of the same size over an extension field. The approach is amicable to the analysis and construction of quasi-cyclic low-density parity-check codes since it takes into account the specific parity-check matrix used for decoding with iterative message-passing algorithms. Based on this approach, the dimension of the codes and parity-check matrices for the dual codes can be determined. Several algebraic and geometric constructions of quasi-cyclic codes are presented as applications along with simulation results showing their performance over additive white Gaussian noise channels decoded with iterative message-passing algorithms. [ABSTRACT FROM PUBLISHER]

Abstract: In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by using the fractional Fourier transform, but most of their encryptions are complex values and need digital hologram technique to record information, which is inconvenient for digital transmission. In this paper, we propose a new approach for image encryption based on the real-valuedness and decorrelation property of the reality-preserving multiple-parameter fractional Fourier transform in order to meet the requirements of the secure image transmission. In the proposed scheme, the original and encrypted images are respectively in the spatial domain and the reality-preserving multiple-parameter fractional Fourier transformed domain determined by the encryption keys. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods. [Copyright &y& Elsevier]

Abstract: Color image encoding and decoding using fractional Fourier transformation (FRFT) associated with wavelet transformation (WT) are proposed in this paper, which is calculated using discrete fractional Fourier transformation and discrete wavelet transformation. A new method for color image encoding and decoding is given. Some examples of computer simulation results are proposed and verified. [Copyright &y& Elsevier]

The authors assume a linear equidistance antenna array as the receiver for a fixed frame-length multiple-access system, which employs variable-gain receiver power and repetition encoding. They propose a robust maximum a posteriori probability (MAP) blind bit-rate detector (BBRD). This detector considers the rate detection (RD) as a multi-hypothesis test and maximises the likelihood functions (LFs) to find the true bit-rate, whereas the complex amplitude of the received signal, the noise variance and the direction of arrival are unknown parameters. First, assuming that the location parameter is known and the information sequence are independent and uniformly distributed random variables, the authors propose a hybrid likelihood ratio test (HLRT). The proposed HLRT requires to solve a set of non-linear equations that have no closed-form solution. Thus, an iterative numerical algorithm is proposed. In addition, a quasi-HLR detector which has a significantly lower computational complexity is also proposed. In the case of unknown location parameter, the authors develop two quasi-HLR methods. They use fast Fourier transform and search to estimate the unknown location. In Q-HLRT-Method-I, the non-linear equation similar to the one in known location parameter is iteratively solved. In Q-HLRT-Method-II, a low complexity solution is proposed. Simulation examples evaluate and compare the performances of the proposed BBRDs. [ABSTRACT FROM AUTHOR]

Abstract: Based on fractional Fourier transform, an image encryption algorithm is proposed and researched. A local random phase encoding is introduced into this algorithm. The data at the local area of complex function is converted by fractional Fourier transform. The local random phase encoding is performed many times. Moreover only one set of random phase data is used in image encryption process. Compare to double random phase encoding, the parameter defining local area can be regarded as the additional key to increase the security of the encryption scheme. Some numerical simulations are achieved to demonstrate the performance of the image encryption scheme. [Copyright &y& Elsevier]

Using numerical simulations, here, we demonstrate that a single sheet of graphene with properly designed inhomogeneous, nonuniform conductivity distributions can act as a convex lens for focusing and collimating the transverse-magnetic (TM) surface plasmon polariton (SPP) surface waves propagating along the graphene. Consequently, we show that the graphene can act as a platform for obtaining spatial Fourier transform of infrared (IR) SPP signals. This may lead to rebirth of the field of Fourier optics on a ] -atom-thick structure [ABSTRACT FROM AUTHOR]

Abstract: Based on random fractional Fourier transform (RFrFT), a novel adaptive watermarking algorithm using fractal dimension is proposed. Under fractal dimension, this algorithm is adaptive in the embedding position and the embedding intensity. The robustness and the imperceptibility of the watermarking algorithm are in good balance when block selection, high amplitude selection and amplitude shift keying are employed in this algorithm. Numerical simulation results have demonstrated the effectiveness of the proposed scheme and shown the robustness against attacks of noising, cropping and JPEG compression. [Copyright &y& Elsevier]

In this paper, we present a damage model and its numerical solution by means of Fast Fourier Transforms (FFT). The FFT-based formulation initially proposed for linear and non-linear composite homogenization (Moulinec and Suquet in CR Acad Sci Paris Ser II 318:1417-1423 ; Comput Methods Appl Mech Eng 157:69-94 ) was adapted to evaluate damage growth in brittle materials. A non-local damage model based on the maximal principal stress criterion was proposed for brittle materials. This non-local model was then connected to the Griffith criterion with the aim of predicting crack growth. By using the proposed model, we carried out several numerical simulations on different specimens in order to assess the fracture process in brittle materials. From these studies, we can conclude that the present FFT-based analysis is capable of dealing with crack initiation and crack growth in brittle materials with high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In the DVB-T2 system with a multiple-input single-output (MISO) transmission mode, Alamouti coded orthogonal frequency division multiplexing (OFDM) signals are transmitted simultaneously from two spatially separated transmitters in a single frequency network (SFN). In such systems, each transmit-receive link may have a distinct carrier frequency offset (CFO) due to the Doppler shift and/or frequency mismatch between the local oscillators. Thus, the received signal experiences dual CFOs. This not only causes dual phase errors in desired data but also introduces inter-carrier interference (ICI), which cannot be removed completely by simply performing a CFO compensation. To overcome this problem, this paper proposes an iterative detection with dual phase errors compensation technique. In addition, we propose a successive-iterative ICI cancellation technique. This technique successively eliminates ICI in the initial iteration by exploiting pre-detected data pairs. Then, in subsequent iterations, it performs a fine interference cancellation using a priori information, iteratively fed back from the channel decoder. In contrast to previous works, the proposed techniques do not require estimates of dual CFOs. Their performances are evaluated via a full DVB-T2 simulator. Simulation results show that the DVB-T2 receiver equipped with the proposed dual phase errors compensation and the successive-iterative ICI cancellation techniques achieves almost the same performance as ideal dual CFOs-free systems, even for large dual CFOs. [ABSTRACT FROM AUTHOR]

Abstract: A numerical investigation, based on the use of split step Fourier transformation algorithm, of all-optical solitons switching in asymmetric directional couplers is presented. The numerical algorithm is described in details. The analysis highlights the influence of the different effective mode area, the phase- and group–velocity mismatch, the different dispersion between two cores on the switching and propagation of short pulses. The investigation indicates that the phase velocity mismatch and the different effective mode area can reduce the coupling length while the different group velocity and the different dispersion between two cores do not change the coupling length. We have also found that the increase of effective mode area ratio can lead to an increase of the switching threshold power but improve significantly the switching steepness, the increase of the phase velocity mismatch can cause a decrease of the switching threshold power but degrade the switching steepness, the increase of the ratio of dispersion can result in a decrease of the switching threshold power and vary the switching steepness, the increase of group velocity mismatch can give rise to an increase of the switching threshold power but improve obviously the switching steepness. Furthermore, the group velocity mismatch can induce solitons pulse to walk off or stretch in the asymmetric directional coupler. [Copyright &y& Elsevier]

A computational simulation of the formation of an ion beam extracted from a magnetically confined ECR plasma is made. The first simulation stage consists of calculating of the electrostatic field produced by an extraction system. The extraction system is composed of three cylindrically hollow symmetrical electrodes and its respective shielding box. For the purpose of calculating the extraction and focalization electrostatic field, a finite-difference algorithm that solves Laplace equation within the ion propagation volume and allows studying the dependency of the electrostatic field on the geometrical configuration of the extraction system is developed. The second stage consists in calculating the electric and magnetic fields due to extracted ions themselves by solving Poisson equation using the fast Fourier transform technique based on a high-order difference approximation with identity expansion scheme. Finally, an algorithm based on Boris integration scheme to calculate ion trajectories with the objective of simulating the movement on an ion beam due to the field generated by electrodes and beam itself is developed. Based upon the results obtained, the search for an optimized ion extraction system from a 14-GHz ECR ion source is begun. Preliminary configurations are obtained and shown. [ABSTRACT FROM PUBLISHER]

Let ϕ be a function in the Wiener amalgam space $\emph{W}_{\infty}(L_1)$ with a non-vanishing property in a neighborhood of the origin for its Fourier transform $\widehat{\phi}$, ${\bf \tau}=\{\tau_n\}_{n\in {{\mathbb Z}}}$ be a sampling set on ℝ and $V_\phi^{\bf \tau}$ be a closed subspace of $L_2(\hbox{\ensuremath{\mathbb{R}}})$ containing all linear combinations of τ-translates of ϕ. In this paper we prove that every function $f\in V_\phi^{\bf \tau}$ is uniquely determined by and stably reconstructed from the sample set $L_\phi^{\bf \tau}(f)=\Big\{\int_{\hbox{\ensuremath{\mathbb{R}}}} f(t) \overline{\phi(t-\tau_n)} dt\Big\}_{n\in {{\mathbb Z}}}$. As our reconstruction formula involves evaluating the inverse of an infinite matrix we consider a partial reconstruction formula suitable for numerical implementation. Under an additional assumption on the decay rate of ϕ we provide an estimate to the corresponding error. [ABSTRACT FROM AUTHOR]

The classical interpolation-based Polar Format Algorithm (PFA) for spotlight synthetic aperture radar (SAR) results in numerous computation load, which, reduces processing speed and increase system complexity. To decrease computation load, this paper proposes a novel non-interpolation PFA algorithm for sensor flying along non-lineal flight trajectories, which are specially designed curves in conical surface. Then an innovative auto-adaptive Pulse Repetition Frequency (PRF) technique is put forward to uniformly sample signal in azimuth direction. The computation load of the new PFA is merely left to azimuth chirp z-transforms (CZTs) and range fast Fourier transforms (FFTs) after dechirp processing and residual video phase (RVP) compensation. Two flight modes (ellipse trajectory mode and hyperbola trajectory mode) are analyzed. A lineal approximation method is proposed to simplify non-lineal sensor trajectory analysis. Computer simulation results for multiple point targets validate the presented approach. Comparison of computation load between this PFA and traditional PFA is represented in Appendix B. [ABSTRACT FROM AUTHOR]

Due to its good orthogonality, slantlet transform (SLT) is used in orthogonal frequency division multiplexing (OFDM) systems to reduce intersymbol interference (ISI) and intercarrier interference (ICI). This eliminates the need for cyclic prefix (CP) and increases the spectral efficiency of the design. Finite Radon transform (FRAT) mapper has the ability to increase orthogonality of subcarriers, is nonsensitive to channel parameters variations, and has a small constellation energy compared with conventional fast-Fourier-transform- (FFT-) based OFDM. It is also able to work as a good interleaver, which significantly reduces the bit error rate (BER). In this paper both FRATmapping technique and SLT modulator are implemented in a new design of an OFDM system. The new structure was tested and compared with conventional FFT-based OFDM, Radon transform-based OFDM, and SLT-based OFDM for additive white Gaussian noise (AWGN) channel, flat fading channel (FFC), and multipath selective fading channel (SFC). Simulation tests were generated for different channel parameters values. The obtained results showed that the proposed system has increased the spectral efficiency, reduced ISI and ICI, and improved BER performance compared with other systems. [ABSTRACT FROM AUTHOR]

Abstract: A novel estimation algorithm based on the fractional Fourier transform (FRFT) is proposed for the multi-path number, the delay and the Doppler shift in the underwater acoustic multipath channel. The FRFT is applied to analyze the received signal. And a series of peaks will appear in the corresponding u domain at a specific order. The relationships between the channel parameters with the intervals among the peaks are induced. Besides, it''s not necessary to search for the order of the received signal due to the invariant characteristic of the chirp rate, which greatly improves the algorithm efficient. The advantage of this algorithm is that the accurate multi-path number, the delay and the Doppler shift can be estimated, however this algorithm is just suitable for the situation where each of the paths has the same Doppler shift and the exact delay estimation of direct path is available. The simulation results show the effectiveness of the algorithm. [Copyright &y& Elsevier]

SUMMARY High-frequency and full waveform synthetic seismograms on a 3-D laterally heterogeneous earth model are simulated using the theory of coupled normal modes. The set of coupled integral equations that describe the 3-D response are simplified into a set of uncoupled integral equations by using the Born approximation to calculate scattered wavefields and the pure-path approximation to modulate the phase of incident and scattered wavefields. This depends upon a decomposition of the aspherical structure into smooth and rough components. The uncoupled integral equations are discretized and solved in the frequency domain, and time domain results are obtained by inverse Fourier transform. Examples show the utility of the normal mode approach to synthesize the seismic wavefields resulting from interaction with a combination of rough and smooth structural heterogeneities. This approach is applied to an ∼4 Hz shallow crustal wave propagation around the site of the San Andreas Fault Observatory at Depth (SAFOD). [ABSTRACT FROM AUTHOR]

Matched filtering of phase history data is the optimum reconstruction algorithm to bistatic synthetic aperture radar (SAR) image formation. However, it comes at great computational expense scaled with complexity O (M2 N2), where M N is the number of pixels in the image. Based on the plane wave assumption, bistatic polar format algorithm (PFA) approximates the matched filtering kernel appropriately, so that the computational complexity in image formation is considerably reduced. In this paper, we propose a novel PFA for bistatic SAR processing. This imaging algorithm is to use non-uniform fast Fourier transform (NUFFT) to compute the matched filtering reconstruction image according the plane wave signal model of bistatic SAR, which scales with complexity O (M Nlog2M N). Numerical simulations are performed to validate the proposed algorithm. The results prove that, compared with the direct computing of matched filtering, the presented algorithm can provide almost identical imaging performance in a relatively very short computation time. [ABSTRACT FROM AUTHOR]

Abstract: For the problem of the instantaneous frequency rate estimation of multi-component linear frequency-modulated (LMF) signals, a new method is presented. And the local polynomial Fourier transform (LPFT) method is applied to estimate instantaneous frequency rate of multi-component LMF signals. By means of doing local polynomial Fourier transform on multi-component LMF signals, we can separate each LMF signal, and then search the value to find the corresponding frequency rate according to the local polynomial of the every LMF signal, so we accurately estimate the instantaneous frequency rate of the multi-component LMF signal. The simulation results verify the availability of the proposed method. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a simple method for processing a 2D wrapped phase map that contains a spatial carrier signal in order to completely eliminate, or greatly reduce, the number of phase wraps in the image. The 2D Fourier transform of the wrapped phase map is calculated. Then the spectrum is shifted to the origin in frequency space. After that, the inverse 2D Fourier transform is computed. Finally, a four-quadrant arctangent function is used to calculate the angle of the complex array that was produced by the inverse 2D Fourier transform. This produces a phase map with a smaller number of 2π phase jumps than the original phase map. In some cases, all of the phase wraps are eliminated and there is therefore no need to unwrap the resultant phase map. The reduction of the number of 2π phase jumps can reduce the execution time and improve the noise performance of some phase unwrapping algorithms such as the Flynn method. The validation of the proposed algorithm is demonstrated experimentally and also via computer-simulation. [Copyright &y& Elsevier]

In the present paper we study an anti-plane nonstationary (transient) problem for a massive structure above the oscillating foundation. The latter is taken as an elastic half-space with an oblique plane seismic wave incoming from below to the boundary surface. The structure is assumed to be considerably more rigid than the foundation. The analytical treatment is achieved by applying the Laplace transform over time. After that the solution in the half-space is constructed by using the Fourier transform along the horizontal coordinate. By satisfying the joining boundary conditions between the rectangle and the foundation, the problem is reduced to an integral equation along the contact zone, which contains the Laplace parameter. We propose a new numerical approach to solve the dual Volterrà—Fredholm integral equations of the arising type. Then we investigate the dynamic properties of the structure for various combinations of physical and geometric parameters. [ABSTRACT FROM PUBLISHER]

Abstract: This paper investigates the space fractional diffusion equation with fractional Feller’s operator. The Green’s function is obtained by using Fourier transform, and the analytical solutions of some space fractional diffusion equations with initial (or initial and boundary) condition are obtained in terms of Green’s function. In addition, numerical simulations are discussed. The results indicate that the effect range of skewness parameter has more effect on probability density than that of parameter . The results also explain the property of the skewness and long tail in the asymmetry diffusion process. [Copyright &y& Elsevier]

We propose constitutive models for polycrystalline aggregates with intergranular cavities and test them against full-field numerical simulations. Such conditions are prevalent in many engineering applications and failure of metallic components (e.g. HIPing and other forming processes, spallation under dynamic loading conditions, etc.), where the dilatational effects associated with the presence of cavities must be accounted for, and standard polycrystalline models for incompressible plasticity are not appropriate. On the other hand, it is not clear that the use of porous plasticity models with isotropic matrix behavior is relevant, particularly, when large deformations can lead to significant texture evolution and therefore to strong matrix anisotropy. Of course, finite strains can also lead to significant changes in the porosity and pore shape, resulting in additional anisotropy development. In this work, we make use of 'variational linear-comparison' homogenization methods to develop constitutive models simultaneously accounting for texture of the matrix, porosity and average pore shape and orientation. The predictions of the models are compared with full-field numerical simulations based on fast Fourier transforms to study the influence of different microstructural features (e.g. overall porosity, texture of the matrix phase, single-crystal anisotropy, etc.) and type of loading (triaxiality) on the dilatational viscoplastic behavior of voided polycrystals. The results are also compared with the predictions of isotropic-matrix porous plasticity models to assess the effect of the possible matrix anisotropy in textured samples. [ABSTRACT FROM AUTHOR]