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Journal articles on the topic 'Parabolic interpolation algorithm'
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1
Zhang, Zhi Qiang, Wen Jin Wang, Jing Zhang, et al. "The Research of NURBS Curve Interpolation Algorithm Based on Parabolic and the First-Order Taylor Expansion Interpolation Algorithm." Advanced Materials Research 1003 (July 2014): 260–63. http://dx.doi.org/10.4028/www.scientific.net/amr.1003.260.
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The NURBS curve interpolation algorithm based on parabolic interpolation error and the first-order Taylor expansion interpolation algorithm is proposed to improve part surface quality and chord error of NURBS curve interpolation algorithm. The part surface quality is improved effectively by the parabolic interpolation algorithm in the conduction that the previous point, the current point and the next point which was computed by the first order Taylor expansion interpolation algorithm were known. The effectiveness of this algorithm is proved by the NURBS curve interpolation simulation.
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Wei, Can Xin. "Numerical Analysis and Performance Test of Interactive Platform Based on Multi-Media Internet Architecture." Applied Mechanics and Materials 556-562 (May 2014): 5705–9. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.5705.
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Streaming media technology is also known as streaming media technology. Users can experience playing while downloading function, which improves the transmission speed of multimedia information on the internet. In this paper, we use streaming media technology, combined with the parabolic interpolation and Newton interpolation algorithm, design multimedia interactive platform of the college students' ideological and political education and comprehensive education. The overall structure of the platform is composed of multimedia, streaming media distribution equipment, school network, clients of teachers and students. On the internet between the teachers and students, student and students they can communicate ideological and political. In order to test the performance of network, we use the iperf software to test packet loss rate and delay characteristics of the network. The results show that Newton interpolation method has better delay characteristics, parabolic interpolation algorithm has low packet loss rate. It provides technical reference for the application of multimedia technology in the ideological and political education.
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Xiao, Ben Xian, Yun Chao Tao, Xue Ping Dong, Mei Ling Zhao, and Jun Xiao. "Study on Interpolation Arithmetic of Tube Bender with Four-Axis CNC System for Spiral Fluorescent Lamp." Applied Mechanics and Materials 48-49 (February 2011): 1172–76. http://dx.doi.org/10.4028/www.scientific.net/amm.48-49.1172.
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Taking tube bender system for producing pagoda-shaped fluorescent tubes as an example in this paper, four coordinates movement equations of CNC system with Parabolic characteristic are derived and an algorithm for nonlinear interpolation of four-axis linkage based on target point tracking algorithm is presented for the spiral fluorescent tube bending machine with CNC system by means of deep analysis of the pulse interval interpolation algorithm. By using this algorithm, coordinated control of four coordinates in tube bender system can be realized and, in addition, software programming procedure can be directly used for this system. Test shows that the system which uses this interpolation method has the characteristic of simple operation, high speed and high single-pulse interpolation accuracy.
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Lu, Zuliang, Fei Cai, Ruixiang Xu, Chunjuan Hou, Xiankui Wu, and Yin Yang. "A posteriori error estimates of hp spectral element method for parabolic optimal control problems." AIMS Mathematics 7, no. 4 (2022): 5220–40. http://dx.doi.org/10.3934/math.2022291.
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<abstract><p>In this paper, we investigate the spectral element approximation for the optimal control problem of parabolic equation, and present a hp spectral element approximation scheme for the parabolic optimal control problem. For improve the accuracy of the algorithm and construct an adaptive finite element approximation. Under the Scott-Zhang type quasi-interpolation operator, a $ L^2(H^1)-L^2(L^2) $ posteriori error estimates of the hp spectral element approximated solutions for both the state variables and the control variable are obtained. Adopting two auxiliary equations and stability results, a $ L^2(L^2)-L^2(L^2) $ posteriori error estimates are derived for the hp spectral element approximation of optimal parabolic control problem.</p></abstract>
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Shen, Ting Ting, Lei Zhu, Lin Kong, Lan Qiang Zhang, and Chang Hui Rao. "Real-Time Image Shift Detection with Cross Correlation Coefficient Algorithm for Correlating Shack-Hartmann Wavefront Sensors Based on FPGA and DSP." Applied Mechanics and Materials 742 (March 2015): 303–11. http://dx.doi.org/10.4028/www.scientific.net/amm.742.303.
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Working on low-contrast, extended, time-varying objects such as the solar granulation, solar adaptive optics (AO) system uses correlation algorithms to detect image shift of the Shack-Hartmann (SH) wavefront sensor (WFS) instead of centroid algorithm in night-time adaptive optics system. An real-time image shift detection processor, which consists of a Xilinx FPGA and a TI DSP, has been developed for a low-order solar AO system based on cross correlation coefficient algorithm. Image shift of integer pixels can be calculated in the FPGA and DSP is responsible for parabolic interpolation to obtain subpixel accuracy. The experimental results show that the processor can obtain correct image shift and satisfy the time latency requirement of the AO system.
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Kumar, Pravesh, Sushil Kumar, Millie Pant, and V. P. Singh. "Interpolation Based Mutation Variants of Differential Evolution." International Journal of Applied Evolutionary Computation 3, no. 4 (2012): 34–50. http://dx.doi.org/10.4018/jaec.2012100103.
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Differential evolution algorithm (DE) is an efficient and versatile population-based search technique for global optimization. In this paper, two novel mutation variants for DE are presented. These mutation variants are based on interpolation rules; first variant is based on Inverse Quadratic Interpolation called IQI-DE and the second variant is based on sequential parabolic interpolation called SPI-DE. Both variants aim at efficiently generating the base vector in the mutation phase of DE. The performance of proposed variants is implemented on 12 benchmark problems and compares with basic DE and five other enhanced versions of DE such as DERL, ODE, jDE, JADE, and LeDE. Experimental results show that the proposed variants are significantly better or at least comparable to other variants in term of convergence speed and solution accuracy.
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Chen, Chuanmiao, Xiangqi Wang, and Hongling Hu. "A High-Efficient Algorithm for Parabolic Problems with Time-Dependent Coefficients." Advances in Applied Mathematics and Mechanics 9, no. 2 (2017): 501–14. http://dx.doi.org/10.4208/aamm.2015.m1281.
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AbstractA high-efficient algorithm to solve Crank-Nicolson scheme for variable coefficient parabolic problems is studied in this paper, which consists of the Function Time-Extrapolation Algorithm (FTEA) and Matrix Time-Extrapolation Algorithm (MTEA). First, FTEA takes a linear combination of previous l level solutions as good initial value of Un(see Time-extrapolation algorithm (TEA) for linear parabolic problems, J. Comput. Math., 32(2) (2014), pp. 183–194), so that Conjugate Gradient (CG)-iteration counts decrease to 1/3~1/4 of direct CG. Second, MTEA uses a linear combination of exact matrix values in level L, L+s, L+2s to predict matrix values in the following s–1 levels, and the coefficients of the linear combination is deduced by the quadric interpolation formula, then fully recalculate the matrix values at time level L+3s, and continue like this iteratively. Therefore, the number of computing the full matrix decreases by a factor 1/s. Last, the MTEA is analyzed in detail and the effectiveness of new method is verified by numerical experiments.
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Nguyen, Thanh-Tuan, Ching-Hwa Cheng, Don-Gey Liu, and Minh-Hai Le. "A Fast Cross-Correlation Combined with Interpolation Algorithms for the LiDAR Working in the High Background Noise." Electronics 11, no. 7 (2022): 985. http://dx.doi.org/10.3390/electronics11070985.
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Processing speed and accuracy of measurements are important factors reflecting the performance quality of light detection and ranging (LiDAR) systems. This study proposed a fast cross-correlation (fCC) algorithm to improve the computation loading in the LiDAR system operating in high background noise environments. To reduce the calculation time, we accumulated cycles of the receiver waveform to increase the signal-to-noise ratio. In this way, the stop pulse can be easily distinguished from the background noise by applying the cross-correlation (CC) on the accumulated receiver waveform with the first start pulse. In addition, the proposed fCC combined with variant interpolation techniques: the parabolic (fCCP), gaussian (fCCG), cosine (fCCC), and cubic spline (fCCS) to increase the measurement accuracy were also investigated and compared. The experiments were performed on the real-time LiDAR system under high background light intensity. The tested results showed that the proposed method fCCP achieved 879 ns per measurement, 38 times faster than the original CC method combined with the same parabolic interpolation algorithm (CCP) 33.5 μs. Meanwhile, the fCCS method resulted in the highest accuracy/precision, reaching 5.193 cm/8.588 cm, respectively. These results demonstrated that our proposed method significantly improves the measurements speed in the LiDAR system operating under strong background light.
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Ding, Zhangliang, Jianrong Zhu, Bingrui Chen, and Daoyang Bao. "A Two-Way Nesting Unstructured Quadrilateral Grid, Finite-Differencing, Estuarine and Coastal Ocean Model with High-Order Interpolation Schemes." Journal of Marine Science and Engineering 9, no. 3 (2021): 335. http://dx.doi.org/10.3390/jmse9030335.
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The balance between the need of improving horizontal resolution in simulating local small-scale ocean processes and computational costs makes it desirable to refine model mesh locally. A three-dimensional, two-way nesting unstructured quadrilateral grid, primitive equations, finite-differencing, estuarine and coastal ocean model is developed for multi-scale modeling. Because the model grid is capable of multi-area nesting and multi-level refinement at each subdomain, the model is highly compatible with simulations involved in complex topography and studies of local small-scale ocean processes. The two-way information exchange is achieved by a virtual grid method, and its basic idea is to implement numerical integrations of variables at nesting interfaces with the support of virtual grid variables, which are interpolated or updated from actual grid variables. The model is novel for two interpolation schemes: the high-order spatial interpolation at the middle temporal level (HSIMT) parabolic interpolation scheme and HSIMT advection-equivalent interpolation scheme, and they have high-order accuracy and good consistency with the advection scheme applied to solving the tracer equations. The conservation of both volume and tracer contents is ensured via a flux correction algorithm. The two original interpolation schemes are examined in an ideal salinity advection experiment in the peak preservation skill, stability, and conservation properties. A realistic application to the Deep Waterway Project area in the Changjiang Estuary showed that the nested grid model can reproduce the hydrodynamic processes at the observed sites successfully while it failed to maintain the performance with the structured grid model in simulating the variance of salinity, for which the enforced conservation had primary responsibility. The HSIMT parabolic interpolation scheme was distinguished from other schemes for its outstanding performances in simulating salinity.
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Ghasemi, M. "An Efficient Algorithm Based on Extrapolation for the Solution of Nonlinear Parabolic Equations." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 1 (2018): 37–51. http://dx.doi.org/10.1515/ijnsns-2017-0060.
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AbstractTwo numerical procedures are developed to approximate the solution of one-dimensional parabolic equations using extrapolated collocation method. By defining two different end conditions and forcing cubic spline to satisfy the interpolation conditions along with one of the end conditions, we obtain fourth- (CBS4) and sixth-order (CBS6) approximations to the solution in spatial direction. Also in time direction, a weighted finite-difference discretization is used to approximate the solution at each time level. The convergence analysis of the methods is discussed in detail and some error bounds are obtained theoretically. Finally, some different examples of Burgers’ equations with applications in fluid mechanics as well as convection–diffusion problems with applications in transport problems are solved to show the applicability and good performance of the procedures.
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Ghasemi, M. "An Efficient Algorithm Based on Extrapolation for the Solution of Nonlinear Parabolic Equations." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 5 (2019): 527–41. http://dx.doi.org/10.1515/ijnsns-2017-0227.
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AbstractTwo numerical procedures are developed to approximate the solution of one-dimensional parabolic equations using extrapolated collocation method. By defining two different end conditions and forcing cubic spline to satisfy the interpolation conditions along with one of the end conditions, we obtain fourth- (CBS4) and sixth-order (CBS6) approximations to the solution in spatial direction. Also in time direction, a weighted finite difference discretization is used to approximate the solution at each time level. The convergence analysis is discussed in detail and some error bounds are obtained theoretically. Finally, some different examples of Burgers’ equation with applications in fluid mechanics as well as convection–diffusion problems with applications in transport are solved to show the applicability and good performance of the procedures.
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Liu, Xiaowei, Guangliang Ren, Xiaoman Yin, Bo Zhang, and Yu Wang. "A Polynomial Inversion-Based Fast Time-Delay Estimation Method for Wideband Large-Scale Antenna Systems." Applied Sciences 12, no. 7 (2022): 3378. http://dx.doi.org/10.3390/app12073378.
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This paper proposes a new fast time-delay estimation (TDE) method based on polynomial inversion which addresses the challenges arising from the requirements for high-precision, low-computational-complexity synchronization error estimation in wideband large-scale antenna systems (LSASs). In this work, we use the convex parabolic extreme point equation as the timing error detector (TED), and develop a polynomial inversion-based function to characterize the one-to-one mapping relationship between true time delay (TTD) and TED estimates using the least square (LS) method, then obtain the time-delay difference with a high accuracy and high computational efficiency. The results of the performance analysis indicate that the Mean Square Error (MSE) of the proposed algorithm is less than 1 dB away from the Cramer–Rao lower bound (CRLB), which is produced in this paper, while adding a few multipliers compared to the convex parabolic interpolation method. Finally, a further example illustrates that the proposed algorithm can achieve a synchronization error of less than 5 ps between channels based on the NI PXI broadband multichannel acquisition platform.
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Guo, Li Jie. "Nonlinear Analysis of Mixed Signal Test Based on Graphic Program Design." Applied Mechanics and Materials 539 (July 2014): 489–92. http://dx.doi.org/10.4028/www.scientific.net/amm.539.489.
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In this paper, based on the parabolic interpolation function of nonlinear Lagrange, we establish the mathematical model of business translation graphical teaching method. In order to verify the availability and reliability of the model and algorithm, we test the performance of graphic business English translation platform. After testing the mixed signal of platform, the current with fault is lower than circuit without fault. The peak voltage of triangular wave is about-6V and 6V. According to the response curves of English translation circuit, different sequencers realize the parallel translation. It improves business English translation speed, and provides the technical reference for the innovation cultivation of business English talents.
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Trad, Daniel. "Interpolation and multiple attenuation with migration operators." GEOPHYSICS 68, no. 6 (2003): 2043–54. http://dx.doi.org/10.1190/1.1635058.
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A hyperbolic Radon transform (RT) can be applied with success to attenuate or interpolate hyperbolic events in seismic data. However, this method fails when the hyperbolic events have apexes located at nonzero offset positions. A different RT operator is required for these cases, an operator that scans for hyperbolas with apexes centered at any offset. This procedure defines an extension of the standard hyperbolic RT with hyperbolic basis functions located at every point of the data gather. The mathematical description of such an operator is basically similar to a kinematic poststack time‐migration equation, with the horizontal coordinate being not midpoint but offset. In this paper, this transformation is implemented by using a least‐squares conjugate gradient algorithm with a sparseness constraint. Two different operators are considered, one in the time domain and the other in the frequency‐wavenumber domain (Stolt operator). The sparseness constraint in the time‐offset domain is essential for resampling and for interpolation. The frequency‐wavenumber domain operator is very efficient, not much more expensive in computation time than a sparse parabolic RT, and much faster than a standard hyperbolic RT. Examples of resampling, interpolation, and coherent noise attenuation using the frequency‐wavenumber domain operator are presented. Near and far offset gaps are interpolated in synthetic and real shot gathers, with simultaneous resampling beyond aliasing. Waveforms are well preserved in general except when there is little coherence in the data outside the gaps or events with very different velocities are located at the same time. Multiples of diffractions are predicted and attenuated by subtraction from the data.
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Gavrilyuk, Ivan, and Boris N. Khoromskij. "Quasi-Optimal Rank-Structured Approximation to Multidimensional Parabolic Problems by Cayley Transform and Chebyshev Interpolation." Computational Methods in Applied Mathematics 19, no. 1 (2019): 55–71. http://dx.doi.org/10.1515/cmam-2018-0021.
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AbstractIn the present paper we propose and analyze a class of tensor approaches for the efficient numerical solution of a first order differential equation {\psi^{\prime}(t)+A\psi=f(t)} with an unbounded operator coefficient A. These techniques are based on a Laguerre polynomial expansions with coefficients which are powers of the Cayley transform of the operator A. The Cayley transform under consideration is a useful tool to arrive at the following aims: (1) to separate time and spatial variables, (2) to switch from the continuous “time variable” to “the discrete time variable” and from the study of functions of an unbounded operator to the ones of a bounded operator, (3) to obtain exponentially accurate approximations. In the earlier papers of the authors some approximations on the basis of the Cayley transform and the N-term Laguerre expansions of the accuracy order {\mathcal{O}(e^{-N})} were proposed and justified provided that the initial value is analytical for A. In the present paper we combine the Cayley transform and the Chebyshev–Gauss–Lobatto interpolation and arrive at an approximation of the accuracy order {\mathcal{O}(e^{-N})} without restrictions on the input data. The use of the Laguerre expansion or the Chebyshev–Gauss–Lobatto interpolation allows to separate the time and space variables. The separation of the multidimensional spatial variable can be achieved by the use of low-rank approximation to the Cayley transform of the Laplace-like operator that is spectrally close to A. As a result a quasi-optimal numerical algorithm can be designed.
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Henry Juang, Hann-Ming, and Song-You Hong. "Forward Semi-Lagrangian Advection with Mass Conservation and Positive Definiteness for Falling Hydrometeors." Monthly Weather Review 138, no. 5 (2010): 1778–91. http://dx.doi.org/10.1175/2009mwr3109.1.
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Abstract A semi-Lagrangian advection scheme is developed for falling hydrometeors in hopes of replacing the conventional Eulerian scheme that has been widely used in the cloud microphysics scheme of numerical atmospheric models. This semi-Lagrangian scheme uses a forward advection method to determine the advection path with or without iteration, and advected mass in a two-time-level algorithm with mass conservation. Monotonicity is considered in mass-conserving interpolation between Lagrangian grids and model Eulerian grids, thus making it a positive definite advection scheme. For mass-conserving interpolation between the two grid systems, the piecewise constant method (PCM), piecewise linear method (PLM), and piecewise parabolic method (PPM) are proposed. The falling velocity at the bottom cell edge is modified to avoid unphysical deformation by scanning from the top layer to the bottom of the model, which enables the use of a large time step with reasonable accuracy. The scheme is implemented and tested in the Weather Research and Forecasting (WRF) Single-Moment 3-Class Microphysics Scheme (WSM3). In a theoretical test bed with constant terminal velocity, the proposed semi-Lagrangian algorithm shows that the higher-order interpolation scheme produces less diffusive features at maximal precipitation. Results from another idealized test bed with mass-weighted terminal velocity demonstrate that the accuracy of the proposed scheme is still satisfactory even with a time step of 120 s when the mean terminal velocity averaged at the departure and arrival points is employed. A two-dimensional (2D) squall-line test using the WSM3 scheme shows that the control run with the Eulerian advection scheme and the semi-Lagrangian run with the PCM method reveal similar results, whereas behaviors using the PLM and PPM are similar with higher-resolution features, such as mammatus-like clouds.
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FATEMI, MOHAMMAD REZA HOSSEINY, HASAN F. ATES, and ROSLI SALLEH. "FAST ALGORITHM ANALYSIS AND BIT-SERIAL ARCHITECTURE DESIGN FOR SUB-PIXEL MOTION ESTIMATION IN H.264." Journal of Circuits, Systems and Computers 19, no. 08 (2010): 1665–87. http://dx.doi.org/10.1142/s0218126610006980.
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The sub-pixel motion estimation (SME), together with the interpolation of reference frames, is a computationally extensive part of the H.264 encoder that increases the memory requirement 16-times for each reference frame. Due to the huge computational complexity and memory requirement of the H.264 SME, its hardware architecture design is an important issue especially in high resolution or low power applications. To solve the above difficulties, we propose several optimization techniques in both algorithm and architecture levels. In the algorithm level, we propose a parabolic based algorithm for SME with quarter-pixel accuracy which reduces the computational budget by 94.35% and the memory access requirement by 98.5% in comparison to the standard interpolate and search method. In addition, a fast version of the proposed algorithm is presented that reduces the computational budget 46.28% further while maintaining the video quality. In the architecture level, we propose a novel bit-serial architecture for our algorithm. Due to advantages of the bit-serial architecture, it has a low gate count, high speed operation frequency, low density interconnection, and a reduced number of I/O pins. Also, several optimization techniques including the sum of absolute differences truncation, source sharing exploiting and power saving techniques are applied to the proposed architecture which reduce power consumption and area. Our design can save between 57.71–90.01% of area cost and improves the macroblock (MB) processing speed between 1.7–8.44 times when compared to previous designs. Implementation results show that our design can support real time HD1080 format with 20.3 k gate counts at the operation frequency of 144.9 MHz.
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Nguyen, Thanh-Tuan, Ching-Hwa Cheng, Don-Gey Liu, and Minh-Hai Le. "Improvement of Accuracy and Precision of the LiDAR System Working in High Background Light Conditions." Electronics 11, no. 1 (2021): 45. http://dx.doi.org/10.3390/electronics11010045.
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Background light noise is one of the major challenges in the design of Light Detection and Ranging (LiDAR) systems. In this paper, we build a single-beam LiDAR module to investigate the effect of light intensity on the accuracy/precision and success rate of measurements in environments with strong background noises. The proposed LiDAR system includes the laser signal emitter and receiver system, the signal processing embedded platform, and the computer for remote control. In this study, two well-known time-of-flight (ToF) estimation methods, which are peak detection and cross-correlation (CC), were applied and compared. In the meanwhile, we exploited the cross-correlation technique combined with the reduced parabolic interpolation (CCP) algorithm to improve the accuracy and precision of the LiDAR system, with the analog-to-digital converter (ADC) having a limited resolution of 125 mega samples per second (Msps). The results show that the CC and CCP methods achieved a higher success rate than the peak method, which is 12.3% in the case of applying emitted pulses 10 µs/frame and 8.6% with 20 µs/frame. In addition, the CCP method has the highest accuracy/precision in the three methods reaching 7.4 cm/10 cm and has a significant improvement over the ADC’s resolution of 1.2 m. This work shows our contribution in building a LiDAR system with low cost and high performance, accuracy, and precision.
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Marescot, Laurent, Sérgio Palma Lopes, Stéphane Rigobert, and Alan G. Green. "Nonlinear inversion of geoelectric data acquired across 3D objects using a finite-element approach." GEOPHYSICS 73, no. 3 (2008): F121—F133. http://dx.doi.org/10.1190/1.2903836.
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We introduce a new finite-element-based scheme for the fast nonlinear inversion of large 3D geoelectric data sets acquired around isolated objects or across the earth’s surface. The principal novelty of this scheme is the combination of a versatile finite-element approach with (1) a method involving minimization of an objective function using a conjugate-gradient algorithm that includes an adjoint-field technique for efficiently establishing the objective-function gradient and (2) parabolic interpolation for estimating suitable inversion step lengths. This scheme is capable of handling large volumes of data acquired using diverse electrode configurations located around or across 3D structures. Only three solutions to the forward problem are required for each iteration. Computation of the Jacobian matrix, which might require computers with a large amount of memory, is not necessary. To minimize artificial irregularities in the inverted models, particularly near the electrodes, we smooth the model parametersafter each iteration. By including the influence of a reference model in the objective function, a priori information can be incorporated in the inversion process. Our new scheme is tested successfully on synthetic data generated for current and potential electrodes distributed around the surface of a complex object of finite extent. We also demonstrate the utility of the new scheme on geoelectric data acquired around a laboratory-scale object. Tomographic inversion of the 52,272 simulated voltage values in terms of an 8775-element model requires less than 45 minutes on a relatively slow Sun workstation. For the inversion of the 1016 observed voltage values in terms of an 81,480-element model, approximately 60 minutes of computer time is required. The rapid and flexible inversion scheme opens up new possibilities for resistivity imaging in geology, hydrology, engineering, nondestructive testing, and even biology and medicine, fields of study in which finite-element models are already used to represent complicated targets.
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Qi, Wei, Qing Chang, Lv Qian Zhang, and Yuan Yu. "An Improved Re-Sampling Interpolation Algorithm for Base-Band Signal Shaping Filtering." Applied Mechanics and Materials 195-196 (August 2012): 205–11. http://dx.doi.org/10.4028/www.scientific.net/amm.195-196.205.
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Research on shaping filtering algorithms in wireless communication systems has important practical value. Based on the digital base-band shaping filter, which is widely used in the area of software radio, an improved re-sampling filtering algorithm is proposed in this paper. By the design of truncated raise cosine filter, the continuous sequence of digital spread-spectrum signal can be restored. The piecewise parabola interpolation filter is established to carry out the signal re-sample, and the Farrow implementation structure is adopted to reduce the calculation cost. The algorithm is validated through the experiment using simulated and true signals respectively, which demonstrate that not only the out band power of frequency division multi signals can be effectively suppressed, but also the steadiness of re-sampling signals is improved during the dynamic environment.
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Reali, Pierluigi, Riccardo Lolatto, Stefania Coelli, Gabriella Tartaglia, and Anna Maria Bianchi. "Information Retrieval from Photoplethysmographic Sensors: A Comprehensive Comparison of Practical Interpolation and Breath-Extraction Techniques at Different Sampling Rates." Sensors 22, no. 4 (2022): 1428. http://dx.doi.org/10.3390/s22041428.
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The increasingly widespread diffusion of wearable devices makes possible the continuous monitoring of vital signs, such as heart rate (HR), heart rate variability (HRV), and breath signal. However, these devices usually do not record the “gold-standard” signals, namely the electrocardiography (ECG) and respiratory activity, but a single photoplethysmographic (PPG) signal, which can be exploited to estimate HR and respiratory activity. In addition, these devices employ low sampling rates to limit power consumption. Hence, proper methods should be adopted to compensate for the resulting increased discretization error, while diverse breath-extraction algorithms may be differently sensitive to PPG sampling rate. Here, we assessed the efficacy of parabola interpolation, cubic-spline, and linear regression methods to improve the accuracy of the inter-beat intervals (IBIs) extracted from PPG sampled at decreasing rates from 64 to 8 Hz. PPG-derived IBIs and HRV indices were compared with those extracted from a standard ECG. In addition, breath signals extracted from PPG using three different techniques were compared with the gold-standard signal from a thoracic belt. Signals were recorded from eight healthy volunteers during an experimental protocol comprising sitting and standing postures and a controlled respiration task. Parabola and cubic-spline interpolation significantly increased IBIs accuracy at 32, 16, and 8 Hz sampling rates. Concerning breath signal extraction, the method holding higher accuracy was based on PPG bandpass filtering. Our results support the efficacy of parabola and spline interpolations to improve the accuracy of the IBIs obtained from low-sampling rate PPG signals, and also indicate a robust method for breath signal extraction.
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Gdanskiy, N. I., A. V. Karpov, and A. A. Bugaenko. "The direct method and algorithm of construction of splines of the third order in the control problems of drives performance movement." Izvestiya MGTU MAMI 7, no. 1-4 (2013): 51–57. http://dx.doi.org/10.17816/2074-0530-67777.
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When using predictions in the controling of the rotational motion arises the need to build a double-smooth trajectory passing through its previously measured key points. As piecewise polynomial curve, providing the desired smoothness, there is considered the interpolation by cubic splines that in the intervals between the nodes are actually the cubic parabola, continuously connecting the nodes with the degree of smoothness. When imposing additional boundary conditions, data splines minimize its total curvature.
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Li, Dong, Xiao Li Wang, Si Mon Chi, Chang Rui Zhao, and Bin Yang. "A Clock Optimization Method in the Digital Zooming of the Image Signal Processing System." Advanced Materials Research 981 (July 2014): 315–18. http://dx.doi.org/10.4028/www.scientific.net/amr.981.315.
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We address the problem of producing an enlarged picture from a given digital image (zooming). We propose a method that tries to take into account the difficulty to apply the very fast clock in the digital zooming unit of an ISP system. The ISP system hardware is realized in the FPGA and the zooming algorithm is parabola interpolation architecture. This paper presents an optimization method by using a synchronization FIFO to greatly reduce the clock frequency of the digital zooming unit, and by this the power consumption is also decreased significantly.
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Chekalin, A. A., M. K. Reshetnikov, V. V. Shpilev, S. V. Borodulina, and S. A. Ryazanov. "MODELING ARCHITECTURAL FORM SURFACE DEPENDENT SECTIONS." Construction and industrial safety, no. 20(72) (2021): 53–58. http://dx.doi.org/10.37279/2413-1873-2021-20-53-58.
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For the design of surfaces in architecture, as a rule, universal techniques developed for other technical industries are used. First of all, these are general kinematic surfaces and interpolation cubic splines for modeling complex piecewise smooth surfaces. The authors propose to use the fourth degree inerodifferential spline developed by them for problems of geometric modeling of architectural forms. For calculations and constructions on a computer, the proposed spline is not much more complicated than traditional cubic splines, since it has one additional parameter - a coefficient. However, this allows you to locally control the shape of a curve or surface during design, that is, to change the shape in individual areas without affecting other areas. The article proposes a method for constructing a geometric model of the kinematic surface of dependent sections with a fourth degree parabola as a generator. When using cubic splines as a guide, the surface is a 3 × 4 non-uniform (heterogeneous) spline. The article shows that the surface on the basis of the proposed mathematical apparatus can be composite piecewise-smooth. A particular case of surface design is considered on the example of creating a model of the surface of the facade of a residential building according to the existing concept. The algorithm can be easily programmed and added as a tool to existing CAD systems.
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"Two Heuristic PID Tuning for a 4-DOF Robot Arm Control." International Journal of Recent Technology and Engineering 8, no. 4 (2019): 9945–50. http://dx.doi.org/10.35940/ijrte.d5205.118419.
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This paper discusses the development of closed-loop position control for the joint motor of a 4-DOF robot arm. In developing a practical robot, types of input and control algorithm are important elements in the control system. The objectives of this paper are to select an input type that could produce smooth arm’s motion and to apply PID control for the joints. Step and parabolic inputs have been tested as reference trajectory where the former used step signal as the constant value of motor angle while the latter requires calculation using spline interpolation method based on initial and end points of each joint motion given by user. From the latter, a parabolic curve input which consists of point-to-point values calculated for each 1ms sampling time was produced. Meanwhile, the PID position control tuned by trial and error and Ziegler Nichols (Z-N) methods were carried out and measured for comparison in terms of steady state error, overshoot and response time in real-time experiments. It could be observed that step input has caused abrupt movements and vibration to the arm body compared to the parabolic input that moved the arm smoothly to imitate motion like human. Meanwhile, the intuitive values of trial and error method were found to produce not much different with the Z-N tuned gains but comparatively produced small error against the parabolic input reference during the transient state. The result from this study is useful in the future to ensure position accuracy of robot joints when attending object for manipulation.
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Rattanadecho, P., and S. Wongwises. "Moving Boundary-Moving Mesh Analysis of Freezing Process in Water-Saturated Porous Media Using a Combined Transfinite Interpolation and PDE Mapping Methods." Journal of Heat Transfer 130, no. 1 (2008). http://dx.doi.org/10.1115/1.2780177.
Full textAbstract:
This paper couples the grid generation algorithm with the heat transport equations and applies them to simulate the thermal behavior of freezing process in water-saturated porous media. Focus is placed on establishing a computationally efficient approach for solving moving boundary heat transfer problem, in two-dimensional structured grids, with specific application to an undirectional solidification problem. Preliminary grids are first generated by an algebraic method, based on a transfinite interpolation method, with subsequent refinement using a partial differential equation (PDE) mapping (parabolic grid generation) method. A preliminary case study indicates successful implementation of the numerical procedure. A two-dimensional solidification model is then validated against available analytical solution and experimental results and subsequently used as a tool for efficient computational prototyping. The results of the problem are in good agreement with available analytical solution and experimental results.