Tighter bounds for the inequalities of Sinc function based on reparameterization

In this paper, we consider a new method for forest canopy height estimation using TanDEM-X single-pass radar interferometry. We exploit available information from sample-based, space-borne LiDAR systems, such as the Global Ecosystem Dynamics Investigation (GEDI) sensor, which offers high-resolution vertical profiling of forest canopies. To respond to this, we have developed a new extended Fourier-Legendre series approach for fusing high-resolution (but sparsely spatially sampled) GEDI LiDAR waveforms with TanDEM-X radar interferometric data to improve wide-area and wall-to-wall estimation of forest canopy height. Our key methodological development is a fusion of the standard uniform assumption for the vertical structure function (the SINC function) with LiDAR vertical profiles using a Fourier-Legendre approach, which produces a convergent series of approximations of the LiDAR profiles matched to the interferometric baseline. Our results showed that in our test site, the Petawawa Research Forest, the SINC function is more accurate in areas with shorter canopy heights (<~27 m). In taller forests, the SINC approach underestimates forest canopy height, whereas the Legendre approach avails upon simulated GEDI forest structural vertical profiles to overcome SINC underestimation issues. Overall, the SINC + Legendre approach improved canopy height estimates (RMSE = 1.29 m) compared to the SINC approach (RMSE = 4.1 m).

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New bounds of Sinc function by using a family of exponential functions

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas ◽

10.1007/s13398-021-01133-0 ◽

2021 ◽

Vol 116 (1) ◽

Author(s):

Xiao-Diao Chen ◽

Hui Wang ◽

Junle Yu ◽

Zhanglin Cheng ◽

Ping Zhu

Keyword(s):

Sinc Function ◽

Exponential Functions

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Nonsmooth and level-resolved dynamics illustrated with a periodically driven tight-binding model

ScienceOpen Research ◽

10.14293/s2199-1006.1.sor-phys.a2cem4.v2 ◽

2015 ◽

Author(s):

Masudul Haque ◽

jiang min zhang

Keyword(s):

Perturbation Theory ◽

Transition Probability ◽

Tight Binding ◽

Coarse Graining ◽

Sinc Function ◽

Tight Binding Model ◽

Binding Model ◽

Periodically Driven ◽

Perturbative Regime ◽

Simple Equality

Abstract We point out that in the first-order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact locations of the eigenvalues in the continuum spectrum, in contrast to coarse-graining ideas. Underlying this nonsmooth and level-resolved dynamics is a simple equality about the sinc function sinc x ≡ sin x/x. These physical effects appear in many systems with approximately equally spaced spectra, and are also robust for larger amplitude coupling beyond the domain of perturbation theory. We use a one-dimensional periodically driven tight-binding model to illustrate these effects, both within and outside the perturbative regime.

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Studying and Analysis of a Novel RK-Sinc Scheme

Applied Computational Electromagnetics Society ◽

10.47037/2020.aces.j.360214 ◽

2021 ◽

Vol 36 (2) ◽

pp. 213-217

Author(s):

Min Zhu

Keyword(s):

Electromagnetic Field ◽

Time Derivative ◽

Strong Stability ◽

Numerical Dispersion ◽

Sinc Function ◽

Order Method ◽

Strong Stability Preserving ◽

High Order Method ◽

Computational Memory ◽

Runge Kutta

In this paper, a novel high-order method, Runge-Kutta Sinc (RK-Sinc), is proposed. The RK-Sinc scheme employs the strong stability preserving Runge-Kutta (SSP-RK) algorithm to substitute time derivative and the Sinc function to replace spatial derivates. The computational efficiency, numerical dispersion and convergence of the RK-Sinc algorithm are addressed. The proposed method presents the better numerical dispersion and the faster convergence rate both in time and space domain. It is found that the computational memory of the RK-Sinc is more than two times of the FDTD for the same stencil size. Compared with the conventional FDTD, the new scheme provides more accuracy and great potential in computational electromagnetic field.

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Optimization of laser ranging algorithm based on asymmetric sinc function fitting

Infrared and Laser Engineering ◽

10.3788/irla201746.0806008 ◽

2017 ◽

Vol 46 (8) ◽

pp. 806008

Author(s):

郭荣幸 Guo Rongxing ◽

赵亚飞 Zhao Yafei ◽

马鹏阁 Ma Pengge ◽

陈恩庆 Chen Enqing

Keyword(s):

Sinc Function ◽

Laser Ranging ◽

Function Fitting

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Very-Long-Period (VLP) Seismic Artifacts during the 2018 Caldera Collapse at Kīlauea, Hawai‘i

Seismological Research Letters ◽

10.1785/0220200083 ◽

2020 ◽

Vol 91 (6) ◽

pp. 3417-3432

Author(s):

Ashton F. Flinders ◽

Ingrid A. Johanson ◽

Phillip B. Dawson ◽

Kyle R. Anderson ◽

Matthew M. Haney ◽

...

Keyword(s):

Amplitude Spectrum ◽

Low Frequency ◽

Seismic Signal ◽

Sinc Function ◽

Caldera Collapse ◽

Velocity Amplitude ◽

Long Period ◽

Ramp Function ◽

Instrument Response ◽

Summit Caldera

Abstract Throughout the 2018 eruption of Kīlauea volcano (Hawai‘i), episodic collapses of a portion of the volcano’s summit caldera produced repeated Mw 4.9–5.3 earthquakes. Each of these 62 events was characterized by a very-long-period (VLP) seismic signal (>40 s). Although collapses in the later stage of the eruption produced earthquakes with significant amplitude clipping on near-summit broadband seismometers, the first 12 were accurately recorded. For these initial collapse events, we compare average VLP seismograms at six near-summit locations to synthetic seismograms derived from displacements at collocated Global Positioning System stations. We show that the VLP seismic signal was generated by a radially outward and upward ramp function in displacement. We propose that at local distances the period of the VLP seismic signal is solely dependent on the duration of this ramp function and the instrument transfer function, that is, the seismic VLP is an artifact of the bandlimited instrument response and not representative of real ground motion. The displacement ramp function imposes a sinc-function velocity amplitude spectrum that cannot be fully recovered through standard seismic instrument deconvolution. Any near-summit VLP signals in instrument-response-corrected velocity or displacement seismograms from these collapse events are subject to severe band limitation. Similarly, the seismic amplitude response is not flat through the low-frequency corner, for example, instrument-response-uncorrected seismograms scaled by instrument sensitivity are equally prone to band limitation. This observation is crucial when attempting to clarify the different contributions to the VLP source signature. Not accounting for this effect could lead to misunderstanding of the magmatic processes involved.

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