Topic
Sinc function
About: Sinc function is a research topic. Over the lifetime, 1306 publications have been published within this topic receiving 20513 citations. The topic is also known as: sinc & cardinal sine function.
Papers published on a yearly basis
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Papers
TL;DR: This work proves sampling theorems for classes of signals and kernels that generalize the classic "bandlimited and sinc kernel" case and shows how to sample and reconstruct periodic and finite-length streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels.
Abstract: The authors consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials. Even though these signals are not bandlimited, we show that they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theorems for classes of signals and kernels that generalize the classic "bandlimited and sinc kernel" case. In particular, we show how to sample and reconstruct periodic and finite-length streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinite-length signals with finite local rate of innovation, we show local sampling and reconstruction based on spline kernels. The key in all constructions is to identify the innovative part of a signal (e.g., time instants and weights of Diracs) using an annihilating or locator filter: a device well known in spectral analysis and error-correction coding. This leads to standard computational procedures for solving the sampling problem, which we show through experimental results. Applications of these new sampling results can be found in signal processing, communications systems, and biological systems.
1,369 citations
TL;DR: In this paper, the capability of embedded piezoelectric wafer active sensors (PWAS) to excite and detect tuned Lamb waves for structural health monitoring is explored.
Abstract: The capability of embedded piezoelectric wafer active sensors (PWAS) to excite and detect tuned Lamb waves for structural health monitoring is explored. First, a brief review of Lamb waves theory is presented. Second, the PWAS operating principles and their structural coupling through a thin adhesive layer are analyzed. Then, a model of the Lamb waves tuning mechanism with PWAS transducers is described. The model uses the space domain Fourier transform. The analysis is performed in the wavenumber space. The inverse Fourier transform is used to return into the physical space. The integrals are evaluated with the residues theorem. A general solution is obtained for a generic expression of the interface shear stress distribution. The general solution is reduced to a closed-form expression for the case of ideal bonding which admits a closed-form Fourier transform of the interfacial shear stress. It is shown that the strain wave response varies like sin a, whereas the displacement response varies like sinc a. ...
986 citations
Book•
24 Jun 1993
TL;DR: Sinc methods as mentioned in this paper are based on the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems, such as problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems.
Abstract: Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Perhaps not so many mathematicians, scientists, and engineers recognize that the Discrete Fourier Transform is one of a family of symbolic formulae called Sinc methods. Sinc methods are based upon the Sinc function, a wavelet-like function replete with identities which yield approximations to all classes of computational problems. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems. Written by the principle authority on the subject, this book introduces Sinc methods to the world of computation. It serves as an excellent research sourcebook as well as a textbook which uses analytic functions to derive Sinc methods for the advanced numerical analysis and applied approximation theory classrooms. Problem sections and historical notes are included.
892 citations
Book•
1 Jan 1987TL;DR: This paper presents numerical methods for solving linear algebra problems on an arc 'Gamma' using the Sinc-Galerkin method, a version of which has already been described in detail in Appendix A.
Abstract: 1. Preliminary material 2. Numerical methods on the real line 3. Numerical methods on an arc 'Gamma' 4. The Sinc-Galerkin method 5. Steady problems 6. Time-dependent problems Appendix A. Linear algebra References.
495 citations
TL;DR: In this article, a general perturbation theory of the propagation of a signal in an optical fiber in the presence of amplification and Kerr nonlinearity was developed, valid for arbitrary pulse shapes.
Abstract: In this paper, we develop a general first-order perturbation theory of the propagation of a signal in an optical fiber in the presence of amplification and Kerr nonlinearity, valid for arbitrary pulse shapes. We obtain a general expression of the sampled signal after optical filtering, coherent detection, and optimal sampling. We include intrachannel and as well as interchannel nonlinear effects. We obtain simplified expressions in the case in which the accumulated dispersion is high (equivalent to the far-field limit in paraxial optics). This general theory is applied in detail to the special case of spectral-efficient sinc pulses. This exercise shows that the characteristics of the neighboring wavelength-division multiplexed channels are essential in determining the nonlinear impairments.
429 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 40 |
| 2024 | 49 |
| 2023 | 69 |
| 2022 | 132 |
| 2021 | 77 |