共查询到20条相似文献,搜索用时 31 毫秒
1.
A method of transforming an ergodic random signal to its deterministic equivalent is presented. The transform requires that the spectral density of the random signal should be known. It also depends on the ability to obtain the inverse Fourier transform of a function. A specific relationship is developed to evaluate the root mean square of a random signal based on its deterministic equivalent. A sample application is presented to demonstrate that a step input can be equivalent to a hyperbolic spectral density. A linear system is subjected to the hyperbolic spectral density and the equivalent step. The calculated root mean square outputs are found to be identical. Deterministic equivalents for other random signals are also indicated. 相似文献
2.
An application of Prony's method for evaluating the acoustic power and location of sound sources from spatially sampled data is described. A sound source considered as a point source has an intensity proportional to the inverse square of the distance between source and observation point. The Fourier transform of this intensity function is an exponential function with a real exponent. The shift property of the Fourier transform results in a spectral change in the phase angle, which is expressed in the transform domain by a multiplicative exponential function of pure imaginary exponent. In this paper the usual time axis of the Fourier pair of time and frequency is treated as a variable denoting the location of the sound source. Accordingly, each spectral component of spatially sampled sound intensity generated by n point sources can be expressed as a linear combination of n complex exponentials. By applying Prony's method to the spectral data, these unknown exponents can be calculated numerically. This paper deals with an estimation procedure to find the location and power of a noise source. The estimation is done by minimizing the sum of the squares of the errors between the model and measured data. The proposed method has general applicability to problems where the so-called inverse square law for intensity can be assumed to be valid. 相似文献
3.
提出了一种基于分数阶傅里叶变换的模式测控一体化方法。利用分数阶傅里叶变换光路对光纤模式耦合态进行空间调制和相位调制,以实现模式的有效分解。与双重傅里叶变换(F2)法以及空间和频谱成像(S2)法相比,采用的分数阶傅里叶变换法,通过改变分数阶参数,控制模式的空间分布以及模式间的叠加状态,更易于分解出高阶模式。基于分数阶傅里叶变换的模式测量方法可在更广泛空间,研究模式的空间和相位叠加以及模式分解,也可退化为F2法和S2法。 相似文献
4.
K. Nagashima 《Optics & Laser Technology》1986,18(3)
An iterative method is presented which can uniformly distribute the Fourier transformed amplitudes of an original object. The method is effective in making phase quantized holograms whose amplitudes have constant values, and further, it is effective for such imaging systems where the decreased spectral information is desirable for transmission and storage. The hologram is produced by iterations of the Fourier transform and inverse Fourier transform operations. The image quality depends upon the number of iterations, however, a great many iterations will not necessarily lead to a marked improvement in the image quality because a rapid improvement is often achieved by only a few iterative operations. From our experiments, the iterative operations have made remarkable improvements in reconstructed images. The proposed method is also suitable for other types of holograms and for applications in imaging systems. 相似文献
5.
Applying the inverse scattering transform method, we show that a soliton modified by an amplitude or phase filter can evolve into several solitons. The oscillation period upon subsequent propagation follows from the wavenumbers of the emerging solitons and the radiation. Our results clarify spectral variations observed in recent supercontinuum experiments. 相似文献
6.
Orientation and spacing are important features of fringe patterns, especially in speckle photography when the displacement information of the object is determined by pointwisely filtering the double-exposure specklegram. The Fourier transform and Radon transform are both simple and effective tools for solving this problem, which extract the information in spectral domain and spatial domain, respectively. A hybrid method combining Radon transform and Fourier transform is also possible. The results can be further improved by enhanced Fourier transform and enhanced Radon transform. The theories, as well as real applications, are given in this paper. 相似文献
7.
A new property involving the recursion operator L and the Hamiltonian operator J of the nonlinear evolution equations integrable by the inverse scattering transform method is derived. It follows that these equations are completely determined in terms of the L and J operators.Unité Associée au CNRS No. 040768. Recherche Coopérative sur Programme No. 080264. 相似文献
8.
A spatial Fourier transform approach is proposed to investigate the effects of polarization changes and beam profile deformation of light during acousto-optic (AO) interaction in isotropic media. The behaviour of the total scattered optical fields inside the AO cell can be properly described by a vector wave equation of which the permittivity is perturbed by an acoustic wave propagating inside the medium. In the Bragg regime, using a spatial Fourier transform approach, two coupled differential equations can be derived from the wave equation to depict AO interaction in the spatial frequency domain. Analytic solutions, which comprise the effects of changing polarization, beam deformation and propagating diffraction, can be found from the coupled equations. Detailed numerical simulations, including Fourier transforming the incident light profile to calculate the spectra of the scattered light beams and, hence, their profiles in space using the inverse transform, are presented. 相似文献
9.
Lung-Hui Chen 《Waves in Random and Complex Media》2019,29(2):204-214
We study an inverse spectral theory in the thermo- and photo-acoustic tomography in imaging science. Under certain non-trapping hypothesis, we study the zero set of the Fourier transform of the observation data. The zero set corresponds to the spectrum of the interior transmission problem. We reduce the problem into an interior transformation problem of two indices of refractions. The inverse spectral problem is to study the inverse uniqueness of the indices of refraction. The zero distribution theory of entire function plays a role. 相似文献
10.
Homotopy perturbation method for modified Camassa-Holm and Degasperis-Procesi equations 总被引:1,自引:0,他引:1
In this Letter, homotopy perturbation method (HPM) is directly applied to modified Camassa-Holm and Degasperis-Procesi equations to obtain their solitary wave solutions. The results show the applicability, accuracy and efficiency of HPM in solving nonlinear differential equations with fully nonlinear dispersion term. It is predicted that HPM can be widely applied in engineering problems. 相似文献
11.
A strip-element method is presented for analyzing wave scattering by a crack in a laminated composite cylinder immersed in a fluid. In this approach, two-nodal-line and three-nodal-line axisymmetric strip elements are employed to model the fluid and laminated cylinder, respectively. Governing equations for the fluid and solid elements in the frequency domain are derived with a variational method and the Hamilton principle. The associated characteristic equations in the wave-number domain are obtained through Fourier transform techniques. Responses of the fluid-loaded cylinder to a line load are found by a modal-analysis method and inverse Fourier transform techniques. Numerical results are presented for cracked laminated composite cylinders submerged in water. Water is found to have strong influence on the scattered wave fields in a cracked laminated composite cylinder. 相似文献
12.
13.
Novel nonlinear superposition formulae are given for solutions of the class of nonlinear evolution equations solvable via the spectral transform associated with the Zakharov-Shabat spectral problem, and an algebraic procedure is provided to construct solutions of these equations. 相似文献
14.
A novel method for distortion-free optical pulse transmission is theoretically proposed and simulated, in which two time lenses formed by dispersion fibers and quadratic phase modulations are utilized. One is used as an optical inverse Fourier transformation (OIFT) device to transform the initial time-domain data to frequency-domain one at the transmitter and the other as an optical Fourier transformation (OFT) device to recover the data at the receiver. By using the unchanged spectral envelope in linear optical fiber communication, the initial data can be recovered. Through simulations, a 10× 100 Gb/s intensity-modulated direct-detection (IM-DD) dense wavelength division multiplexing (DWDM) system over 20000 km transmission without the compensation for polarization mode dispersion (PMD) and dispersion slope is achieved, which can be used to upgrade the current 100Gb/s IM-DD system to a 100-Gb/s one directly. 相似文献
15.
16.
A new method of stability investigation is presented for solutions of nonlinear equations integrable with the help of the inverse scattering transform (IST). The stability problem for periodic nonlinear waves in weakly dispersive media is solved with respect to transverse perturbations. It is shown that for positive dispersion media one-dimensional waves are unstable, and for negative dispersion such waves are stable. 相似文献
17.
基于投影栅线法测量物体三维轮廓的一点改进 总被引:1,自引:1,他引:0
研究了利用投影栅线法测量光滑鼠标的三维轮廓。对传统的傅里叶变换轮廓术提出了一点改进,在傅里叶变换之后,不对频谱部分频移,而是直接滤出需要的高、低频部分,再分别进行傅里叶逆变换,就可以得到与高度有关的相位差。该方法与传统的方法相比,减少了3次频移的过程,大大减少了计算量,也提高了滤波的精度。实验结果表明:只需要0.1 s就可以完成测量过程,测量精度达到0.2 mm, 可以成功实现光滑物体的三维轮廓测量。 相似文献
18.
A. Tadeu C. S. Chen J. Antόnio & Nuno Simõ es 《advances in applied mathematics and mechanics.》2011,3(5):572-585
Fourier transform is applied to remove the time-dependent variable in the
diffusion equation. Under non-harmonic initial conditions this gives rise to a
non-homogeneous Helmholtz equation, which is solved by the method of
fundamental solutions and the method of particular solutions. The particular
solution of Helmholtz equation is available as shown in [4, 15].
The approximate solution in frequency domain is then inverted
numerically using the inverse Fourier transform algorithm. Complex frequencies
are used in order to avoid aliasing phenomena and to allow the computation of
the static response. Two numerical examples are given to illustrate the
effectiveness of the proposed approach for solving 2-D diffusion equations. 相似文献
19.
差分吸收光谱法(differential optical absorption spectroscopy,DOAS)是一种常用的污染气体监测方法,对所监测的光谱数据去噪可以提高反演精度。可采用傅里叶变换(fast Fourier transform, FFT)滤波法滤除光谱数据中的噪声,但该算法本身会引入误差。提出一种线性调频Z变换法(chirp Z transform,CZT),通过对傅里叶变换之后的频谱进行局部细化,能够在保留傅里叶变换滤波法去噪效果的基础上,对算法的误差进行补偿,从而进一步提高反演精度。实验配置了SO2及NO2进行浓度反演,结果表明,直接采用相除法反演浓度时误差较大且很不稳定,线性调频Z变换法能够获得比傅里叶变换滤波法更高的反演精度。模拟了SO2和NO2混合气体实验,频谱分析结果表明FFT算法无法解决特征吸收结构被扭曲、削弱等问题,CZT算法能完成特定频段频谱的精细化重构。 相似文献
20.
Dongqi Yang Jieqiu Zhang Jianqi Zhang Biwu Chen Jiafu Wang Yongfeng Li 《Applied Physics A: Materials Science & Processing》2012,109(2):477-480
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. 相似文献