共查询到20条相似文献,搜索用时 859 毫秒
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Fractional Fourier transform (FRFT) plays an important role in many fields of optics and signal processing. This paper considers the problem of reconstructing a fractional bandlimited signal with FRFT. We propose a novel reconstruction method for fractional bandlimited signals using the fractional Fourier series (FRFS). The advantage is that the sampling expansion can be deduced directly not based on the Shannon theorem. By utilizing the generalized form of Parseval’s relation for complex FRFS, we obtain the sampling expansion for fractional bandlimited signals with FRFT. We show that the sampling expansion for fractional bandlimited signals with FRFT is a special case of Parseval’s relation for complex FRFS. 相似文献
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Fractional Fourier transform (FRFT) plays an important role in many fields of optics and signal processing. This paper considers the problem of real-time measurement of the spectrum of a signal in the FRFT domain. In this paper, we propose two approaches for real-time measurement of the FRFT of a signal based on modulation and bandpass filtering systems. The relation is established between the linear frequency modulation (LFM or chirp) spectrum and the FRFT of its envelope. In addition, two applications for spectrum measurement are presented in the FRFT domain. The LFM signal can be bandlimited in the Fourier transform (FT) domain through spectrum measurement associated with bandpass filtering method. The results can also be useful in the problems related to swept-frequency filter for measurement in the FRFT domain. 相似文献
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A fractional Gabor transform (FRGT) is proposed. This new transform is a generalization of the conventional Gabor transform (GT) based on the Fourier transform to the windowed fractional Fourier transform (FRFT). The FRGT provides analyses of signals in both the real space and the FRFT frequency domain simultaneously. The space-FRFT frequency pattern can be rotated as the fractional order changes. The FRGT has an additional freedom, compared with the conventional GT, i.e., the transform order. The FRGT may offer a useful tool for guiding optimal filter design in the FRFT domain in signal processing. 相似文献
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An optical waveform pre-distortion method is proposed in reducing the temporal broadening of pulse based on the optical implementation of time domain fractional Fourier transform (FRFT). Moreover, a new analysis of the dispersion and self-phase modulation effects is investigated. The simulation results show that prechirp coefficient and proper fractional orders of FRFT can be beneficial in mitigating pulse broadening. 相似文献
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利用Wigner分布函数(WDF)方法,对光束的分数傅里叶变换特性进行了研究.以厄米 高斯(H G)光束为例,导出了H G光束在分数傅里叶变换面上光强分布的解析公式和H G光束在分数傅里叶变换面上束宽的解析计算公式.通过数值计算研究了H G光束光强随分数傅里叶变换阶数变化的规律.研究表明:选取适当的分数傅里叶变换阶数p,在x,y方向可以得到相等束宽的对称光强分布.
关键词:
Wigner分布函数
厄米 高斯(H G)光束
分数傅里叶变换 相似文献
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We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT), is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite-Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M=+∞, M=4k(k is a natural number), and M=4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided. 相似文献
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A new kind of laser beams named the elliptical Hermite-sinusoidal-Gaussian beams (EHSGBs) is introduced and defined by use of tensor method, and the elliptical Hermite-cosh-Gaussian beam (EHChGB) can be regarded as special case of EHSGBs. The fractional Fourier transform (FRFT) is applied to treat the propagation of EHChGBs. An analytical expression for an EHChGB passing through an FRFT system is derived by using vector integration. Some numerical simulations are illustrated for the propagation properties of EHChGBs through FRFT systems. 相似文献
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Luís M. Bernardo 《Optics Communications》1997,140(4-6):195-198
A study of Talbot self-imaging associated with fractional Fourier transforms (FRFTs) of real and complex orders, as realised by bulk lenses, is presented. Self-images of a periodic object, corresponding to different orders, can be observed in different FRFT planes, herein called Talbot-FRFT planes. The spatial scaling factor of the self-images is shown to be a harmonic function of the FRFT order. 相似文献
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Several properties of fractional Fourier transform (FRFT) have been studied recently and many are being investigated at present. In this article, scaling property of the FRFT is generalized and some of its applications are suggested. Some extensions of the sampling relations in the FRFT domain are also presented. The issues related to connections between the FRFT and other signal transforms such as scale transform, fractional Mellin transform, and chirp z-transform, are also investigated. 相似文献
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Based on Collins integral formula and the fact that a hard aperture function can be expanded into a finite sum of complex Gaussian functions, the propagation properties of cosh-squared-Gaussian beam passing through ideal and apertured FRFT systems have been studied, and some comparisons between using the methods of analytical formula and diffraction integral formula have been done. Further, the studies indicate that the normalized intensity distributions on FRFT plane depend on the fractional order, truncation parameter and initial beam parameter Ω. Variations of normalized intensity distributions with FRFT order are periodic: when the impact of aperture cannot be ignored, the variation period is 4; and when the impact of aperture can be ignored, the variation period is 2. 相似文献
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Based on the generalized Huygens–Fresnel integral, the analytical expressions for Airy beams through three types of fractional Fourier transform (FRFT) optical systems (Lohmann I, Lohmann II and quadratic graded-index systems) are derived. Using the two analytical expressions, the propagation properties of Airy beams for the three types of FRFT optical systems are discussed in detail with numerical examples. Results indicate that the intensity of Airy beams periodically changes and remains form-invariant with the changing of fractional order p for the three types of FRFT optical systems. 相似文献
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Cosh-Gaussian beams are of practical interest because they are more efficient at extracting energy from conventional laser amplifiers, and they have some important applications because their profiles can closely resemble the flat-top field distribution by choosing suitable beam parameters of cosh parts. The fractional Fourier transform (FRFT) is applied to treat the propagation of off-axial elliptical cosh-Gaussian beams (EChGBs). By the use of vector integration, the analytical expression for an off-axial EChGB passing through a FRFT system is derived in terms of tensor method. Our formula provides a convenient way for studying the FRFT of off-axial EChGBs; some numerical simulations are also given. 相似文献
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为研究非相干的1维线阵离轴高斯光束通过分数傅里叶变换(FRFT)系统的传输特性,利用Collins积分公式,导出了其在FRFT面上的光强分布解析式,并利用此解析式作数值计算和分析。研究表明:非相干的1维线阵离轴高斯光束在FRFT面上的光强分布由FRFT的阶数和子光束数目共同决定,其归一化的光强分布随FRFT的阶数周期性变化,周期为2;子光束数目的大小及其奇偶性对归一化光强分布的影响取决于FRFT的阶数;轴上归一化光强分布也随FRFT的阶数周期性变化,变化周期也为2。 相似文献
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An analytical expression of an Airy beam passing through a fractional Fourier transform (FRFT) system is presented. The effective beam size of the Airy beam in the FRFT plane is also derived. The influences of the order of FRFT, the modulation parameter, and the transverse scale on the normalized intensity distribution and the effective beam size of an Airy beam in the FRFT plane are examined. The order of FRFT controls the effective beam size and the orientation of the beam spot. The modulation parameter affects the effective beam size and the number of lateral side lobes. The normalized intensity distribution and the effective beam size are both proportional to the transverse scale. 相似文献