共查询到14条相似文献,搜索用时 78 毫秒
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分数傅里叶变换是傅里叶变换的广义形式,提供了介于时域和频域之间的多分数域信号表征,为非平稳信号处理和线性时变系统分析开辟了新途径,应用十分广泛。本文首先总结近年来分数傅里叶变换的理论研究成果,包括分数傅里叶变换的数值计算、衍生的离散分数变换、分数域采样、分数域滤波与参数估计、多分数域分析。然后介绍分数傅里叶变换在工程和实践中的应用,包括雷达、通信、图像加密、光学干涉测量、医学、生物、机械仪器等。最后对分数傅里叶变换理论及其应用的未来研究方向进行展望。
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针对强混响背景下经典的最小均方误差(Least Mean Square,LMS)滤波算法难以有效地实现信混分离的问题,提出一种基于分数阶傅里叶变换的自适应LMS算法。首先将混响信号和自适应LMS滤波算法中的参考信号进行分数阶傅里叶变换,寻找最优变换域,并在分数阶域进行带通滤波,然后将得到的信号进行分数阶傅里叶反变换,最后将基于正态分布曲线的变步长LMS算法应用于此混响条件下进行滤波。仿真和海试数据验证结果表明,在信混比为0 dB的情况下,算法仍可以有效地滤除混响,使信混比提高6dB。 相似文献
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A novel double-image encryption algorithm is proposed, which can simultaneously encrypt two images into a single one as the amplitude of a fractional Fourier transform with two different groups of fractional orders. The two original images can be retrieved independently by fractional Fourier transforms with two different groups of fractional orders, one public phase mask, and two different private phase masks. The proposed approach can enlarge the key space, achieve faster convergence in the iterative process, and avoid cross-talk between the two images in reconstruction. Numerical simulations are presented to verify its validity and efficiency. 相似文献
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A new modification of the output plane constraint is used in the iterative algorithm for designing diffractive phase plates (DPPs) to produce spatial beam smoothing in the fractional Fourier (FRT) domain. Compared with previously published algorithms, this algorithm can provide faster convergence, more powerful ability to overcome the local minimum problem and better smoothing quality. By computer simulation, it has shown that the DPP designed by this algorithm has the advantages of high uniformity at the main lobe, low profile error and steep edge. 相似文献
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Alieva T Calvo ML 《Journal of the Optical Society of America. A, Optics, image science, and vision》2003,20(3):533-541
The importance of the amplitude and phase in the fractional Fourier transform (FT) domain is analyzed on the basis of the rectangular signal and the real-world image. The quality of signal restoration from only the amplitude or from only the phase of its fractional FT by applying the inverse fractional FT is considered. It is shown that the signal reconstructed from the amplitude of the fractional FT usually reveals the main features of the original signal only for relatively low fractional orders. On the basis of phase information in the fractional FT domains, significant details of the signal can be obtained for nearly all fractional orders. 相似文献
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We first discuss the discrete fractional Fourier transform and present some essential properties. We then propose a recursive algorithm to implement phase retrieval from two intensities in the fractional Fourier transform domain. This approach can significantly simplify computational manipulations and does not need an initial phase estimate compared with conventional iterative algorithms. Simulation results show that this approach can successfully recover the phase from two intensities. 相似文献
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Chirp filtering in the fractional Fourier domain 总被引:2,自引:0,他引:2
In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of the Wigner-distribution function by an angle connected with the FRT order. Thus with the FRT tool a chirp and a delta function can be transformed one into the other. Taking the chirp as additive noise, the FRT is used for filtering the line delta function in the appropriate fractional Fourier domain. Experimental filtering results for a Gaussian input function, which is modulated by an additive chirp noise, are shown. Excellent agreement between experiments and computer simulations is achieved. 相似文献
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Durak L Ozdemir AK Arikan O 《Journal of the Optical Society of America. A, Optics, image science, and vision》2008,25(3):765-772
A joint fractional domain signal representation is proposed based on an intuitive understanding from a time-frequency distribution of signals that designates the joint time and frequency energy content. The joint fractional signal representation (JFSR) of a signal is so designed that its projections onto the defining joint fractional Fourier domains give the modulus square of the fractional Fourier transform of the signal at the corresponding orders. We derive properties of the JFSR, including its relations to quadratic time-frequency representations and fractional Fourier transformations, which include the oblique projections of the JFSR. We present a fast algorithm to compute radial slices of the JFSR and the results are shown for various signals at different fractionally ordered domains. 相似文献
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Gopinathan U Situ G Naughton TJ Sheridan JT 《Journal of the Optical Society of America. A, Optics, image science, and vision》2008,25(1):108-115
The signal extraction method based on intensity measurements in two close fractional Fourier domains is examined by using the phase space formalism. The fractional order separation has a lower bound and an upper bound that depend on the signal at hand and the noise in the optical system used for measurement. On the basis of a theoretical analysis, it is shown that for a given optical system a judicious choice of fractional order separation requires some a priori knowledge of the signal bandwidth. We also present some experimental results in support of the analysis. 相似文献
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By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions. We introduce what we believe to be a new Fourier domain preconditioned conjugate gradient (FD-PCG) algorithm for atmospheric tomography, and we compare its performance against an existing multigrid preconditioned conjugate gradient (MG-PCG) approach. Numerical results indicate that on conventional serial computers, FD-PCG is as accurate and robust as MG-PCG, but it is from one to two orders of magnitude faster for atmospheric tomography on 30 m class telescopes. Simulations are carried out for both natural guide stars and for a combination of finite-altitude laser guide stars and natural guide stars to resolve tip-tilt uncertainty. 相似文献
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为了提高传统双随机相位编码图像光学加密系统的安全性,并减少其所需要处理的数据量,提出了一种基于压缩感知及量子Logistic混沌映射的彩色图像非对称光学加密方法。针对彩色图像加密过程中所需要处理数据量过大问题,首先利用压缩感知理论减少加密系统所需要处理的数据量,其次,将彩色图像三通道转换为单通道加密来减少数据量。针对传统光学加密系统为线性系统问题,采用基于相位截断的非对称光学加密方法进行加密。针对光学加密系统加密密钥为随机相位板不方便传输问题,利用量子混沌产生系统所需要的随机相位板。结果表明,此算法可以获得较为理想的图像加密和解密效果。 相似文献