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线性调频信号分数阶频谱特征分析 总被引:3,自引:0,他引:3
线性调频信号是一种典型的非平稳信号,广泛应用于雷达、声纳、通信等领域.分数阶Fourier变换是一种新兴的时频变换,由于其独特的性质,成为线性调频信号检测与参数估计的一种良好工具.尤其是,作为一种线性变换,分数阶Fourier变换在处理多分量线性调频信号时能够避免交叉项的干扰.但是,多分量线性调频信号在分数阶Fourier域也存在相互影响的问题.为了分析该问题,研究线性调频信号在分数阶Fourier域的频谱分布特征是非常必要的.本文根据分数阶Fourier变换的定义以及分数阶Fourier变换与时频分布的关系,分析了线性调频信号在分数阶Fourier域的频谱分布特征,以及线性调频信号的分数阶频谱分布与分数阶旋转角α的变化关系;根据离散分数阶Fourier变换的实现算法,讨论了线性调频信号在离散分数阶Fourier变换条件下的分数阶频谱的分布特征,以及线性调频信号在分数阶Fourier域的能量谱的近似表达式.最后,利用LFM信号的分数阶频谱的分布特征,分析了多分量LFM信号中的信号尖峰偏移问题,并给出信号尖峰发生偏移的条件.本文为定量分析分数阶Fourier域多分量线性调频信号之间的相互影响奠定了基础,为改善分数阶Fourier变换对多分量线性调频信号的处理能力提供了参考. 相似文献
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本文从分数阶Fourier变换与时频分布的关系入手,在离散分数阶Fourier变换算法基础上导出了单分量chirp信号分数阶Fourier谱强度的近似表达,并依据分数阶Fourier变换的线性性质,得到了调频率不同的两分量chirp信号间分数阶Fourier谱相互遮蔽的量化结果,给出了图例分析,并进行了仿真验证.通过本文的分析可以知道分数阶Fourier域中调频率不同的多分量chirp信号间的相互遮蔽主要取决于各自的幅度、调频率和采样时间.当多分量chirp信号幅度、调频率确定后,可以通过延长采样时间来降低各分量间的相互遮蔽. 相似文献
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海杂波FRFT域的分形特性及目标检测 总被引:3,自引:1,他引:2
通过对实测海杂波数据的仿真分析,论证了海杂波在分数阶Fourier变换域具有分形特征,而且有目标单元和无目标单元存在分数维差异,这种分数维差异在分数阶Fourier变换域存在一个最大值。基于此特征提出了基于分数阶Fourier变换域海杂波分数维差异的目标检测方法,此方法通过检测回波信号分数阶Fourier变换域分数维的变化的最大值达到检测目标的目的,这比基于时域分数维差异的方法具有更好的检测效果。最后通过对实测海杂波数据进行仿真,证实了该方法的有效性。 相似文献
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作为处理非平稳信号的一种重要工具,模糊函数(ambiguity function,AF)已经被广泛应用于雷达信号处理、声纳技术等领域,并对线性调频信号信号的参数估计具有极好的处理能力。但对应用于众多领域的二次调频信号,模糊函数就显得无能为力了。作为Fourier变换的更广义形式,分数阶Fourier变换(Fractional Fourier transform)近年来受到了广泛关注。为解决二次调频信号的估计问题,本文研究了基于分数阶Fourier变换的模糊函数,给出了这种变换的一些新的重要性质,如共轭对称性、Moyal公式、时移性等,推导出了它与经典模糊函数、基于分数阶Fourier变换的Wigner分布、短时Fourier变换、小波变换等其他时频变换的关系。作为应用,最后本文用这种分数阶模糊函数来估计二次调频信号,应用实例的仿真结果表明了分数阶模糊函数在估计二次调频信号参数方面的可行性和有效性。 相似文献
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基于分数阶Fourier变换的反辐射导弹检测技术 总被引:1,自引:0,他引:1
针对反辐射导弹的检测问题,主要是消除载机信号的干扰.本文研究了单频信号和线性调频信号的分数阶Fourier变换模函数的时移特性.研究表明,单频信号和线性调频信号的FRFT模函数具有不同的时移特性.分数阶Fourier变换是线性变换,不存在交叉项,采用分数阶Fourier变换搜索匹配动目标信号,使其能量汇聚.根据以上特点本文提出了一种基于观测信号以及其时延信号的分数阶Fourier变换模之差的反辐射导弹检测方法.此方法可以有效的消除载机信号的干扰,并且对背景噪声幅度有一定的抑制作用.仿真结果表明,在低信噪比下能有效的检测出反辐射导弹. 相似文献
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介绍了一种从分数阶Fourier变换(FRFT)思想导出的分数阶Fourier级数(FRFS)展开方法,可以看作为Fourier级数的进一步推广,在研究非平稳信号中有着重要的应用。分数阶Fourier级数以一组有限时域内的正交Chirp信号为基函数来逼近分析信号,与Fourier级数相比,在分析非平稳信号中具有更大的灵活性。文中给出了Chirp信号FRFS分解的解析表示,分析了FRFS展开系数的振荡特性;同时对不同参数下的FRFS收敛速度进行了研究和计算机仿真,对于工程实际中的计算具有较好的参考价值。 相似文献
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线性调频(LFM或Chirp)信号在雷达信号中已得到广泛使用。文中定性地分析了Radon-Wigner变换、分数阶Fourier变换和修正Chirp-Fourier变换检测离散Chirp信号的性能,计算了其对离散Chirp信号的能量聚集峰值。仿真试验表明,三种方法在信号长度为256点、信噪比为-5dB下都取得了较好的检测效果,相比之下,Radon-Wigner变换对离散Chirp信号的检测性能最优。 相似文献
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分数阶Fourier变换作为最新提出的一种分析工具,其变换域同时具有信号的时域信息和频域信息,其实质是Fourier变换的一种广义形式,较适合处理非平稳信号。文中提出一种基于分数阶Fourier变换的多分量LFM信号参数估计与分离方法。通过在分数阶Fourier域搜索峰值点来对多分量LFM信号进行检测和参数估计,同时结合逐次消去思想来分离多个未知参数的LFM信号,抑制了强信号分量对弱信号分量的遮蔽干扰。 相似文献
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分数阶傅立叶变换比傅立叶变换更具有一般性,多年来引起人们深入研究.由于连续的分数阶傅立叶变换在工程实现时都要抽样离散化,直接对连续分数阶傅立叶变换的核离散化会失去很多重要的性质,因此人们研究它的离散实现并保持它具有与连续分数阶变换同样的性质.本文提出了一种新的交换矩阵实现离散分数阶傅立叶变换,其变换的离散核矩阵与连续变换的分数阶傅立叶变换核有相似性,诸如酉特性、可加性、正交性和可逆性.仿真结果证实了所提出的分数阶傅立叶变换核与连续分数阶傅立叶变换核的相似性以及两种变换对矩形信号这种典型信号的分数阶傅立叶变换的相似性. 相似文献
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Closed-form discrete fractional and affine Fourier transforms 总被引:15,自引:0,他引:15
Soo-Chang Pei Jian-Jiun Ding 《Signal Processing, IEEE Transactions on》2000,48(5):1338-1353
The discrete fractional Fourier transform (DFRFT) is the generalization of discrete Fourier transform. Many types of DFRFT have been derived and are useful for signal processing applications. We introduce a new type of DFRFT, which are unitary, reversible, and flexible; in addition, the closed-form analytic expression can be obtained. It works in performance similar to the continuous fractional Fourier transform (FRFT) and can be efficiently calculated by the FFT. Since the continuous FRFT can be generalized into the continuous affine Fourier transform (AFT) (the so-called canonical transform), we also extend the DFRFT into the discrete affine Fourier transform (DAFT). We derive two types of the DFRFT and DAFT. Type 1 is similar to the continuous FRFT and AFT and can be used for computing the continuous FRFT and AFT. Type 2 is the improved form of type 1 and can be used for other applications of digital signal processing. Meanwhile, many important properties continuous FRFT and AFT are kept in the closed-form DFRFT and DAFT, and some applications, such as filter design and pattern recognition, are also discussed. The closed-form DFRFT we introduce has the lowest complexity among all current DFRFTs that is still similar to the continuous FRFT 相似文献
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The speech signal and noise signal are the typical non-stationary signals,however the speech signa is short-stationary synchronously.Presently,the denoising methods are always executed in frequency domain due to the short-time stationarity of the speech signal.In this article,an improved speech denoising algorithm based on discrete fractional Fourier transform(DFRFT)is pre sented.This algorithm contains linear optimal filtering and median filtering.The simulation shows that it can easily eliminate the noise compared to Wiener filtering improve the signal to noise ratio(SNR),and enhance the original speech signal. 相似文献
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Discrete Fractional Fourier Transform Based on New Nearly Tridiagonal Commuting Matrices 总被引:1,自引:0,他引:1
《Signal Processing, IEEE Transactions on》2006,54(10):3815-3828
Based on discrete Hermite–Gaussian-like functions, a discrete fractional Fourier transform (DFRFT), which provides sample approximations of the continuous fractional Fourier transform, was defined and investigated recently. In this paper, we propose a new nearly tridiagonal matrix, which commutes with the discrete Fourier transform (DFT) matrix. The eigenvectors of the new nearly tridiagonal matrix are shown to be DFT eigenvectors, which are more similar to the continuous Hermite–Gaussian functions than those developed before. Rigorous discussions on the relations between the eigendecomposition of the newly proposed nearly tridiagonal matrix and the DFT matrix are described. Furthermore, by appropriately combining two linearly independent matrices that both commute with the DFT matrix, we develop a method to obtain DFT eigenvectors even more similar to the continuous Hermite–Gaussian functions (HGFs). Then, new versions of DFRFT produce their transform outputs closer to the samples of the continuous fractional Fourier transform, and their applications are described. Related computer experiments are performed to illustrate the validity of the works in this paper. 相似文献
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Soo-Chang Pei Min-Hung Yeh Chien-Cheng Tseng 《Signal Processing, IEEE Transactions on》1999,47(5):1335-1348
The continuous fractional Fourier transform (FRFT) performs a spectrum rotation of signal in the time-frequency plane, and it becomes an important tool for time-varying signal analysis. A discrete fractional Fourier transform has been developed by Santhanam and McClellan (see ibid., vol.42, p.994-98, 1996) but its results do not match those of the corresponding continuous fractional Fourier transforms. We propose a new discrete fractional Fourier transform (DFRFT). The new DFRFT has DFT Hermite eigenvectors and retains the eigenvalue-eigenfunction relation as a continous FRFT. To obtain DFT Hermite eigenvectors, two orthogonal projection methods are introduced. Thus, the new DFRFT will provide similar transform and rotational properties as those of continuous fractional Fourier transforms. Moreover, the relationship between FRFT and the proposed DFRFT has been established in the same way as the conventional DFT-to-continuous-Fourier transform 相似文献
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针对脉冲Chirp类信号的时延估计问题,理论推导了基于离散分数阶Fourier变换的脉冲Chirp信号的特性,分析了当时延参量等效的分数阶Fourier域的频率大于采样率时,脉冲Chirp信号的分数阶Fourier域谱产生混叠,造成时延估计模糊的问题,并提出基于离散分数阶Fourier变换(DFRFT)双通道互谱法进行时延估计,给出两个通道采样率选取的原则及算法的性能分析,实验结果表明,在一定的采样率下,算法能够快速精确地估计脉冲Chirp信号的时延参数. 相似文献
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The discrete fractional Fourier transform 总被引:3,自引:0,他引:3
We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of Hermite-Gaussian functions. The definition is exactly unitary, index additive, and reduces to the DFT for unit order. The fact that this definition satisfies all the desirable properties expected of the discrete fractional Fourier transform supports our confidence that it will be accepted as the definitive definition of this transform 相似文献