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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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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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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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高斯白噪声背景下的LFM信号的分数阶Fourier域信噪比分析 总被引:7,自引:0,他引:7
目标大机动运动使雷达回波表现为频率和调频率参数均未知的LFM信号。未知参数LFM信号的检测和估计采用分数阶Fourier变换来实现受到越来越多的关注,为此本文着重分析其分数阶Fourier变换的信噪比。首先推导出时限线性调频信号的分数阶Fourier变换模平方,给出了在分数阶Fourier域的峰值点与未知参数的关系,然后研究了附加白噪声LFM信号在分数阶Fourier域的统计特性,确定了其信噪比,并与理想情况(即参数频率和调频率参数已知)下线性相位匹配滤波器的输出信噪比进行了比较。 相似文献
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采用分数阶Fourier变换对线性调频信号(Linear Frequency Modulation,LFM)进行检测与参数估计时,由于信号的特征未知,需要运用二维搜索方法确定分数阶Fourier变换的最佳旋转角度.该方法运算量巨大.为减少运算量,本文推导了欠采样前后LFM信号的分数阶Fourier变换最佳能量聚集旋转角度关系,证明了无噪LFM信号的调频率估计可以完全不受Nyquist采样定理的限制;通过推导分析欠采样含噪LFM信号在最佳分数阶Fourier域的信噪比,给出了欠采样倍数M对LFM信号检测的影响及其选取原则;最终提出一种基于欠采样理论的LFM信号快速检测方法.实验结果表明,当M选取合适时,利用原始信号的欠采样样本即可对LFM信号实现有效检测,快速确定其调频率. 相似文献
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针对高斯白噪声中多分量线性调频信号参数估计问题,提出了一种基于积分二次相位函数(IQPF)和分数阶Fourier变换的新方法。分析了IQPF估计线性调频信号调频率的原理,指出IQPF有压制弱信号的缺点。为解决强度相差较大的多分量线性调频信号中弱分量信号的参数估计问题,提出利用分数阶Fourier变换域的信号分离技术,逐次估计强信号分量的参数并将其消去,来提高多分量信号参数估计的可靠性。最后通过计算机仿真,验证了该方法的有效性。这种方法与Radon-Winger变换法、Radon-Ambiguity变换法和单纯的分数阶Fourier变换法相比,极大的简化了计算。因此,该方法非常适合于多分量LFM信号的快速参数估计。 相似文献
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Sampling and Sampling Rate Conversion of Band Limited Signals in the Fractional Fourier Transform Domain 总被引:5,自引:0,他引:5
Ran Tao Bing Deng Wei-Qiang Zhang Yue Wang 《Signal Processing, IEEE Transactions on》2008,56(1):158-171
The fractional Fourier transform (FRFT) has become a very active area in signal processing community in recent years, with many applications in radar, communication, information security, etc., This study carefully investigates the sampling of a continuous-time band limited signal to obtain its discrete-time version, as well as sampling rate conversion, for the FRFT. Firstly, based on product theorem for the FRFT, the sampling theorems and reconstruction formulas are derived, which explain how to sample a continuous-time signal to obtain its discrete-time version for band limited signals in the fractional Fourier domain. Secondly, the formulas and significance of decimation and interpolation are studied in the fractional Fourier domain. Using the results, the sampling rate conversion theory for the FRFT with a rational fraction as conversion factor is deduced, which illustrates how to sample the discrete-time version without aliasing. The theorems proposed in this study are the generalizations of the conventional versions for the Fourier transform. Finally, the theory introduced in this paper is validated by simulations. 相似文献
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本文主要研究海杂波在分数阶傅里叶变换(FRFT)域所表现出的多重分形特性及其在海杂波目标检测中的应用。由FRFT数学定义的尺度性质可推得,自相似过程在某一变换阶数下的FRFT谱在各尺度下不具有统一的自相似特性。针对这一特性,本文将多重分形理论引入到对海杂波FRFT谱的自相似结构分析中并研究FRFT域多重分形参数的影响因素,经S波段和C波段雷达实测数据验证表明,海杂波FRFT谱具有多重分形特性且FRFT域广义Hurst指数对海杂波和目标具有良好的区分能力。在此基础上,本文利用FRFT域广义Hurst指数与双参数恒虚警检测器相结合设计海杂波中目标检测方法并分析检测性能,结果表明本文所提方法相比于经典的时域分形检测方法具有较明显地性能提升。 相似文献
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In this article, we investigate the multiplicative filtering in the fractional Fourier transform (FRFT) domain based on the generalized convolution theorem which states that the convolution of two signals in time domain results in simple multiplication of their FRFTs in the FRFT domain. In order to efficiently implement multiplicative filtering, we express the generalized convolution structure by the conventional convolution operation. Utilizing the generalized convolution structure, we convert the multiplicative filtering in the FRFT domain easily to the time domain. Based on the model of multiplicative filtering in the FRFT domain, a practical method is proposed to achieve the multiplicative filtering through convolution in the time domain. This method can be realized by classical Fast Fourier transform (FFT) and has the same capability compared with the method achieved in the FRFT domain. As convolution can be performed by FFT, this method is more useful from practical engineering perspective. 相似文献
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为了改善时变系统中的LMS算法收敛速度,一般可以在变换域进行自适应处理。通过研究和分析分数阶傅里叶变换与时-频平面的关系,提出在分数阶傅里叶变换域进行自适应时-频滤波。所提出的方法首先搜索最佳变换域,然后在分数阶傅里叶变换域进行LMS自适应滤波。仿真结果表明,与目前一些基于变换域的方法对比,新方法通过对时-频平面的旋转,可以显著加速算法收敛性。 相似文献
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双曲余弦-高斯光束的分数傅里叶变换特性研究 总被引:1,自引:1,他引:1
基于分数傅里叶变换(FRFT)与维格纳分布函数(WDF)旋转等效的性质.推导出了双曲余弦-高斯(ChG)光束在分数傅里叶变换面上光强分布和束宽的解析公式,研究了双曲余弦-高斯光束光强和束宽随分数傅里叶变换阶数的变化规律,分析了偏心参量对双曲余弦-高斯光束分数傅里叶变换特性的影响,并对数值计算结果进行了分析和讨论。结果表明,对给定偏心参量的双曲余弦-高斯光束,可以使其经过一定阶数的分数傅里叶变换来获得平顶光束。 相似文献
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针对雷达回波为多分量LFM信号时,时频分析存在的交叉项干扰问题,提出了一种基于分数阶Fourier变换(Fractional Fourier Transform,FRFT)的伪Wigner分布(PWD).该方法通过在参数平面按阈值进行峰值搜索确定变换域阶次,再在相应的分数阶Fourier域计算PWD,有效地抑制了交叉项的干扰,有利于更好地提取信号的时频信息.仿真实验证明了在强背景噪声下该算法的有效性. 相似文献
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Qi-Wen Ran Hui Zhao Li-Ying Tan Jing Ma 《Circuits, Systems, and Signal Processing》2010,29(3):459-467
Fractional Fourier transformed bandlimited signals are shown to form a reproducing kernel Hilbert space. Basic properties
of the kernel function are applied to the study of a sampling problem in the fractional Fourier transform (FRFT) domain. An
orthogonal sampling basis for the class of bandlimited signals in the FRFT domain is then given. A nonuniform sampling theorem
for bandlimited signals in the FRFT domain is also presented. Numerical experiments are given to demonstrate the effectiveness
of the proposed nonuniform sampling theorem. 相似文献
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《Signal processing》2007,87(12):3147-3154
The transition bandwidth of window-based FIR filters is proportional to the window main-lobe width, which in turn is proportional to the length of the window function. As such, transition bandwidth of FIR filters can be directly tuned by varying window length for on-line tuning applications. However, analysis of window functions in fractional Fourier domain, a generalization of Fourier domain, also establishes the dependence of window main-lobe width on the order of fractional Fourier transform (FRFT). Thus, an alternative methodology to tune the transition bandwidth, based on FRFT, is developed in this work. The proposed methodology is useful for frequency domain filtering and introduces a comparative ease in tuning by eliminating the need to re-compute the impulse response coefficients. Also, significant computational saving has been achieved using FRFT. However, it is observed that the direct approach can introduce a lot more adjustability in the transition bandwidth than the FRFT approach. Apart from Kaiser window, considered to be optimum for FIR filter design, another window with a high side-lobe fall-off-rate (SLFOR), viz, Parzen-cos6 (πt) (PC6), has also been used in the proposed on-line filter tuning. Better performance of windows with high SLFOR in on-line sharpening is illustrated with the aid of simulation results. 相似文献
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分数阶傅里叶变换相对于传统的傅里叶变换具有灵活的时频分析特性,在最优分数阶傅里叶域进行滤波可以实现对某些非平稳信号的最优检测和参数估计以及对某些干扰和噪声的滤除.分数阶傅里叶域滤波器组理论的提出弥补了分数阶傅里叶域滤波不具备多尺度分析以及运算量过大的缺点,但现有的分数阶傅里叶域准确重建滤波器组设计方法不具备形式一般化的特点,很难满足很多实际工程的需要.本文从分数阶傅里叶域多抽样率信号处理基本理论和分数阶卷积定理出发,推导出了分数阶傅里叶域准确重建滤波器组的一般化设计方法,为分数阶傅里叶域滤波器组理论在实际工程中的推广应用奠定了理论基础.最后,仿真实验验证了本文所提分数阶傅里叶域滤波器组一般化设计方法的有效性. 相似文献