基于FRFT的复杂电磁环境下未知信号辨识
|
摘要
信息化战争中，由于作战双方在相对有限的战场空间内大量使用各种电子信息武器装备、电子干扰设备以及探测系统，加上空间内已有的众多电磁辐射体，导致在该范围内形成了一个信号特征繁杂、信号密集度极大的电磁环境——复杂电磁环境。随着信息化进程的推进，复杂电磁环境将成为战场环境的重要表现形态，并将对现有系统中的电子信息设备的效能发挥带来多方面影响。在此背景下，为了提高电子信息武器系统的抗干扰能力，同时又能够实施有针对性地电子干扰，就要求对各种侦察及干扰信号能够实现精、准、快的检测、分选与识别。然而，由于复杂电磁环境中的信号具有种类多、频段宽、体制新、分布广等特点，信号本身多呈现非平稳特性，信号之间存在严重的时频耦合。因此，要从如此复杂多变的环境中分选出未知的干扰信号极其困难，传统的信号处理方法已无法胜任。
分数阶Fourier变换(FRFT, Fractional Fourier Transform)是一种新兴的非平稳信号处理方法，其具有较高的时频分辨率，是一种全时域的线性变换，不存在交叉项干扰问题，因此分数阶Fourier变换对分析和处理多分量时频信号具有优良的特性。本文将分数阶Fourier变换应用到复杂电磁环境下未知信号的处理中，对典型时频交叠信号的快速检测与特征参数估计进行了深入研究，主要体现在：
1、对分数阶Fourier变换的基本原理及性质进行学习与研究，重点讨论了基于分数阶Fourier变换的二维搜索检测法以及基于分数阶频谱四阶原点矩的一维搜索检测法的信号检测原理，并通过仿真实验对两种方法的检测性能进行了比较分析。
2、针对现有基于分数阶Fourier变换的Chirp信号参数估计算法具有一定的应用局限性的问题，论文通过对实际观测信号形式进行分析，推导得出现有估计算法的估计误差，在此基础上提出了一种通用的参数估计方法，并且进一步将新方法推广应用到了时变幅度Chirp信号的参数估计中。
3、研究并提出了两种最佳分数阶Fourier变换旋转角度的快速确定方法，即基于FRFT的Chirp信号快速检测方法。方法一，在研究了基于FRFT的Chirp信号欠采样快速检测算法的基础上，从离散分数阶Fourier变换的角度出发，证明了将欠采样技术推广应用于基于分数阶频谱四阶原点矩的Chirp信号检测方法的可行性，进而从欠采样信号处理的角度，降低该Chirp信号一维搜索检测方法的运算量。第二种方法则是利用Chirp信号分数阶频谱四阶原点矩的对称特性，推导得出最佳FRFT旋转角度理论值与粗搜索检测估计结果的差值，进而在粗搜索的基础上快速计算得到更为准确的最佳FRFT旋转角度估计值。
4、针对当前基于FRFT的多分量时频信号检测中，一轮检测迭代只检测一个最强分量的情况，在研究了多分量Chirp信号间的遮蔽关系的基础上，提出了一种基于分数阶频谱四阶原点矩的多分量Chirp信号快速检测的阈值设置方法，利用该阈值设置方法可实现在一轮检测迭代中同时检测出未发生遮蔽的多个信号分量，进而提高检测效率。
5、在对复杂电磁环境的定义及构建准则进行研究的基础上，在一定范围内构造了由常规通信信号、雷达信号、以及干扰信号等组成的复杂电磁环境仿真系统，并利用该仿真系统产生的复杂电磁环境信号验证了论文所提出的基于分数阶Fourier变换的复杂电磁环境下未知信号的识别分选系统架构的有效性。
In the future information warfare, numerous electronic weapons and equipments willbe widely used in a relatively limited space in the battlefield. With the addition of exsitingelectromagnetic radiation, a special electromagnetic environment will be formed which iscalled complex electromagnetic environment. There are many kinds of intense signals inthe complex electromagnetic environment. Thus, in order to improve the anti-interferenceability of the electronic weapons and equipments, the jamming signals need to be detectedand identified precisely and quickly. However, the signals in the complex electromagneticenvironment are usually non-stationary and there are serious time frequency couplingbetween different signals. As a result, the traditional signal processing methods can not bequalified for detecting and recognizing signals in the complex electromagneticenvironment.
As a newly emerged signal processing method, fractional Fourier transform (FRFT) issuitable for dealing with non-stationary signals. What’s more, FRFT is a lineartransformation and there is no cross-term interference. So fractional Fourier transform canachieve good performance when processing multi-component time-frequency signals. Thispaper applies FRFT to the recognition of unknown signal in the complex electromagneticenvironment. The fast detection methods and parameter estimation of typicaltime-frequency signals based on FRFT are studied in depth. The main contributions of thisthesis are summarized as follows.
1. The fundamentals and properties of FRFT is studied and analized. On that basis, thesignal detection method based on fractional Fourier transform is researched, especially themethod based on the2-D peak searching and the one based on the fourth order originmoment of fractional spectrum (OMFrS). The performance of these methods is comparedthrough simulations.
2. On the basis of analyzing the practical signal form, the estimation error of theexisting parameter estimation method is derived and then a novel and universal parameterestimation method is proposed. Furthermore, the proposed algorithm is developed whichallows estimation of the practical observed Gaussian windowed chirp signal.
3. The fast detection method of the optimal transform angle of FRFT is studied andtwo new algorithms are proposed. The first method is realized based on sub-Nyquistsampling. The relationship between the optimal transform angle of the undersampledsignal and that of the original signal is studied. It is proved that the chirp-rate of noiselessChirp signal can be estimated correctly even though the signal is undersampled. Thesecond method is based on the symmetric property of the fourth order OMFrS of chirpsignal. By deducing the difference between the theoretical optimal transform angle and thedetected result, a more accurate estimation can be obtained. Compared to the existingmethods, the proposed algorithm achieves better accuracy with high detection speed.
4. The existing detection methods based on FRFT is usually only detects one Chirpcomponent that has the largest energy accumulation in each iteration. Thus, it will needseveral iterations to detect multicomponent Chirp signals. In order to improve the detectionefficiency, the shading relations between the fourth order OMFrS of different Chirpcomponent is studied. On this basis, a new threshold setting method for rapid detection ofmulticomponent Chirp signals based on the fourth order OMFrS is proposed. Byemploying the proposed method, several LFM components whose fourth order OMFrS attheir own optimal rotation angles are not shadowed by strong components can be detectedat the same time in one iteration.
5. The connotative meaning of complex electromagnetic environment and itsconstruction principle is studied. On this basis, a simulation system of complexelectromagnetic environment is realized by adopting the computer simulation. Using thecomplex signals produced by the simulation system, the recognition method of unknownsignal in the complex electromagnetic environment using FRFT which is proposed basedon the works of this thesis is verified.
分数阶Fourier变换(FRFT, Fractional Fourier Transform)是一种新兴的非平稳信号处理方法，其具有较高的时频分辨率，是一种全时域的线性变换，不存在交叉项干扰问题，因此分数阶Fourier变换对分析和处理多分量时频信号具有优良的特性。本文将分数阶Fourier变换应用到复杂电磁环境下未知信号的处理中，对典型时频交叠信号的快速检测与特征参数估计进行了深入研究，主要体现在：
1、对分数阶Fourier变换的基本原理及性质进行学习与研究，重点讨论了基于分数阶Fourier变换的二维搜索检测法以及基于分数阶频谱四阶原点矩的一维搜索检测法的信号检测原理，并通过仿真实验对两种方法的检测性能进行了比较分析。
2、针对现有基于分数阶Fourier变换的Chirp信号参数估计算法具有一定的应用局限性的问题，论文通过对实际观测信号形式进行分析，推导得出现有估计算法的估计误差，在此基础上提出了一种通用的参数估计方法，并且进一步将新方法推广应用到了时变幅度Chirp信号的参数估计中。
3、研究并提出了两种最佳分数阶Fourier变换旋转角度的快速确定方法，即基于FRFT的Chirp信号快速检测方法。方法一，在研究了基于FRFT的Chirp信号欠采样快速检测算法的基础上，从离散分数阶Fourier变换的角度出发，证明了将欠采样技术推广应用于基于分数阶频谱四阶原点矩的Chirp信号检测方法的可行性，进而从欠采样信号处理的角度，降低该Chirp信号一维搜索检测方法的运算量。第二种方法则是利用Chirp信号分数阶频谱四阶原点矩的对称特性，推导得出最佳FRFT旋转角度理论值与粗搜索检测估计结果的差值，进而在粗搜索的基础上快速计算得到更为准确的最佳FRFT旋转角度估计值。
4、针对当前基于FRFT的多分量时频信号检测中，一轮检测迭代只检测一个最强分量的情况，在研究了多分量Chirp信号间的遮蔽关系的基础上，提出了一种基于分数阶频谱四阶原点矩的多分量Chirp信号快速检测的阈值设置方法，利用该阈值设置方法可实现在一轮检测迭代中同时检测出未发生遮蔽的多个信号分量，进而提高检测效率。
5、在对复杂电磁环境的定义及构建准则进行研究的基础上，在一定范围内构造了由常规通信信号、雷达信号、以及干扰信号等组成的复杂电磁环境仿真系统，并利用该仿真系统产生的复杂电磁环境信号验证了论文所提出的基于分数阶Fourier变换的复杂电磁环境下未知信号的识别分选系统架构的有效性。
In the future information warfare, numerous electronic weapons and equipments willbe widely used in a relatively limited space in the battlefield. With the addition of exsitingelectromagnetic radiation, a special electromagnetic environment will be formed which iscalled complex electromagnetic environment. There are many kinds of intense signals inthe complex electromagnetic environment. Thus, in order to improve the anti-interferenceability of the electronic weapons and equipments, the jamming signals need to be detectedand identified precisely and quickly. However, the signals in the complex electromagneticenvironment are usually non-stationary and there are serious time frequency couplingbetween different signals. As a result, the traditional signal processing methods can not bequalified for detecting and recognizing signals in the complex electromagneticenvironment.
As a newly emerged signal processing method, fractional Fourier transform (FRFT) issuitable for dealing with non-stationary signals. What’s more, FRFT is a lineartransformation and there is no cross-term interference. So fractional Fourier transform canachieve good performance when processing multi-component time-frequency signals. Thispaper applies FRFT to the recognition of unknown signal in the complex electromagneticenvironment. The fast detection methods and parameter estimation of typicaltime-frequency signals based on FRFT are studied in depth. The main contributions of thisthesis are summarized as follows.
1. The fundamentals and properties of FRFT is studied and analized. On that basis, thesignal detection method based on fractional Fourier transform is researched, especially themethod based on the2-D peak searching and the one based on the fourth order originmoment of fractional spectrum (OMFrS). The performance of these methods is comparedthrough simulations.
2. On the basis of analyzing the practical signal form, the estimation error of theexisting parameter estimation method is derived and then a novel and universal parameterestimation method is proposed. Furthermore, the proposed algorithm is developed whichallows estimation of the practical observed Gaussian windowed chirp signal.
3. The fast detection method of the optimal transform angle of FRFT is studied andtwo new algorithms are proposed. The first method is realized based on sub-Nyquistsampling. The relationship between the optimal transform angle of the undersampledsignal and that of the original signal is studied. It is proved that the chirp-rate of noiselessChirp signal can be estimated correctly even though the signal is undersampled. Thesecond method is based on the symmetric property of the fourth order OMFrS of chirpsignal. By deducing the difference between the theoretical optimal transform angle and thedetected result, a more accurate estimation can be obtained. Compared to the existingmethods, the proposed algorithm achieves better accuracy with high detection speed.
4. The existing detection methods based on FRFT is usually only detects one Chirpcomponent that has the largest energy accumulation in each iteration. Thus, it will needseveral iterations to detect multicomponent Chirp signals. In order to improve the detectionefficiency, the shading relations between the fourth order OMFrS of different Chirpcomponent is studied. On this basis, a new threshold setting method for rapid detection ofmulticomponent Chirp signals based on the fourth order OMFrS is proposed. Byemploying the proposed method, several LFM components whose fourth order OMFrS attheir own optimal rotation angles are not shadowed by strong components can be detectedat the same time in one iteration.
5. The connotative meaning of complex electromagnetic environment and itsconstruction principle is studied. On this basis, a simulation system of complexelectromagnetic environment is realized by adopting the computer simulation. Using thecomplex signals produced by the simulation system, the recognition method of unknownsignal in the complex electromagnetic environment using FRFT which is proposed basedon the works of this thesis is verified.
引文
[1]李楠,张雪飞.战场复杂电磁环境构成分析[J].装备环境工程,2008,5(1):16-19.
[2]谢虹.复杂电磁环境究竟复杂在哪.解放军报,2007(2),第012版.
[3]谢金波.构建复杂电磁环境的几点思考.战士报,2007(6),第003版.
[4]刘伟,罗鹏程.复杂电磁环境对现代战争的影响及对策[J].国防科技,2007(11):71-76.
[5]王建新，宋辉.基于星座图的数字调制方式识别[J].通信学报.2004,6:166-173.
[6]陈怀新，南建设，肖先赐.基于统计特征主分量的信号调制识别[J].电子科技大学学报.2004,6:231-324.
[7] Fang Xiangqian, Huo Lei, Duan Tiandong．Cyclic correlation based symbol durationestimation for OFDM signals[C]．2006International Conference on WirelessCommunications, Networking and Mobile Computing, WiCOM2006.2007,1:1-4.
[8]郑文秀,李国庆,罗明.基于高阶循环累积量的OFDM子载波盲估计[J].电子与信息学报.2008,30(2):346-349.
[9]刘澍，王宏远.基于RBF神经网络的调制识别[J].系统工程与电子技术。2008，Vol.3,7:1241-1244.
[10]叶健,葛临东,吴月娴.一种优化的RBF神经网络在调制识别中的应用[J].自动化学报.2007, Vol.33,6:652-654.
[11]赵知劲,庄婵飞,于立.调制样式BP神经网络分类器[J].现代雷达,2003,25(10):23-28.
[12]李娜，张国毅.某型装备数字通信信号识别能力的改进[J].吉林大学学报.2008,26(20):141-146.
[13]孙建成，张太镒，刘枫.基于支持向量机的多类数字调制方式自动识别算法[J].西安交通大学学报.2004,6:619-622.
[14] Octavia A.Dobre etc. A Survey of Automatic Modulation classification Techniques:Classical Approaches and New Trends[A], Prodedding of Sarnoff Sympsium[C].Prineceton2006.
[15] J.A.Sills. Maximum-likelihood modulation classification for PSK/QAM[J].IEEEMILCOM,1999,4:57-61.
[16] K.Kim, A.polydoros. Digital modulation classification: the BPSK versus QPSKcase[J].IEEE MILCOM,1999,11:431-436.
[17] P.Panagiotou, A.Anastasoupoulos, A.Polydoros. Likelihood ratio tests for modulationclassification[J].IEEE MILCOM,2000,8:670-674.
[18]朱庆厚.通信侦察中信号的搜索与截获[J].电子对抗,2005,5:11-12.
[19]蔡晓霞,陈红,徐云.通信搜索接收机性能分析与仿真[J].现代电子技术.2008,31(7):99-102.
[20]王瑜,王红军.对舰载跳频通信信号的侦察概率分析[J].舰船科学技术.2005,27(2):84-86.
[21]刘世刚.基于循环相关的符号速率盲估计[J].信号处理,2004,20(4):356-359.
[22]张仔兵,李立萍. MPSK信号的循环谱检测及码元速率估计[J].系统工程与电子技术.2005,27(5):803-806.
[23] Cohen L. Time-frequency distribution-a review. Proc.IEEE,1989,77(7):941-981.
[24] Xue mei, Ouyang. Short-Time Fourier Transform Receiver for NonstationaryInterference Excision in Direct Sequence Spread Spectrum Communications. IEEE Trans.on Signal Processing,1997,49(4):851-863.
[25] H.K.Kwok, D.L.Jones. Improved instantaneous frequency estimation using anadaptive short-time Fourier transform. IEEE Trans. on Signal Processing,2000,48(5):2964-2972.
[26] Durak, Arikan. Short-Time Fourier Transform: Two Fundamental: Properties andan Optimal Implementation. IEEE trans. on signal processing,2003,51(5):1231-1242.
[27] Henry K., Kwok, Douglas L. Jones. Improved Instantaneous Frequency EstimationUsing an Adaptive Short-Time Fourier Transform. IEEE trans. on signal processing,2000,48(10):2964-2972.
[28]刘忠英,张毅,姚富强.基于STFT与G函数相结合的短波DFH跳检测方法[J].电子学报.2003,31(1):1-4.
[29]朱明哲,姬红兵,金艳.基于自适应抽取STFT的混合DS/FH扩频信号参数估计[J].系统工程与电子技术.2010,32(3):454-457.
[30] Zhao Zhao, Shi Xiangquan. FM interference suppression for PRC-CW radar based onadaptive STFT and time-varying filtering. Journal of Systems Engineering and Electronics.2010,21(2):219-223.
[31] Mest O. Ventricular late potentials Characterization in time-frequency domain bymeans of a wavelet transform. IEEE Biomedical Engineering.1994,41(7):625-634.
[32] Uros Lotric. Wavelet based denoising integrated into multilayered perceptron.Neurocomputing.2004,62(5):179-196.
[33]阮秀凯,张志涌.基于小波变换的调制自动识别新方法研究[J].南京邮电大学学报（自然科学版）.2007,27(1):35-39.
[34] R.W.-P.LUK, R.I.Damper. Non-parametric linear time-invariant system identificationby discrete wavelet transforms. Digital Signal Processing.2006,16(3):303-319.
[35] Rodrigo Capobianco Guido, Jan Frans Willem Slaets, Roland K berle. A newtechnique to construct a wavelettransform matching a specified signal with applications todigital, real time, spike, and overlap pattern recognition.2006,16(1):24-44.
[36]李月琴,栗苹,闫晓鹏,陈慧敏.无线电引信信号去噪的最优小波基选择[J].北京理工大学学报.2008,28(8):723-726.
[37] Wigner E.P. On the quantum correction for thermodynamic equilibrium. Phys. Rev.1932,40:749-759.
[38] Claasen T.A.C., Mecklenbrauker W.F.G.. The Wigner distribution-a tool fortime-frequency signal analysis, part1: continuous-time signals. Philips Journal of Research.1980,35(3):217-251.
[39] Claasen T.A.C., Mecklenbrauker W.F.G.. The Wigner distribution-a tool fortime-frequency signal analysis, part2: discrete-time signals. Philips Journal of Research.1980,35(4-5):276-300.
[40] Claasen T.A.C., Mecklenbrauker W.F.G.. The Wigner distribution-a tool fortime-frequency signal analysis, part3: relations with other time-frequency signaltransformations. Philips Journal of Research.1980,35(6):372-389.
[41] Martin W, Flandrin P. Wigner-Ville spectral analysis of nonstationary processes. IEEEtrans. On ASSP.1985,33(6):1461-1469.
[42] F.Peyrin, R.A.Prost. A unified definition for the discrete-time, discrete-frequency, anddiscrete-time/frequency Wigner distribution. IEEE Trans.on Acoustic, Speech and SignalProcessing.1986,34(4):858-867.
[43] B.Boashash, P.Black. An efficient real time implementation of the Wigner-Villedistribution. IEEE Trans.on Acoustic, Speech and Signal Processing.1987,35(11):1611-1618.
[44] Velez E.F., Absher R.G.. Spectral estimation based on the Wigner-Ville representation.Signal Processing.1990,20(4):134-142.
[45] Andrieux J.C., Feix M.R., et al. Optimum smooth of the Winger-Ville disrtibution.IEEE trans. On ASSP.1985,33(6):1461-1469.1987,35(6):764-769.
[46] Bikdash M.U, Yu K.B.. Analysis and filtering using the optimally smoothed Wingerdistribution. IEEE trans. Signal Processing.1993,41(4):1603-1617.
[47] Sun M.G, et al. Effieient computation of the diserete pseudo-Wigner distribution.IEEE trans. On ASSP.1989,37(11):1735-1741.
[48] Boashash B. Note on the use of the Winger distribution for time-fequeney singalanalysis. IEEE trans. On ASSP.1988,36(9):1518-1521.
[49] Jeong J.C., Williams W.J. Kernel desing for reduced interference distributions. IEEETrans. Signal Processing.1992,40(2):402-411.
[50] Zhang B.L., Sato S.S.. A time-frequency distribution of Cohen’s class with acompound kernel and its application to speech signal processing. IEEE Trans. SignalProcessing.1994,42(1):54-64.
[51] Gao Z.Y, Durand L.G., Lee H.C.. The time-frequency distributions of nonstationarysignals based on a bessel kemel. IEEE Trans. Signal Processing.1994,42(7):1700-1707.
[52] Hough P.V.C. Method and means for recognizing complex patterns. U.S. Patent3069654,1962.
[53] Barbarossa, S. Analysis of multicomponent LFM signals by a combinedWigner-Hough transform. IEEE Trans. Signal Processing.1995,43(6):1511-1515.
[54]刘建成,王雪松,肖顺平,王国玉.基于Wigner-Hough变换的径向加速度估计[J].电子学报.2005,33(12):2235-2238.
[55]李钢虎,李亚安,王军,崔海英. Wigner．Hough变换在水下目标信号检测中的应用[J].兵工学报.2006,27(1)：121-125.
[56]刘建成,王雪松,刘忠,肖顺平,王国玉.基于Wigner-Hough变换的LFM信号检测性能分析[J].电子学报.2007,35(6):1212-1216.
[57] Liu Feng, Sun Da-Peng, Huang Yu, Tao Ran, Wang Yue. Multi-component LFMsignal feature extraction based on improved Wigner-Hough transform. Transactions ofBeijing Institute of Technology.2008,28(10):914-917.
[58] Li Zhi, Xu Can, Shi Lei. An new estimator for Doppler parameters based on improvedWigner Hough Transform.2011IEEE International Conference on Computer Science andAutomation Engineering (CSAE).2011,269-272.
[59] V. Namias. The fractional order Fourier transform and its applications to quantummechanics. Journal of Institute Applied Math.1980,25(3):241-265.
[60] A.C.Mcbride, F.H.Kerr. On Namias’ fractional Fourier transform. IMA J Appl Math.1987,39:159-175
[61] D.Mendlovic, H.M.Ozaktas. Fractional Fourier transforms and their opticalimplementation (I). J Opt Sco AM A.1993,10(10):1875-1881.
[62] H.M.Ozaktas, D.Mendlovic. Fractional Fourier transforms and their opticalimplementation (II). J Opt Sco AM A.1993,10(12):2522-2531.
[63] H.M.Ozaktas, M.A.Kutay, Z.Zalevsky. The Fractional Fourier Transform withApplications in Optics and Signal Processing. New York: John Wiley&Sons,2000.
[64] L.B.Almeida. The fractional Fourier transform and time-frequency representation.IEEE Trans. Signal Processing.1994,42(10):3084-3091.
[65] A.W.Lachmann, B.H.Soffer. Relationship between the Radon-Wigner and fractionalFourier transform. Journal of Optics Society of American.1994,11:1798-180.
[66] H. M. Ozaktas, Orhan Arikan, et al. Digital Computation of the Fractional FourierTransform[J]. IEEE Trans. Signal Processing,1996,44(9):2141-2150.
[67] S.C.Pei, M.H.Yeh, C.C.Tseng. Discrete fractional Fourier transform based onorthogonal projections. IEEE Tran. Signal Processing.1999,47(5):1335-1348.
[68] C. Candan, M. A. Kutay, H. M. Ozaktas. The discrete fractional Fourier transform.IEEE Tran. Signal Processing.2000,48(5):1329-1337.
[69] S.C.Pei, C.C.Tseng, M.H.Yeh. A new discrete fractional Fourier transform based onconstrained eigendecomposition of DFT matrix by largrange multiplier method. IEEETrans. Circuits Syst.Ⅱ,1999,46:1240-1245.
[70] A. Bultheel, H. E. M. Sulbaran. Computation of the fractional Fourier transform.Applied and Computational Harmonic Analysis.2004,16:182-202.
[71] S. C. Pei, J. J. Ding. Closed-form discrete fractional and affine Fourier transforms.IEEE Tran. Signal Processing.2000,48(5):1338-1353.
[72] B. Santhanam, J. H. McClellan. The discrete rotational Fourier transform. IEEE Tran.Signal Processing.1996,44(4):994-998.
[73] M. H. Yeh, S. C. Pei. A method for the discrete fractional Fourier transformcomputation. IEEE Tran. Signal Processing.2003,51(3):889-891.
[74]陶然,邓兵,王越.分数阶傅里叶变换及其应用[M].北京:清华大学出版社,2009.
[75]平先军,陶然,周思永,王越.一种新的分数阶傅立叶变换快速算法[J].电子学报.2001,29(3):406-408.
[76]赵兴浩,陶然,邓兵,王越．分数阶傅里叶变换的快速计算新方法[J].电子学报.2007,35(6):1089-1093.
[77]赵兴浩,邓兵,陶然.分数阶傅里叶变换数值计算中的量纲归一化[J].北京理工大学学报,2005,25(4):360-364.
[78]刘锋,徐会法,陶然.分数阶Fourier变换中量纲归一化因子的选取[J].系统工程与电子技术.2011,33(2):237-241.
[79]张卫强,陶然.分数阶傅里叶变换域上带通信号的采样定理[J].电子学报.2005,33(7):1196-1199.
[80]邓兵,陶然,张惠云.抽样率转换的分数阶Fourier域分析[J].电子学报.2006,34(12):2190-2194.
[81] Tao Ran, Deng Bing, Zhang Wei-Qiang, Wang Yue. Sampling and sampling rateconversion of band limited signals in the fractional Fourier transform domain. IEEE Tran.Signal Processing.2008,56(1):158-171.
[82] Tao Ran, Zhang Feng, Wang Yue. Sampling random signals in a fractional Fourierdomain. Signal Processing.2011,91(6):1394-1400.
[83]董永强,陶然.含未知参数的多分量Chirp信号的分数阶傅里叶分析[J].北京理工大学学报.1999,19(5):612-616.
[84]赵兴浩,陶然,周思永,王越．基于Radon-Ambiguity变换和分数阶傅里叶变换的chirp信号检测及多参数估计[J].北京理工大学学报.2003,23(3):371-374.
[85]齐林,陶然,等.基于分数阶Fourier变换的多分量LFM信号的检测和参数估计[J].中国科学E辑.2003,33(8):749-759.
[86]邓兵,陶然,曲长文.分数阶Fourier域中多分量chirp信号的遮蔽分析[J].电子学报.2007,35(6):1094-1098.
[87]杨小明,陶然.基于分数阶傅里叶变换的线性调频信号二维波到达方向估计[J].电子学报.2008,36(9):1737-1740.
[88]刘锋,黄宇,陶然,王越．分数阶Fourier变换对多分量Chirp信号中心频率的分辨能力[J].兵工学报.2009,30(1):15-18.
[89]刘锋,徐会法,陶然.基于FRFT的对称三角LFMCW信号检测与参数估计[J].电子与信息学报.2011,33(8):1864-1870.
[90]邓兵,王旭,陶然,刘贤忠.基于分数阶傅里叶变换的线性调频脉冲时延估计特性分析[J].兵工学报.2012,33(6):765-768.
[91]齐林,陶然,周思永,王越．基于分数阶傅里叶变换的线性调频信号的自适应时频滤波[J].兵工学报.2003,24(4):499-503.
[92]齐林,陶然,周思永,王越．LFM信号的一种最优滤波算法[J].电子学报.2004,32(9):1464-1467.
[93]邓兵,陶然,齐林,刘锋.分数阶Fourier变换与时频滤波[J].系统工程与电子技术.2004,26(10):1357-1359.
[94]董永强,陶然,等.基于分数阶Fourier变换的SAR运动目标检测与成像[J].兵工学报.1999,20(2):132-136.
[95]赵兴浩,陶然.基于分数阶相关的无源雷达动目标检测方法[J].电子学报.2005,33(9):1567-1570.
[96]邓兵,陶然,平殿发,马路.基于分数阶傅里叶变换补偿多普勒徙动的动目标检测算法[J].兵工学报.2009,30(10):1303-1309.
[97]张南,陶然,王越.基于变标处理和分数阶傅里叶变换的运动目标检测算法[J].电子学报.2010,38(3):683-688.
[98] Akay Olcay，Boudreaux-Bartels G Faye. Fractional autocorrelation and its applicationto detection and estimation of linear FM signals. Proceedings of the IEEE-SP InternationalSymposium on Time-Frequency and Time-Scale Analysis.1998:213-216.
[99] T. Alieva, M. J. Bastiaans, On fractional Fourier transform moments. IEEE SignalProcessing Letters.2000,7(11):320–323.
[100] T. Alieva, M. J. Bastiaans, L. Stankovic. Signal reconstruction from two closefractional Fourier power spectra. IEEE Tran. Signal Processing.2003,51(1):112-123.
[101] M. G. Ertosun, H. Atli, H. M. Ozaktas, B. Barshan. Complex signal recovery fromfractional Fourier transform intensities. IEEE12th Signal Processing and CommunicationsApplications Conference.2004,308-311.
[102] L. Qi, R. Tao, S. Y. Zhou, Y. Wang. Detection and parameter estimation ofmulticomponent LFM signal based on the fractional Fourier transform. Science in China F:Information Science.2004,47:184-198.
[103] X. L. Chen, J. Guan. A Fast FRFT Based Detection Algorithm of Multiple MovingTargets in Sea Clutter. IEEE International Radar Conference.2010,402-406.
[104]李靖,王树勋,汪飞.基于分数阶傅里叶变换的chirp信号时频分析[J].系统工程与电子技术.2005,27(6):988-990.
[105]汪飞,曹凡.基于时频空间奇异值分解的多分量线性调频信号分离与增强[J].数据采集与处理.2009,24(6):767-771.
[106] Z. P. Yin, D. C. Zhang, W. D. Chen, D. J. Wang. LFM signal detection using theorigin moment of fractional spectrum. International Conference on Signal Processing.2008.
[107]尹治平,张义安,陈卫东,王东进.基于分数阶功率谱的LFM信号检测[J].系统工程与电子技术.2009,31(1):45-48.
[108]卫红凯,王平波,蔡志明,姚万军.分数阶Fourier变换极值搜索算法研究[J].电子学报.2010,38(12):2949-2952.
[109] Wei Hong kai, Wang Ping bo, Cai Zhiming, Fu Yinfeng. Comparison of intelligentoptimization methods in the fractional Fourier transform. The Second InternationalConference on Computer Modeling and Simulation.2010,552-555.
[110]陶然,邓兵,王越.分数阶Fourier变换在信号处理领域的研究进展[J].中国科学E辑.2006,36(2):113-136.
[111]邓兵,陶然,平殿发.基于分数阶Fourier变换的chirp-rate调制[J].电子学报.2008,36(6):1078-1083.
[112]肇启明,张钦宇,张乃通.多进制chirp-rate键控调制及分数傅里叶变换法解调[J].通信学报.2010,31(6):1-6.
[113]张贤达，保铮.非平稳信号分析与处理[M].北京:国防工业出版社,1998.
[114] J. Tsao, B. D. Steinberg. Reduction of sidelobe and speckle artifacts in microwaveimaging: the CLEAN technique. IEEE Transactions on Antennas and Propagation.1988,36(4):543-556.
[115] M. I. Ahmad, Z. W. Liu, Y. G. Xu. Order selection in fractional Fourier transformbased beamforming. Journal of Systems Engineering and Electronics,2010,21(3):361-369.
[116] Y. L. Zhang, Q. Y. Zhang, S. H. Wu. Biomedical Signal Detection Based onFractional Fourier Transform. International Conference on Information Technology andApplication in Biomedicine.2008:349–352.
[117] F. Cao, S. X. Wang, F. Wang. A New Time-Frequency Analysis Method ofMulti-Component Chirp Signal. International Conference on Signal Processing.2006.
[118] M. Wang, A.K. Chan, C.K. Chui. Linear Frequency-Modulated Signal DetectionUsing Radon-Ambiguity Transform. IEEE Transactions on Signal Processing.1998,46(3):571-586.
[119] C. Capus, K. Brown. Fractional Fourier transform of the Gaussian and fractionaldomain signal support. IEE Proceedings of Vision, Image and Signal Processing.2003,150(2):99-106.
[120]仇兆炀,陈蓉,汪一鸣.基于FRFT的线性调频信号欠采样快速检测方法[J].电子学报.2012,40(11):2165-2170.
[121]许旭. E-2C2000预警机和APS-145(V)雷达附E-2T预警机简介[J].电子工程信息.2004(3):52-54.
[122] DAVID A Shnidman．Generalized Radar Clutter Model [J]．IEEE Trans on AES.1999,35(3)：857-865．
[123] BLACKNELL D．New Method for the Simulation of Correlated K-distributedClutter [J]．IEE Proc-Radar, Sonar Navigation.1994,141(1)：53-58．
[124]刘娜,时海,杨建华.虚拟战场电磁环境雷达信号建模方法[J].指挥控制与仿真.2007,29(6):98-102.
[2]谢虹.复杂电磁环境究竟复杂在哪.解放军报,2007(2),第012版.
[3]谢金波.构建复杂电磁环境的几点思考.战士报,2007(6),第003版.
[4]刘伟,罗鹏程.复杂电磁环境对现代战争的影响及对策[J].国防科技,2007(11):71-76.
[5]王建新，宋辉.基于星座图的数字调制方式识别[J].通信学报.2004,6:166-173.
[6]陈怀新，南建设，肖先赐.基于统计特征主分量的信号调制识别[J].电子科技大学学报.2004,6:231-324.
[7] Fang Xiangqian, Huo Lei, Duan Tiandong．Cyclic correlation based symbol durationestimation for OFDM signals[C]．2006International Conference on WirelessCommunications, Networking and Mobile Computing, WiCOM2006.2007,1:1-4.
[8]郑文秀,李国庆,罗明.基于高阶循环累积量的OFDM子载波盲估计[J].电子与信息学报.2008,30(2):346-349.
[9]刘澍，王宏远.基于RBF神经网络的调制识别[J].系统工程与电子技术。2008，Vol.3,7:1241-1244.
[10]叶健,葛临东,吴月娴.一种优化的RBF神经网络在调制识别中的应用[J].自动化学报.2007, Vol.33,6:652-654.
[11]赵知劲,庄婵飞,于立.调制样式BP神经网络分类器[J].现代雷达,2003,25(10):23-28.
[12]李娜，张国毅.某型装备数字通信信号识别能力的改进[J].吉林大学学报.2008,26(20):141-146.
[13]孙建成，张太镒，刘枫.基于支持向量机的多类数字调制方式自动识别算法[J].西安交通大学学报.2004,6:619-622.
[14] Octavia A.Dobre etc. A Survey of Automatic Modulation classification Techniques:Classical Approaches and New Trends[A], Prodedding of Sarnoff Sympsium[C].Prineceton2006.
[15] J.A.Sills. Maximum-likelihood modulation classification for PSK/QAM[J].IEEEMILCOM,1999,4:57-61.
[16] K.Kim, A.polydoros. Digital modulation classification: the BPSK versus QPSKcase[J].IEEE MILCOM,1999,11:431-436.
[17] P.Panagiotou, A.Anastasoupoulos, A.Polydoros. Likelihood ratio tests for modulationclassification[J].IEEE MILCOM,2000,8:670-674.
[18]朱庆厚.通信侦察中信号的搜索与截获[J].电子对抗,2005,5:11-12.
[19]蔡晓霞,陈红,徐云.通信搜索接收机性能分析与仿真[J].现代电子技术.2008,31(7):99-102.
[20]王瑜,王红军.对舰载跳频通信信号的侦察概率分析[J].舰船科学技术.2005,27(2):84-86.
[21]刘世刚.基于循环相关的符号速率盲估计[J].信号处理,2004,20(4):356-359.
[22]张仔兵,李立萍. MPSK信号的循环谱检测及码元速率估计[J].系统工程与电子技术.2005,27(5):803-806.
[23] Cohen L. Time-frequency distribution-a review. Proc.IEEE,1989,77(7):941-981.
[24] Xue mei, Ouyang. Short-Time Fourier Transform Receiver for NonstationaryInterference Excision in Direct Sequence Spread Spectrum Communications. IEEE Trans.on Signal Processing,1997,49(4):851-863.
[25] H.K.Kwok, D.L.Jones. Improved instantaneous frequency estimation using anadaptive short-time Fourier transform. IEEE Trans. on Signal Processing,2000,48(5):2964-2972.
[26] Durak, Arikan. Short-Time Fourier Transform: Two Fundamental: Properties andan Optimal Implementation. IEEE trans. on signal processing,2003,51(5):1231-1242.
[27] Henry K., Kwok, Douglas L. Jones. Improved Instantaneous Frequency EstimationUsing an Adaptive Short-Time Fourier Transform. IEEE trans. on signal processing,2000,48(10):2964-2972.
[28]刘忠英,张毅,姚富强.基于STFT与G函数相结合的短波DFH跳检测方法[J].电子学报.2003,31(1):1-4.
[29]朱明哲,姬红兵,金艳.基于自适应抽取STFT的混合DS/FH扩频信号参数估计[J].系统工程与电子技术.2010,32(3):454-457.
[30] Zhao Zhao, Shi Xiangquan. FM interference suppression for PRC-CW radar based onadaptive STFT and time-varying filtering. Journal of Systems Engineering and Electronics.2010,21(2):219-223.
[31] Mest O. Ventricular late potentials Characterization in time-frequency domain bymeans of a wavelet transform. IEEE Biomedical Engineering.1994,41(7):625-634.
[32] Uros Lotric. Wavelet based denoising integrated into multilayered perceptron.Neurocomputing.2004,62(5):179-196.
[33]阮秀凯,张志涌.基于小波变换的调制自动识别新方法研究[J].南京邮电大学学报（自然科学版）.2007,27(1):35-39.
[34] R.W.-P.LUK, R.I.Damper. Non-parametric linear time-invariant system identificationby discrete wavelet transforms. Digital Signal Processing.2006,16(3):303-319.
[35] Rodrigo Capobianco Guido, Jan Frans Willem Slaets, Roland K berle. A newtechnique to construct a wavelettransform matching a specified signal with applications todigital, real time, spike, and overlap pattern recognition.2006,16(1):24-44.
[36]李月琴,栗苹,闫晓鹏,陈慧敏.无线电引信信号去噪的最优小波基选择[J].北京理工大学学报.2008,28(8):723-726.
[37] Wigner E.P. On the quantum correction for thermodynamic equilibrium. Phys. Rev.1932,40:749-759.
[38] Claasen T.A.C., Mecklenbrauker W.F.G.. The Wigner distribution-a tool fortime-frequency signal analysis, part1: continuous-time signals. Philips Journal of Research.1980,35(3):217-251.
[39] Claasen T.A.C., Mecklenbrauker W.F.G.. The Wigner distribution-a tool fortime-frequency signal analysis, part2: discrete-time signals. Philips Journal of Research.1980,35(4-5):276-300.
[40] Claasen T.A.C., Mecklenbrauker W.F.G.. The Wigner distribution-a tool fortime-frequency signal analysis, part3: relations with other time-frequency signaltransformations. Philips Journal of Research.1980,35(6):372-389.
[41] Martin W, Flandrin P. Wigner-Ville spectral analysis of nonstationary processes. IEEEtrans. On ASSP.1985,33(6):1461-1469.
[42] F.Peyrin, R.A.Prost. A unified definition for the discrete-time, discrete-frequency, anddiscrete-time/frequency Wigner distribution. IEEE Trans.on Acoustic, Speech and SignalProcessing.1986,34(4):858-867.
[43] B.Boashash, P.Black. An efficient real time implementation of the Wigner-Villedistribution. IEEE Trans.on Acoustic, Speech and Signal Processing.1987,35(11):1611-1618.
[44] Velez E.F., Absher R.G.. Spectral estimation based on the Wigner-Ville representation.Signal Processing.1990,20(4):134-142.
[45] Andrieux J.C., Feix M.R., et al. Optimum smooth of the Winger-Ville disrtibution.IEEE trans. On ASSP.1985,33(6):1461-1469.1987,35(6):764-769.
[46] Bikdash M.U, Yu K.B.. Analysis and filtering using the optimally smoothed Wingerdistribution. IEEE trans. Signal Processing.1993,41(4):1603-1617.
[47] Sun M.G, et al. Effieient computation of the diserete pseudo-Wigner distribution.IEEE trans. On ASSP.1989,37(11):1735-1741.
[48] Boashash B. Note on the use of the Winger distribution for time-fequeney singalanalysis. IEEE trans. On ASSP.1988,36(9):1518-1521.
[49] Jeong J.C., Williams W.J. Kernel desing for reduced interference distributions. IEEETrans. Signal Processing.1992,40(2):402-411.
[50] Zhang B.L., Sato S.S.. A time-frequency distribution of Cohen’s class with acompound kernel and its application to speech signal processing. IEEE Trans. SignalProcessing.1994,42(1):54-64.
[51] Gao Z.Y, Durand L.G., Lee H.C.. The time-frequency distributions of nonstationarysignals based on a bessel kemel. IEEE Trans. Signal Processing.1994,42(7):1700-1707.
[52] Hough P.V.C. Method and means for recognizing complex patterns. U.S. Patent3069654,1962.
[53] Barbarossa, S. Analysis of multicomponent LFM signals by a combinedWigner-Hough transform. IEEE Trans. Signal Processing.1995,43(6):1511-1515.
[54]刘建成,王雪松,肖顺平,王国玉.基于Wigner-Hough变换的径向加速度估计[J].电子学报.2005,33(12):2235-2238.
[55]李钢虎,李亚安,王军,崔海英. Wigner．Hough变换在水下目标信号检测中的应用[J].兵工学报.2006,27(1)：121-125.
[56]刘建成,王雪松,刘忠,肖顺平,王国玉.基于Wigner-Hough变换的LFM信号检测性能分析[J].电子学报.2007,35(6):1212-1216.
[57] Liu Feng, Sun Da-Peng, Huang Yu, Tao Ran, Wang Yue. Multi-component LFMsignal feature extraction based on improved Wigner-Hough transform. Transactions ofBeijing Institute of Technology.2008,28(10):914-917.
[58] Li Zhi, Xu Can, Shi Lei. An new estimator for Doppler parameters based on improvedWigner Hough Transform.2011IEEE International Conference on Computer Science andAutomation Engineering (CSAE).2011,269-272.
[59] V. Namias. The fractional order Fourier transform and its applications to quantummechanics. Journal of Institute Applied Math.1980,25(3):241-265.
[60] A.C.Mcbride, F.H.Kerr. On Namias’ fractional Fourier transform. IMA J Appl Math.1987,39:159-175
[61] D.Mendlovic, H.M.Ozaktas. Fractional Fourier transforms and their opticalimplementation (I). J Opt Sco AM A.1993,10(10):1875-1881.
[62] H.M.Ozaktas, D.Mendlovic. Fractional Fourier transforms and their opticalimplementation (II). J Opt Sco AM A.1993,10(12):2522-2531.
[63] H.M.Ozaktas, M.A.Kutay, Z.Zalevsky. The Fractional Fourier Transform withApplications in Optics and Signal Processing. New York: John Wiley&Sons,2000.
[64] L.B.Almeida. The fractional Fourier transform and time-frequency representation.IEEE Trans. Signal Processing.1994,42(10):3084-3091.
[65] A.W.Lachmann, B.H.Soffer. Relationship between the Radon-Wigner and fractionalFourier transform. Journal of Optics Society of American.1994,11:1798-180.
[66] H. M. Ozaktas, Orhan Arikan, et al. Digital Computation of the Fractional FourierTransform[J]. IEEE Trans. Signal Processing,1996,44(9):2141-2150.
[67] S.C.Pei, M.H.Yeh, C.C.Tseng. Discrete fractional Fourier transform based onorthogonal projections. IEEE Tran. Signal Processing.1999,47(5):1335-1348.
[68] C. Candan, M. A. Kutay, H. M. Ozaktas. The discrete fractional Fourier transform.IEEE Tran. Signal Processing.2000,48(5):1329-1337.
[69] S.C.Pei, C.C.Tseng, M.H.Yeh. A new discrete fractional Fourier transform based onconstrained eigendecomposition of DFT matrix by largrange multiplier method. IEEETrans. Circuits Syst.Ⅱ,1999,46:1240-1245.
[70] A. Bultheel, H. E. M. Sulbaran. Computation of the fractional Fourier transform.Applied and Computational Harmonic Analysis.2004,16:182-202.
[71] S. C. Pei, J. J. Ding. Closed-form discrete fractional and affine Fourier transforms.IEEE Tran. Signal Processing.2000,48(5):1338-1353.
[72] B. Santhanam, J. H. McClellan. The discrete rotational Fourier transform. IEEE Tran.Signal Processing.1996,44(4):994-998.
[73] M. H. Yeh, S. C. Pei. A method for the discrete fractional Fourier transformcomputation. IEEE Tran. Signal Processing.2003,51(3):889-891.
[74]陶然,邓兵,王越.分数阶傅里叶变换及其应用[M].北京:清华大学出版社,2009.
[75]平先军,陶然,周思永,王越.一种新的分数阶傅立叶变换快速算法[J].电子学报.2001,29(3):406-408.
[76]赵兴浩,陶然,邓兵,王越．分数阶傅里叶变换的快速计算新方法[J].电子学报.2007,35(6):1089-1093.
[77]赵兴浩,邓兵,陶然.分数阶傅里叶变换数值计算中的量纲归一化[J].北京理工大学学报,2005,25(4):360-364.
[78]刘锋,徐会法,陶然.分数阶Fourier变换中量纲归一化因子的选取[J].系统工程与电子技术.2011,33(2):237-241.
[79]张卫强,陶然.分数阶傅里叶变换域上带通信号的采样定理[J].电子学报.2005,33(7):1196-1199.
[80]邓兵,陶然,张惠云.抽样率转换的分数阶Fourier域分析[J].电子学报.2006,34(12):2190-2194.
[81] Tao Ran, Deng Bing, Zhang Wei-Qiang, Wang Yue. Sampling and sampling rateconversion of band limited signals in the fractional Fourier transform domain. IEEE Tran.Signal Processing.2008,56(1):158-171.
[82] Tao Ran, Zhang Feng, Wang Yue. Sampling random signals in a fractional Fourierdomain. Signal Processing.2011,91(6):1394-1400.
[83]董永强,陶然.含未知参数的多分量Chirp信号的分数阶傅里叶分析[J].北京理工大学学报.1999,19(5):612-616.
[84]赵兴浩,陶然,周思永,王越．基于Radon-Ambiguity变换和分数阶傅里叶变换的chirp信号检测及多参数估计[J].北京理工大学学报.2003,23(3):371-374.
[85]齐林,陶然,等.基于分数阶Fourier变换的多分量LFM信号的检测和参数估计[J].中国科学E辑.2003,33(8):749-759.
[86]邓兵,陶然,曲长文.分数阶Fourier域中多分量chirp信号的遮蔽分析[J].电子学报.2007,35(6):1094-1098.
[87]杨小明,陶然.基于分数阶傅里叶变换的线性调频信号二维波到达方向估计[J].电子学报.2008,36(9):1737-1740.
[88]刘锋,黄宇,陶然,王越．分数阶Fourier变换对多分量Chirp信号中心频率的分辨能力[J].兵工学报.2009,30(1):15-18.
[89]刘锋,徐会法,陶然.基于FRFT的对称三角LFMCW信号检测与参数估计[J].电子与信息学报.2011,33(8):1864-1870.
[90]邓兵,王旭,陶然,刘贤忠.基于分数阶傅里叶变换的线性调频脉冲时延估计特性分析[J].兵工学报.2012,33(6):765-768.
[91]齐林,陶然,周思永,王越．基于分数阶傅里叶变换的线性调频信号的自适应时频滤波[J].兵工学报.2003,24(4):499-503.
[92]齐林,陶然,周思永,王越．LFM信号的一种最优滤波算法[J].电子学报.2004,32(9):1464-1467.
[93]邓兵,陶然,齐林,刘锋.分数阶Fourier变换与时频滤波[J].系统工程与电子技术.2004,26(10):1357-1359.
[94]董永强,陶然,等.基于分数阶Fourier变换的SAR运动目标检测与成像[J].兵工学报.1999,20(2):132-136.
[95]赵兴浩,陶然.基于分数阶相关的无源雷达动目标检测方法[J].电子学报.2005,33(9):1567-1570.
[96]邓兵,陶然,平殿发,马路.基于分数阶傅里叶变换补偿多普勒徙动的动目标检测算法[J].兵工学报.2009,30(10):1303-1309.
[97]张南,陶然,王越.基于变标处理和分数阶傅里叶变换的运动目标检测算法[J].电子学报.2010,38(3):683-688.
[98] Akay Olcay，Boudreaux-Bartels G Faye. Fractional autocorrelation and its applicationto detection and estimation of linear FM signals. Proceedings of the IEEE-SP InternationalSymposium on Time-Frequency and Time-Scale Analysis.1998:213-216.
[99] T. Alieva, M. J. Bastiaans, On fractional Fourier transform moments. IEEE SignalProcessing Letters.2000,7(11):320–323.
[100] T. Alieva, M. J. Bastiaans, L. Stankovic. Signal reconstruction from two closefractional Fourier power spectra. IEEE Tran. Signal Processing.2003,51(1):112-123.
[101] M. G. Ertosun, H. Atli, H. M. Ozaktas, B. Barshan. Complex signal recovery fromfractional Fourier transform intensities. IEEE12th Signal Processing and CommunicationsApplications Conference.2004,308-311.
[102] L. Qi, R. Tao, S. Y. Zhou, Y. Wang. Detection and parameter estimation ofmulticomponent LFM signal based on the fractional Fourier transform. Science in China F:Information Science.2004,47:184-198.
[103] X. L. Chen, J. Guan. A Fast FRFT Based Detection Algorithm of Multiple MovingTargets in Sea Clutter. IEEE International Radar Conference.2010,402-406.
[104]李靖,王树勋,汪飞.基于分数阶傅里叶变换的chirp信号时频分析[J].系统工程与电子技术.2005,27(6):988-990.
[105]汪飞,曹凡.基于时频空间奇异值分解的多分量线性调频信号分离与增强[J].数据采集与处理.2009,24(6):767-771.
[106] Z. P. Yin, D. C. Zhang, W. D. Chen, D. J. Wang. LFM signal detection using theorigin moment of fractional spectrum. International Conference on Signal Processing.2008.
[107]尹治平,张义安,陈卫东,王东进.基于分数阶功率谱的LFM信号检测[J].系统工程与电子技术.2009,31(1):45-48.
[108]卫红凯,王平波,蔡志明,姚万军.分数阶Fourier变换极值搜索算法研究[J].电子学报.2010,38(12):2949-2952.
[109] Wei Hong kai, Wang Ping bo, Cai Zhiming, Fu Yinfeng. Comparison of intelligentoptimization methods in the fractional Fourier transform. The Second InternationalConference on Computer Modeling and Simulation.2010,552-555.
[110]陶然,邓兵,王越.分数阶Fourier变换在信号处理领域的研究进展[J].中国科学E辑.2006,36(2):113-136.
[111]邓兵,陶然,平殿发.基于分数阶Fourier变换的chirp-rate调制[J].电子学报.2008,36(6):1078-1083.
[112]肇启明,张钦宇,张乃通.多进制chirp-rate键控调制及分数傅里叶变换法解调[J].通信学报.2010,31(6):1-6.
[113]张贤达，保铮.非平稳信号分析与处理[M].北京:国防工业出版社,1998.
[114] J. Tsao, B. D. Steinberg. Reduction of sidelobe and speckle artifacts in microwaveimaging: the CLEAN technique. IEEE Transactions on Antennas and Propagation.1988,36(4):543-556.
[115] M. I. Ahmad, Z. W. Liu, Y. G. Xu. Order selection in fractional Fourier transformbased beamforming. Journal of Systems Engineering and Electronics,2010,21(3):361-369.
[116] Y. L. Zhang, Q. Y. Zhang, S. H. Wu. Biomedical Signal Detection Based onFractional Fourier Transform. International Conference on Information Technology andApplication in Biomedicine.2008:349–352.
[117] F. Cao, S. X. Wang, F. Wang. A New Time-Frequency Analysis Method ofMulti-Component Chirp Signal. International Conference on Signal Processing.2006.
[118] M. Wang, A.K. Chan, C.K. Chui. Linear Frequency-Modulated Signal DetectionUsing Radon-Ambiguity Transform. IEEE Transactions on Signal Processing.1998,46(3):571-586.
[119] C. Capus, K. Brown. Fractional Fourier transform of the Gaussian and fractionaldomain signal support. IEE Proceedings of Vision, Image and Signal Processing.2003,150(2):99-106.
[120]仇兆炀,陈蓉,汪一鸣.基于FRFT的线性调频信号欠采样快速检测方法[J].电子学报.2012,40(11):2165-2170.
[121]许旭. E-2C2000预警机和APS-145(V)雷达附E-2T预警机简介[J].电子工程信息.2004(3):52-54.
[122] DAVID A Shnidman．Generalized Radar Clutter Model [J]．IEEE Trans on AES.1999,35(3)：857-865．
[123] BLACKNELL D．New Method for the Simulation of Correlated K-distributedClutter [J]．IEE Proc-Radar, Sonar Navigation.1994,141(1)：53-58．
[124]刘娜,时海,杨建华.虚拟战场电磁环境雷达信号建模方法[J].指挥控制与仿真.2007,29(6):98-102.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |