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王海彬 , 黄峥 , 文瑞虎 . 太赫兹技术在引信中应用的探讨 [J ] . 探测与控制学报 , 2016 , 38 ( 6 ): 1 - 6 .

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岳凯 , 郝新红 , 栗苹 , 等 . 基于分数阶傅里叶变换的线性调频引信定距方法 [J ] . 兵工学报 , 2015 , 36 ( 5 ): 801 - 808 . DOI: 10.3969/j.issn.1000-1093.2015.05.006 http://doi.org/10.3969/j.issn.1000-1093.2015.05.006 针对调频（FM）引信，为了在较小的调制频偏内获得较高定距精度，提出了基于分数阶域瞬时初始频率估计和基于分数阶相关的两种定距方法。论述了两种方法的定距原理，分析了其距离分辨力与抗噪声性能，并进行了仿真验证。结果表明：较FM谐波定距方法，两种方法具有较高的距离分辨力，且受FM带宽影响较小；同时定距方法通过FM发射、接收信号与单载波混频方法，在分数阶域避免了FM率估计，降低了算法复杂度，具有工程可实现性；较初始频率估计方法，基于分数阶相关的FM定距方法抗噪声性能更好，适合于低信噪比环境下信号检测。

YUE K , HAO X H , LI P , et al. Research on ranging method for linear frequency modulation radio fuze based on fractional Fourier transform [J ] . Acta Armamentarii , 2015 , 36 ( 5 ): 801 - 808 .( in Chinese) DOI: 10.3969/j.issn.1000-1093.2015.05.006 http://doi.org/10.3969/j.issn.1000-1093.2015.05.006 To improve the ranging accuracy of the frequency modulation（FM）radio fuze under the limit of the little frequency deviation, two ranging methods, i.e. instantaneous initial frequency estimation method and fractional correlation method, for linear FM radio fuze based on fractional Fourier transform (FRFT) are proposed. The ranging principles of the two methods are described, their range resolutions and anti-noise performances are analyzed, and the simulations are carried out to validate these methods. The simulation results demonstrate that the ranging resolutions of the two methods which are affected by the modulation bandwidth rarely are much better than that of the ranging method based on the harmonic wave method. For the known frequency modulation rate, the complexity of the methods is reduced and acceptable for engineering realization. The fractional correlation method is better than the instantaneous initial frequency estimation method in anti-noise performance and can be used in the low signal-to-noise ratio circumstance.

SWIERCZ E , JANCZAK D , KONOPKO K . Detection of LFM radar signals and chirp rate estimation based on time-frequency rate distribution [J ] . Sensors , 2021 , 21 ( 16 ): 5415 - 5416 . DOI: 10.3390/s21165415 http://doi.org/10.3390/s21165415 https://www.mdpi.com/1424-8220/21/16/5415 https://www.mdpi.com/1424-8220/21/16/5415 Linear frequency-modulated (LFM) signals are the most significant example of waveform used in low probability of intercept (LPI) radars, synthetic aperture radars and modern communication systems. Thus, interception and parameter estimation of the signals is one of the challenges in Electronic Support (ES) systems. The methods, which are widely used to accomplish this task are mainly based on transformations from time to time-frequency domain, which concentrate the energy of signals along an instantaneous frequency (IF) line. The most popular examples of such transforms are the short time Fourier transform (STFT) and Wigner-Ville distribution (WVD). However, for LFM waveforms, methods that concentrate signal energy along a line in the time-frequency rate domain may allow to obtain better detection and estimation performance. This type of transformation can be obtained using the cubic phase (CP) function (CPF). In the paper, the detection of LFM waveform and its chirp rate (CR) parameter estimation based on the extended forms of the standard CPF is proposed. The CPF was originally introduced for instantaneous frequency rate (IFR) estimation for quadratic frequency modulated (QFM) signals i.e., cubic phase signals. Summation or multiplication operations on time cross-sections of the CPF allow to formulate the extended forms of the CPF. Based on these forms, detection test statistics and the estimation procedure of LFM signal parameters have been proposed. The widely known estimation methods assure satisfying accuracy for high SNR levels, but for low SNRs the reliable estimation is a challenge. The proposed approach based on joint analysis of detection and estimation characteristics allows to increase the reliability of chirp rate estimates for low SNRs. The results of Monte-Carlo simulation investigations on LFM signal detection and chirp rate estimation evaluated by the mean squared error (MSE) obtained by the proposed methods with comparisons to the Cramer-Rao lower bound (CRLB) are presented.

ZHANG Z C , LI D , CHEN Y J , et al. Linear canonical wigner distribution of noisy LFM signals via multiobjective optimization analysis involving Variance-SNR [J ] . IEEE Commnications Letters , 2021 , 25 ( 2 ): 1 - 1 .

张庆辉 , 栗苹 , 钱龙 , 等 . 基于时频分析的伪码调相引信自适应干扰对消器设计 [J ] . 兵工学报 , 2006 , 27 ( 5 ): 807 - 810 . 时频分析是识别宽带扩频信号中窄带干扰的有效方法。采用扩展离散Wigner-Ville分布( EDTWD)的时频分析方法提取和重构伪码调相引信回波信号中的窄带干扰，然后通过自适应干扰对消将干扰消除。该方法不需要干扰信号的先验知识，滤除干扰的同时使目标回波信号失真很小，也适用于存在多个干扰源的情况。介绍其算法原理和设计过程，并给出仿真结果。

ZHANG Q H , LI P , QIAN L , et al. Design of adaptive interference canceller for PN code phase modulation fuze based on time-frequency analysis [J ] . Acta Armamentarii , 2006 , 27 ( 5 ): 807 - 810 . (in Chinese)

齐林 , 陶然 , 周思永 , 等 . 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 . 本文提出了一种基于分数阶傅里叶变换的线性调频(LFM)信号的自适应滤波方法，利用该变换等同于对信号在时频平面进行旋转这一重要特性，将混迭有噪声的信号以特定的旋转角作分数阶傅里叶变换，使得信号与噪声在变换域中的交迭达到最小;在此基础上，通过窄带通滤波器对LFIVI信号进行抽取，去除大部分的噪声能量，然后，再经过分数阶傅里叶反变换，恢复出原来的LFM信号。理论分析和仿真表明，该方法不仅可获得明显的信噪比的改善，而且具有算法简单及信号失真小等特点，和其它基于二维时频分析工具的滤波算法相比，降低了计算的复杂度，其实现更为简便。

QI L , TAO R , ZHOU S Y , et al. Adaptive time-frequency filtering of LFM signal based on fractional fourier transform [J ] . Acta Armamentarii , 2003 , 24 ( 4 ): 499 - 503 . (in Chinese)

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罗强 , 任庆利 , 杨万海 . 小波变换在无线电引信中的应用 [J ] . 兵工学报 , 2003 , 24 ( 2 ): 153 - 156 .

LUO Q , REN Q L , YANG W H . Application of wavelet transform in radio fuze [J ] . Acta Armamentarii , 2003 , 24 ( 2 ): 153 - 156 . (in Chinese)

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GERASIMOV M , DYUNIN E , GERASIMOV J , et al. Application of wigner distribution function for THz propagation analysis [J ] . Sensors , 2021 , 22 ( 1 ): 240 - 241 . DOI: 10.3390/s22010240 http://doi.org/10.3390/s22010240 https://www.mdpi.com/1424-8220/22/1/240 https://www.mdpi.com/1424-8220/22/1/240 The construction of a transmission line (TL) for a wide tunable broad-spectrum THz radiation source is not a simple task. We present here a platform for the future use of designs of the TL through our homemade simulations. The TL is designed to be a component of the construction of an innovative accelerator at the Schlesinger Family Center for Compact Accelerators, Radiation Sources and Applications (FEL). We developed a three-dimensional space-frequency tool for the analysis of a radiation pulse. The total electromagnetic (EM) field on the edge of the source is represented in the frequency domain in terms of cavity eigenmodes. However, any pulse can be used regardless of its mathematical function, which is the key point of this work. The only requirement is the existence of the original pulse. This EM field is converted to geometric-optical ray representation through the Wigner transform at any desired resolution. Wigner’s representation allows us to describe the dynamics of field evolution in future propagation, which allows us to determine an initial design of the TL. Representation of the EM field by rays gives access to the ray tracing method and future processing, operating in the linear and non-linear regimes. This allows for fast work with graphics cards and parallel processing, providing great flexibility and serving as future preparation that enables us to apply advanced libraries such as machine learning. The platform is used to study the phase-amplitude and spectral characteristics of multimode radiation generation in a free-electron laser (FEL) operating in various operational parameters.

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