基于分数阶Fourier变换的Chirp-COTR-UWB系统窄带干扰抑制

对基于Chirp的正交码发送参考超宽带（Chirp—COTR—UWB）系统进行研究,推导了窄带单音干扰和窄带BPSK干扰条件下接牧机干扰输出分量的表达式,证明了窄带平稳干扰信号经过去斜脉冲压缩后将被展宽成两个具有不同中心频率的非平稳线性调频干扰。采用分数阶Fourier变换的时频分析方法对线性调频干扰进行抑制,并对该系统抗干扰性能进行了仿真分析。结果表明采用FrFT时频方法可有效抑制Chirp—COTR—UWB信号中的窄带干扰,并改善系统的抗干扰性能,     

Intermittent Clutter Removal Approach for Wind Profiler Data Based on Fractional Fourier Transform

Through the analysis of the target characteristics and according to the intermittent clutter bursting and short duration characteristics, a new method for the clutter recognition based on the fractional Fourier transform (FRFT) is proposed. This method is predicated on the fact that the FRFT perfectly localizes a chirp signal as an impulse when the angle parameter of the transform matches the chirp rate of the chirp signal. The method involves detecting the presence of the intermittent clutter and correctly estimating its orientation in the time-frequency plane, removing the intermittent clutter in the fractional domain, and completing wind estimation by the power spectrum. By testing the artificial WPR-like signal and data measured from the field, we verify that the FRFT-based method is very effective.     

Intermittent Clutter Removal Approac for wind Profiler Data Based on Fractional Fourier Transform

Through the analysis of the target characteristics and according to the intermittent clutter bursting and short duration characteristics, a new method for the clutter recognition based on the fractional Fourier transform (FRFT) is proposed. This method is predicated on the fact that the FRFT perfectly localizes a chirp signal as an impulse when the angle parameter of the transform matches the chirp rate of the chirp signal. The method involves detecting the presence of the intermittent clutter and correctly estimating its orientation in the time-frequency plane, removing the intermittent clutter in the fractional domain, and completing wind estimation by the power spectrum. By testing the artificial WPR-like signal and data measured from the field, we verify that the FRFT-based method is very effective.     

Novel LFM Jammer Suppression Algorithm for DSSS in FRFT Domain

A novel algorithm is proposed to resolve the defects in the traditional linear frequency modulation (LFM) jamming suppression algorithm in the fractional Fourier transform (FRFT) domain. The traditional LFM jamming suppression algorithm in the FRFT domain has some defects. For example, the exact threshold is difficult to set and both the signal-to-noise ratio (SNR) loss and spectrum leakage are serious in strong jamming-to-signal ratio (JSR) situations. Windowing, overlapping and inverse windowing techniques are used in the FRFT domain to reduce the spectrum leakage and the SNR loss. Under the condition that only the direct sequence spread spectrum (DSSS) signal and white Gaussian noise are present, the amplitude of the received signal after FRFT is assumed to be Rayleigh distributed. Based on the distribution characteristic, hypothesis testing is used to suppress the jamming spectrum using the algorithm. Simulation results show that the performance of proposed algorithm is better than that of the conventional algorithms, especially in a strong jamming and multi component LFM jamming environment.     

一种基于神经网络的干扰抑制系统

为抑制扩频系统中的干扰信号,提出变换域信息信号识别(TDISI)干扰抑制系统,其中采用了扩展BP神经网络(EBPNN).TDISI首先利用快速傅立叶变换(FFT)将输入信号映射到变换域,提高系统收敛速度;然后通过EBPNN对变换系数进行信息信号的自适应识别,其具有复杂度低、鲁棒性好的特点.理论分析得到采用TDISI后接收信号的干信比(ISR)抑制量、信噪比(SNR)损失量和误码率(BER)的数学表达式.仿真结果表明:在干扰信号相同的情况下,此系统的干信比抑制量较2种现有系统分别提高29.9%和8.9%,信噪比损失量分别降低了54.3%和21.2%.     

Chirp-Rate Resolution of Fractional Fourier Transform in Multi-component LFM Signal

Distinguishing close chirp-rates of different linear frequency modulation (LFM) signals under concentrated and complicated signal environment was studied. Firstly, detection and parameter estimation of multi-component LFM signal were used by discrete fast fractional Fourier transform (FrFT). Then the expression of chirp-rate resolution in fractional Fourier domain (FrFD) was deduced from discrete normalize time-frequency distribution, when multi-component LFM signal had only one center frequency. Furthermore, the detail influence of the sampling time, sampling frequency and chirp-rate upon the resolution was analyzed by partial differential equation. Simulation results and analysis indicate that increasing the sampling time can enhance the resolution, but the influence of the sampling frequency can be omitted. What’s more, in multi-component LFM signal, the chirp-rate resolution of FrFT is no less than a minimal value, and it mainly dependent on the biggest value of chirp-rates, with which it has an approximately positive exponential relationship.     

窄带干扰环境高动态双二进制偏移载波信号捕获

针对窄带干扰环境下高动态双二进制偏移载波信号捕获困难的问题，提出奇异值分解结合最小描述长度准则以及离散多项式相位变换，部分匹配滤波器和分数阶傅里叶变换加频谱校正的捕获算法。首先，利用奇异值分解将含窄带干扰的信号分为信号子空间和干扰子空间，利用最小描述长度准则确定目标信号和干扰信号的界限，完成干扰抑制；然后，使用定阶算法确定信号动态阶数并完成降阶；最后，完成仅含一阶多普勒变化率信号的捕获。仿真结果表明，所提算法在较好地保留原始信号特征的同时自适应完成干扰精确抑制，且性能稳定。此外，所提捕获算法在相同条件下与未校正相比，捕获概率有约2 dB的增益。     

Performance analysis of hybrid carrier DS CDMA communication system

A hybrid carrier (HC) DS CDMA communication system is proposed, combining 4-weighted fractional Fourier transform (4-WFRFT) with code division multiple access (CDMA) technique. The signals are modulated in a certain order fractional Fourier domain and transformed by 4-WFRFT to compose the hybrid carrier signals. In the time domain CDMA technique is adopted for multiple accesses and time diversity gain. Compared to orthogonal frequency division multiplexing (OFDM) system, in which Fourier transform is adopted, the signal energy in HC system is distributed on the time-frequency plane more evenly and symmetrically. Thus, when there is a deep fading notch or single-frequency interference in the channel, the proposed method can split the interference to a broader range in order to reduce the influence, resulting in the better system performance. Moreover, the performances of the proposed system, such as peak-to-average power rate (PAPR) and security are also discussed in the paper.     

基于时频分析的LFM信号检测与参数估计

基于Radon Wigner变换、分数阶Fourier变换与时频分布的关系,利用其对线性调频(linearityfrquencymodulation,LFM)信号良好的时频聚集性,通过计算Radon Wigner变换或分数阶Fourier变换,对线性调频信号LFM信号进行检测和参数估计。理论分析和计算机仿真证明:2种方法对于LFM信号的分析好于Wigner Ville变换等常用的时频变换。     

Multi-channel sampling theorems for band-limited signals with fractional Fourier transform

Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies. Supported partially by the National Natural Science Foundation of China (Grant Nos. 60232010 and 60572094) and the National Natural Science Foundation of China for Distinguished Young Scholars (Grant No. 60625104)     

Improved Spectral Representation for Birdcall Based on Fractional Fourier Transform

A novel spectral representation based on fractional Fourier transform (FrFT) is proposed and applied to birdcall analysis. The FrFT-based spectrogram of a signal is derived and compared with its FT-based counterpart,and the spectrum gathering method is used to show the energy distribution related to the pitch frequency. The fixed transform order and adaptive orders for FrFT are tested. The fixed order can be obtained empirically or calculated according to the known chirp rate. The adaptive optimal orders are determined by using ambiguity function. Experimental results with birdcalls show that the FrFT-based spectrogram with an optimal transform order has higher resolution than its STFT-based counterpart,and the better performance can be achieved if adaptive orders are used.     

函数拟合连续信号的频谱分析

用插值函数拟合代替抽样函数求有限长连续信号和周期信号的频谱 ,推导出用离散信号傅里叶变换公式求拟合连续信号频谱的方法 ,该方法能用离散傅里叶变换的公式更准确地求出连续信号的频谱 .该方法可以非常方便地改进现有信号分析仪性能价格比     

High Resolution Multipath Time Delay Estimation Based on FLOCCS-ESPRIT

The non-Gaussian α-stable distribution is introduced to model impulsive noise. Based on the theory of fractional lower order statistics （FLOS）, the fractional lower order cross-covariance （FLOCC） sequence for two received signals is obtained and the fractional lower order cross-covariance spectrum （FLOCCS） can be approached by taking a Fourier transform for the FLOCC sequence. When the FLOCCS is treated as a sequence in the time domain, the problem of multipath time delay estimation （TDE） may be converted into one on multi-frequencies estimation or directions of arrival estimation. Accordingly, the high resolution multipath TDE can be realized with the ESPRIT technology. This idea on multipath TDE is referred to as FLOCCS-ESPRIT in this paper. Computer simulations show that this method has good performance both in a Gaussian noise and in an impulsive noise environment.     

基于广义功率谱密度的分布压缩宽带频谱感知

为实现在Alpha稳定分布噪声下宽带频谱感知,扩展了传统功率谱密度概念,提出广义功率谱密度的概念,在此基础上提出基于广义功率谱密度的分布压缩宽带频谱感知。此方法能有效地抑制Alpha稳定分布噪声。首先,将接收的宽带信号进行分数低阶处理,计算自相关函数,再结合压缩感知原理将分数低阶自相关向量压缩和融合重构,最后经傅立叶变换得到广义功率谱密度。仿真结果表明,该方法具有良好的宽带功率谱密度估计性能,在Alpha稳定分布噪声下能较好地完成宽带频谱感知。     

Research Progress on Discretization of Linear Canonical Transform

Linear canonical transformation(LCT) is a generalization of the Fourier transform and fractional Fourier transform. The recent research has shown that the LCT is widely used in signal processing and applied mathematics, and the discretization of the LCT becomes vital for the applications of LCT. Based on the development of discretization LCT, a review of important research progress and current situation is presented, which can help researchers to further understand the discretization of LCT and can promote its engineering application. Meanwhile, the connection among different discretization algorithms and the future research are given.     

Research Progress of the Sampling Theorem Associated with the Fractional Fourier Transform

Sampling is a bridge between continuous-time and discrete-time signals, which is important to digital signal processing. The fractional Fourier transform(FrFT) that serves as a generalization of the FT can characterize signals in multiple fractional Fourier domains, and therefore can provide new perspectives for signal sampling and reconstruction. In this paper, we review recent developments of the sampling theorem associated with the FrFT, including signal reconstruction and fractional spectral analysis of uniform sampling, nonuniform samplings due to various factors, and sub-Nyquist sampling, where bandlimited signals in the fractional Fourier domain are mainly taken into consideration. Moreover, we provide several future research topics of the sampling theorem associated with the FrFT.     

基于延时相关和FRFT的编队目标架次分辨方法

为较好满足窄带雷达的防空作战需求,提出了一种基于延时相关和分数阶傅里叶变换(FRFT)的空中编队目标架次分辨方法.该方法首先利用延时相关法粗略估计出回波信号的多普勒调频斜率,依据调频斜率和FRFT阶次的对应关系,获得最优变换阶次的粗略值;然后以FRFT后信号的熵值为最小化目标函数,提出一种精确搜索最优变换阶次算法,并以此最优变换阶次对回波信号进行FRFT,从而实现在分数阶多普勒域的目标架次分辨.仿真结果表明,本文所提方法具有较好的多普勒分辨性能,编队目标架次识别准确率较传统的短时傅里叶变换(STFT)、维格纳分布(WVD)分析方法有显著提高.     

Adaptive Short-Time Fractional Fourier Transform Based on Minimum Information Entropy

Traditional short-time fractional Fourier transform(STFrFT) has a single and fixed window function, which can not be adjusted adaptively according to the characteristics of frequency and frequency change rate. In order to overcome the shortcomings, the STFrFT method with adaptive window function is proposed. In this method, the window function of STFrFT is adaptively adjusted by establishing a library containing multiple window functions and taking the minimum information entropy as the criterion, so as to obtain a time-frequency distribution that better matches the desired signal. This method takes into account the time-frequency resolution characteristics of STFrFT and the excellent characteristics of adaptive adjustment to window function, improves the time-frequency aggregation on the basis of eliminating cross term interference,and provides a new tool for improving the time-frequency analysis ability of complex modulated signals.     

基于广义随机共振的Chirp信号检测性能分析

为便于提取多个chirp信号叠加噪声模型中目标chirp信号的参数信息,本文研究了该混合信号激励过阻尼双稳系统的随机共振现象。但由于chirp信号在频域能量的非聚焦性,传统刻画随机共振的信噪比指标失效。因此,基于chirp信号在分数阶傅里叶变换域上的能量分布特性,对非线性随机动力系统的畸变输出信号进行变换域上的最优滤波,给出最优分数阶傅里叶变换域上的信干比定义形式,并以此作为目标chirp信号经过系统后的性能增益的度量和广义随机共振现象的判别依据。数值仿真结果表明,在存在多个chirp信号驱动的过阻尼双稳系统中,当目标chirp信号或噪声能量不足以激发粒子跃迁时,干扰chirp信号能在一定程度上协助粒子发生跃迁,产生协同随机共振现象,从而提高对目标chirp信号的检测性能。     

基于MPDFRFT的数字水印算法

基于多参量离散分数阶Fourier变换(MPDFRFT)理论提出了一种数字水印算法,该算法首先将水印经Arnold变换进行置乱,然后根据分数阶Fourier变换具有空域和频域双域信息表达能力,分别对载体图象和所加水印进行不同阶次向量的多参量分数阶Fourier变换;将变换后的水印信息直接叠加到载体图象的特征区域内,然后进行反变换得到水印图象。在噪声、滤波、剪切和JPEG压缩等攻击方式下,对算法进行了鲁棒性分析,仿真实验结果表明该算法具有较强的鲁棒性和安全性。