The quaternion approach to solve the coupled nonlinear Schrodinger equations （CNSEs） in fibers is proposed, converting the CNSEs to a single variable equation by using a conception of eigen-quaternion of coupled qua...The quaternion approach to solve the coupled nonlinear Schrodinger equations （CNSEs） in fibers is proposed, converting the CNSEs to a single variable equation by using a conception of eigen-quaternion of coupled quater- nion. The crosstalk of quarter-phase-shift-key signals caused by fiber nonlinearity in polarization multiplexing systems with 100 Cbps bit-rate is investigated and simulated. The results demonstrate that the crosstalk is like a rotated ghosting of input constellation. For the 50 km conventional fiber link, when the total power is less than 4roW, the crosstalk effect can be neglected; when the power is larger than 20roW, the crosstalk is very obvious. In addition, the crosstalk can not be detected according to the output eye diagram and state of polarization in Poincare sphere in the trunk fiber, making it difficult for the monitoring of optical trunk link.展开更多
An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the pola...An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.展开更多
This paper examines the direction of arrival(DOA)estimation for polarized signals impinging on a sparse vector sensor array which is based on the maximum interelement spacing constraint(MISC).The vector array effectiv...This paper examines the direction of arrival(DOA)estimation for polarized signals impinging on a sparse vector sensor array which is based on the maximum interelement spacing constraint(MISC).The vector array effectively utilizes the polarization domain information of incident signals,and the quaternion model is adopted for signals polarization characteristic maintenance and computational burden reduction.The features of MISC arrays are crucial to the mutual coupling effects reduction and higher degrees of freedom(DOFs).The quaternion data model based on vector MISC arrays is established,which extends the scalar MISC array into the vector MISC array.Based on the model,a quaternion multiple signal classification(MUSIC)algorithm based on vector MISC arrays is proposed for DOA estimation.The algorithm combines the advantages of the quaternion model and the vector MISC array to enhance the DOA estimation performance.Analytical simulations are performed to certify the capability of the algorithm.展开更多
This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selec...This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selecting suitable parameters to handle different levels of noise.In particular,the quaternion analytic signal,which is an effective tool in color image processing,can also be produced by quaternion Hardy filtering with specific parameters.Based on the QHF and the improved Di Zenzo gradient operator,a novel color edge detection algorithm is proposed;importantly,it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique.From the experimental results,we conclude that the minimum PSNR improvement rate is 2.3%and the minimum SSIM improvement rate is 30.2%on the CSEE database.The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.展开更多
The quaternion linear canonical transform (QLCT) is defined in this paper, with proofs given for its reversibility property, its linear property, its odd-even invariant property and additivity property. Meanwhile, the...The quaternion linear canonical transform (QLCT) is defined in this paper, with proofs given for its reversibility property, its linear property, its odd-even invariant property and additivity property. Meanwhile, the quaternion convolution (QCV), quaternion correlation (QCR) and product theorem of LCT are deduced. Their physical interpretation is given as classical convolution, correlation and product theorem. Moreover, the fast algorithm of QLCT (FQLCT) is obtained, whose calculation complexity for different signals is similar to FFT. In addition, the paper presents the relationship between the convolution and correlation in LCT domains, and the convolution and correlation can be calculated via product theorem in Fourier transform domain using FFT.展开更多
为了解决相干信号的极化平滑算法在小快拍数和低信噪比条件下估计性能较差的问题,结合四元数的正交特性和协方差张量方法,提出了一种基于张量四元数的极化平滑多重信号分类(Multiple Signal Classification,MUSIC)解相干算法。首先,为...为了解决相干信号的极化平滑算法在小快拍数和低信噪比条件下估计性能较差的问题,结合四元数的正交特性和协方差张量方法,提出了一种基于张量四元数的极化平滑多重信号分类(Multiple Signal Classification,MUSIC)解相干算法。首先,为了充分利用接收数据样本中的多维结构信息,建立了由张量四元数表示的柱面共形阵列极化平滑信号模型;其次,将平滑后的张量协方差矩阵通过高阶奇异值分解得到信号子空间;最后,通过极化秩亏MUSIC算法对入射相干信号分别进行二维波达方向(Direction of Arrival,DOA)估计和极化参数估计。仿真结果表明,该算法在小快拍数和低信噪比条件下具有更高的估计精度和分辨能力。展开更多
为提高声场空域中目标参数估计的精度,将四元数理论应用于均匀圆型声矢量阵列的二维空间角度估计中,建立了基于四元数模型的信号接收模型,推导了圆型声矢量阵的四元数导向矢量,给出了二维波达角估计的四元数域空间谱算法。考虑算法的软...为提高声场空域中目标参数估计的精度,将四元数理论应用于均匀圆型声矢量阵列的二维空间角度估计中,建立了基于四元数模型的信号接收模型,推导了圆型声矢量阵的四元数导向矢量,给出了二维波达角估计的四元数域空间谱算法。考虑算法的软硬件可实现性,理论分析了算法的内存占用空间和计算量。此外,分析了圆阵半径对侧向性能的影响,为实际工作中圆阵的半径选取提供了一定的依据。仿真结果表明,基于四元数模型的MUSIC(Multiple Signal Classification)算法的分辨力较高,抗干扰能力较强,提高了信号参数估计的精度。展开更多
研究了基于两分量简化电磁矢量传感器阵列的多个信号波达方向(Direction of arrival,DOA)跟踪问题,提出了一种基于四元数模型的数据投影(Quaternion data projection method,QDPM)跟踪算法。此算法对初始化条件引起的波动具有很强的鲁棒...研究了基于两分量简化电磁矢量传感器阵列的多个信号波达方向(Direction of arrival,DOA)跟踪问题,提出了一种基于四元数模型的数据投影(Quaternion data projection method,QDPM)跟踪算法。此算法对初始化条件引起的波动具有很强的鲁棒性,并且具有比常规DPM(Data projection method)算法更快的收敛速度,尤其在信号角度变化较剧烈时体现得更明显。此外,在低信噪比的情况下,QDPM算法比DPM算法具有更高的DOA跟踪精度。最后通过仿真实验验证了算法的有效性。展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 61275075the Beijing Natural Science Foundation under Grant Nos 4132035 and 4144080
文摘The quaternion approach to solve the coupled nonlinear Schrodinger equations （CNSEs） in fibers is proposed, converting the CNSEs to a single variable equation by using a conception of eigen-quaternion of coupled quater- nion. The crosstalk of quarter-phase-shift-key signals caused by fiber nonlinearity in polarization multiplexing systems with 100 Cbps bit-rate is investigated and simulated. The results demonstrate that the crosstalk is like a rotated ghosting of input constellation. For the 50 km conventional fiber link, when the total power is less than 4roW, the crosstalk effect can be neglected; when the power is larger than 20roW, the crosstalk is very obvious. In addition, the crosstalk can not be detected according to the output eye diagram and state of polarization in Poincare sphere in the trunk fiber, making it difficult for the monitoring of optical trunk link.
基金supported by Startup Foundation for Phd Research of Henan Normal University(No.5101119170155).
文摘An uncertainty principle(UP),which offers information about a signal and its Fourier transform in the time-frequency plane,is particularly powerful in mathematics,physics and signal processing community.Under the polar coordinate form of quaternion-valued signals,the UP of the two-sided quaternion linear canonical transform(QLCT)is strengthened in terms of covariance.The condition giving rise to the equal relation of the derived result is obtained as well.The novel UP with covariance can be regarded as one in a tighter form related to the QLCT.It states that the product of spreads of a quaternion-valued signal in the spatial domain and the QLCT domain is bounded by a larger lower bound.
基金supported by the National Natural Science Foundation of China(62031015).
文摘This paper examines the direction of arrival(DOA)estimation for polarized signals impinging on a sparse vector sensor array which is based on the maximum interelement spacing constraint(MISC).The vector array effectively utilizes the polarization domain information of incident signals,and the quaternion model is adopted for signals polarization characteristic maintenance and computational burden reduction.The features of MISC arrays are crucial to the mutual coupling effects reduction and higher degrees of freedom(DOFs).The quaternion data model based on vector MISC arrays is established,which extends the scalar MISC array into the vector MISC array.Based on the model,a quaternion multiple signal classification(MUSIC)algorithm based on vector MISC arrays is proposed for DOA estimation.The algorithm combines the advantages of the quaternion model and the vector MISC array to enhance the DOA estimation performance.Analytical simulations are performed to certify the capability of the algorithm.
基金supported in part by the Science and Technology Development Fund,Macao SAR FDCT/085/2018/A2the Guangdong Basic and Applied Basic Research Foundation(2019A1515111185)。
文摘This paper presents a robust filter called the quaternion Hardy filter(QHF)for color image edge detection.The QHF can be capable of color edge feature enhancement and noise resistance.QHF can be used flexibly by selecting suitable parameters to handle different levels of noise.In particular,the quaternion analytic signal,which is an effective tool in color image processing,can also be produced by quaternion Hardy filtering with specific parameters.Based on the QHF and the improved Di Zenzo gradient operator,a novel color edge detection algorithm is proposed;importantly,it can be efficiently implemented by using the fast discrete quaternion Fourier transform technique.From the experimental results,we conclude that the minimum PSNR improvement rate is 2.3%and the minimum SSIM improvement rate is 30.2%on the CSEE database.The experiments demonstrate that the proposed algorithm outperforms several widely used algorithms.
文摘The quaternion linear canonical transform (QLCT) is defined in this paper, with proofs given for its reversibility property, its linear property, its odd-even invariant property and additivity property. Meanwhile, the quaternion convolution (QCV), quaternion correlation (QCR) and product theorem of LCT are deduced. Their physical interpretation is given as classical convolution, correlation and product theorem. Moreover, the fast algorithm of QLCT (FQLCT) is obtained, whose calculation complexity for different signals is similar to FFT. In addition, the paper presents the relationship between the convolution and correlation in LCT domains, and the convolution and correlation can be calculated via product theorem in Fourier transform domain using FFT.
文摘为了解决相干信号的极化平滑算法在小快拍数和低信噪比条件下估计性能较差的问题,结合四元数的正交特性和协方差张量方法,提出了一种基于张量四元数的极化平滑多重信号分类(Multiple Signal Classification,MUSIC)解相干算法。首先,为了充分利用接收数据样本中的多维结构信息,建立了由张量四元数表示的柱面共形阵列极化平滑信号模型;其次,将平滑后的张量协方差矩阵通过高阶奇异值分解得到信号子空间;最后,通过极化秩亏MUSIC算法对入射相干信号分别进行二维波达方向(Direction of Arrival,DOA)估计和极化参数估计。仿真结果表明,该算法在小快拍数和低信噪比条件下具有更高的估计精度和分辨能力。
文摘为提高声场空域中目标参数估计的精度,将四元数理论应用于均匀圆型声矢量阵列的二维空间角度估计中,建立了基于四元数模型的信号接收模型,推导了圆型声矢量阵的四元数导向矢量,给出了二维波达角估计的四元数域空间谱算法。考虑算法的软硬件可实现性,理论分析了算法的内存占用空间和计算量。此外,分析了圆阵半径对侧向性能的影响,为实际工作中圆阵的半径选取提供了一定的依据。仿真结果表明,基于四元数模型的MUSIC(Multiple Signal Classification)算法的分辨力较高,抗干扰能力较强,提高了信号参数估计的精度。
文摘研究了基于两分量简化电磁矢量传感器阵列的多个信号波达方向(Direction of arrival,DOA)跟踪问题,提出了一种基于四元数模型的数据投影(Quaternion data projection method,QDPM)跟踪算法。此算法对初始化条件引起的波动具有很强的鲁棒性,并且具有比常规DPM(Data projection method)算法更快的收敛速度,尤其在信号角度变化较剧烈时体现得更明显。此外,在低信噪比的情况下,QDPM算法比DPM算法具有更高的DOA跟踪精度。最后通过仿真实验验证了算法的有效性。
