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Adaptive Short-Time Fractional Fourier Transform Based on Minimum Information Entropy 基于最小信息熵的自适应短时分数傅里叶变换
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.033
B. Deng, Dan Jin, Junbao Luan
{"title":"Adaptive Short-Time Fractional Fourier Transform Based on Minimum Information Entropy","authors":"B. Deng, Dan Jin, Junbao Luan","doi":"10.15918/J.JBIT1004-0579.2021.033","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.033","url":null,"abstract":"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.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"265-273"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48824006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Uncertainty Inequalities on Fisher Information Associated with LCT 与LCT相关的Fisher信息的广义不确定性不等式
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.025
Guanlei Xu, Xiaogang Xu, Xiaotong Wang
{"title":"Generalized Uncertainty Inequalities on Fisher Information Associated with LCT","authors":"Guanlei Xu, Xiaogang Xu, Xiaotong Wang","doi":"10.15918/J.JBIT1004-0579.2021.025","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.025","url":null,"abstract":"Uncertainty principle plays an important role in multiple fields such as physics, mathematics, signal processing, etc. The linear canonical transform (LCT) has been used widely in optics and information processing and so on. In this paper, a few novel uncertainty inequalities on Fisher information associated with linear canonical transform are deduced. These newly deduced uncertainty relations not only introduce new physical interpretation in signal processing, but also build the relations between the uncertainty lower bounds and the LCT transform parameters a, b, c and d for the first time, which give us the new ideas for the analysis and potential applications. In addition, these new uncertainty inequalities have sharper and tighter bounds which are the generalized versions of the traditional counterparts. Furthermore, some numeric examples are given to demonstrate the efficiency of these newly deduced uncertainty inequalities.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"217-227"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43093969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and Uniqueness Analysis for Fractional Differential Equations with Nonlocal Conditions 非局部条件下分数阶微分方程的存在唯一性分析
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.027
Chun Wang
{"title":"Existence and Uniqueness Analysis for Fractional Differential Equations with Nonlocal Conditions","authors":"Chun Wang","doi":"10.15918/J.JBIT1004-0579.2021.027","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.027","url":null,"abstract":"Fractional differential equations and systems are gradually becoming an essential approach to real world applications in science and engineering technology. The boundary value problems of the fractional differential equations and systems were investigated by using several different methods. Recently, much attention has been paid to investigate fractional differential equations with nonlocal conditions by using the fixed point method. In this paper, by using the Banach fixed point theorem and Krasnoselkii fixed point theorem, the existence and uniqueness of the solutions to the initial value problem of the nonlinear fractional differential equations with nonlocal conditions are investigated, and some sufficient conditions are obtained. We extend some results that already exist. Finally, an example is given to show the usefulness of the theoretical results.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"244-248"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41821669","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Adaptive Turbo Equalization for Probabilistic Constellation Shaped Underwater Acoustic Communications 概率星座型水声通信的自适应Turbo均衡
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.030
Xisheng Wu, Yanbo Wu, Min Zhu, Dong Li
{"title":"Adaptive Turbo Equalization for Probabilistic Constellation Shaped Underwater Acoustic Communications","authors":"Xisheng Wu, Yanbo Wu, Min Zhu, Dong Li","doi":"10.15918/J.JBIT1004-0579.2021.030","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.030","url":null,"abstract":"To increase the spectral efficiency of the underwater acoustic (UWA) communication system, the high order quadrature amplitude modulations (QAM) are deployed. Recently, the probabilistic constellation shaping (PCS) has been a novel technology to improve the spectral efficiency. The PCS with high-order QAM is introduced into the UWA communication system. A turbo equalization scheme with PCS was proposed to cancel the severe inter-symbol interference (ISI). The non-zero a priori information is available for the equalizer and decoder before turbo iteration. A priori hard decision approach is proposed to improve the detection performance and the equalizer convergence speed. At the initial turbo iteration, the relation between the a priori information and the probability of the amplitude of 16QAM symbols in one dimension is given. The simulation results verified the efficiency of the proposed method, and compared to the uniform distribution (UD), the PCS-16QAM had a significant improvement of the bit error rate (BER) performance with PCS-adaptive turbo equalization (PCS-ATEQ). The UWA communication experiments further verified the performance superiority of the proposed method.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"280-289"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44985298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Research Progress on Discretization of Linear Canonical Transform 线性正则变换离散化的研究进展
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.036
Yannan Sun, Bingzhao Li, Ran Tao
{"title":"Research Progress on Discretization of Linear Canonical Transform","authors":"Yannan Sun, Bingzhao Li, Ran Tao","doi":"10.15918/J.JBIT1004-0579.2021.036","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.036","url":null,"abstract":"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.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"205-216"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44642332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Speech Encryption in Linear Canonical Transform Domain Based on Chaotic Dynamic Modulation 基于混沌动态调制的线性正则变换域语音加密
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.038
Liyun Xu, Tong Zhang, Chao Wen
{"title":"Speech Encryption in Linear Canonical Transform Domain Based on Chaotic Dynamic Modulation","authors":"Liyun Xu, Tong Zhang, Chao Wen","doi":"10.15918/J.JBIT1004-0579.2021.038","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.038","url":null,"abstract":"In order to transmit the speech information safely in the channel, a new speech encryption algorithm in linear canonical transform (LCT) domain based on dynamic modulation of chaotic system is proposed. The algorithm first uses a chaotic system to obtain the number of sampling points of the grouped encrypted signal. Then three chaotic systems are used to modulate the corresponding parameters of the LCT, and each group of transform parameters corresponds to a group of encrypted signals. Thus, each group of signals is transformed by LCT with different parameters. Finally, chaotic encryption is performed on the LCT domain spectrum of each group of signals, to realize the overall encryption of the speech signal. The experimental results show that the proposed algorithm is extremely sensitive to the keys and has a larger key space. Compared with the original signal, the waveform and LCT domain spectrum of obtained encrypted signal are distributed more uniformly and have less correlation, which can realize the safe transmission of speech signals.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"295-304"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47347100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Tensor Factorization Based on the Discrete Simplified Fractional Fourier Transform 基于离散简化分数阶傅里叶变换的张量分解方法
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.037
Xinhua Su, R. Tao
{"title":"A New Tensor Factorization Based on the Discrete Simplified Fractional Fourier Transform","authors":"Xinhua Su, R. Tao","doi":"10.15918/J.JBIT1004-0579.2021.037","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.037","url":null,"abstract":"Tensor analysis approaches are of great importance in various fields such as computation vision and signal processing. Thereinto, the definitions of tensor-tensor product (t-product) and tensor singular value decomposition (t-SVD) are significant in practice. This work presents new t-product and t-SVD definitions based on the discrete simplified fractional Fourier transform (DSFRFT). The proposed definitions can effectively deal with special complex tenors, which further motivates the transform based tensor analysis approaches. Then, we define a new tensor nuclear norm induced by the DSFRFT based t-SVD. In addition, we analyze the computational complexity of the proposed t-SVD, which indicates that the proposed t-SVD can improve the computational efficiency.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"274-279"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41959346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Uncertainty Principle for the Quaternion Linear Canonical Transform in Terms of Covariance 协方差下四元数线性正则变换的不确定性原理
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.034
Yan-Na Zhang
{"title":"Uncertainty Principle for the Quaternion Linear Canonical Transform in Terms of Covariance","authors":"Yan-Na Zhang","doi":"10.15918/J.JBIT1004-0579.2021.034","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.034","url":null,"abstract":"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.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"238-243"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45628211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Discrete Convolution Associated with Fractional Cosine and Sine Series 与分数余弦和正弦级数相关的离散卷积
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.040
Xiuxiu Gao, Qiang Feng, Yinyin Mei, Yi Xiang
{"title":"Discrete Convolution Associated with Fractional Cosine and Sine Series","authors":"Xiuxiu Gao, Qiang Feng, Yinyin Mei, Yi Xiang","doi":"10.15918/J.JBIT1004-0579.2021.040","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.040","url":null,"abstract":"Fractional sine series (FRSS) and fractional cosine series (FRCS) are the discrete form of the fractional cosine transform (FRCT) and fractional sine transform (FRST). The recent studies have shown that discrete convolution is widely used in optics, signal processing and applied mathematics. In this paper, firstly, the definitions of fractional sine series (FRSS) and fractional cosine series (FRCS) are presented. Secondly, the discrete convolution operations and convolution theorems for fractional sine and cosine series are given. The relationship of two convolution operations is presented. Lastly, the discrete Young’s type inequality is established. The proposed theory plays an important role in digital filtering and the solution of differential and integral equations.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"305-310"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48654445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Detection of T-wave Alternans in ECG Signals Using FRFT and Tensor Decomposition 用FRFT和张量分解检测心电信号中的T波交替
Journal of Beijing Institute of Technology (English Edition) Pub Date : 2021-09-30 DOI: 10.15918/J.JBIT1004-0579.2021.035
Chuan-sheng Ge, Shuli Zhao, Xin Yi
{"title":"Detection of T-wave Alternans in ECG Signals Using FRFT and Tensor Decomposition","authors":"Chuan-sheng Ge, Shuli Zhao, Xin Yi","doi":"10.15918/J.JBIT1004-0579.2021.035","DOIUrl":"https://doi.org/10.15918/J.JBIT1004-0579.2021.035","url":null,"abstract":"T-wave alternans (TWA) refers to the periodic beat-to-beat variation in the amplitude of T-wave in the electrocardiogram (ECG) signal in an ABAB-pattern. TWA has been proven to be a very important indicator of malignant arrhythmia risk stratification. A new method to detect TWA by combining fractional Fourier transform (FRFT) and tensor decomposition is proposed. First, the T-wave vector is extracted from the ECG of each heartbeat, and its FRFT amplitudes at multiple orders are arranged to form a T-wave matrix. Then, a third-order tensor is composed of T-wave matrices of several consecutive heart beats. After tensor decomposition, projection matrices are obtained in three dimensions. The complexity of the projection matrix is measured by Shannon entropy to obtain feature vector to detect the presence of TWA. Results show that the sensitivity, specificity, and accuracy of the algorithm on the MIT-BIH database are 91.16%, 94.25%, and 92.68%, respectively. This method effectively utilizes the fractional domain information of ECG, and shows the promising potential of the FRFT in ECG signal processing.","PeriodicalId":39252,"journal":{"name":"Journal of Beijing Institute of Technology (English Edition)","volume":"30 1","pages":"290-294"},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48044149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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