摘要翻译：
本文研究了有理传递函数在FIR和Takenaka-Malmquist(TM)基下的稀疏系数向量{θ}的重构问题。我们提出在传递函数的表示中串联有限数量的FIR和TM基函数，并证明了定义在无限维函数空间中的FIR和TM基对的稀疏表示的唯一性。给出了利用FIR和TM基在上单位圆上随机抽样的l_1最优解代替l_0最优解的充分条件，作为重构的基础。仿真结果表明，l_1最小化方法可以较高的概率重构系数向量{θ}。结果表明，级联FIR基和TM基给出了一个更稀疏的表示，与仅使用FIR基函数相比，重构阶数低得多，与仅使用TM基函数相比，对系统真极点知识的依赖性小得多。
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英文标题：
《Sparse System Identification in Pairs of FIR and TM Bases》
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作者：
Dan Xiong, Li Chai, Jingxin Zhang
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  This paper considers the reconstruction of a sparse coefficient vector {\theta} for a rational transfer function, under a pair of FIR and Takenaka-Malmquist (TM) bases and from a limited number of linear frequency-domain measurements. We propose to concatenate a limited number of FIR and TM basis functions in the representation of the transfer function, and prove the uniqueness of the sparse representation defined in the infinite dimensional function space with pairs of FIR and TM bases. The sufficient condition is given for replacing the l_0 optimal solution by the l_1 optimal solution using FIR and TM bases with random samples on the upper unit circle, as the foundation of reconstruction. The simulations verify that l_1 minimization can reconstruct the coefficient vector {\theta} with high probability. It is shown that the concatenated FIR and TM bases give a much sparser representation, with much lower reconstruction order than using only FIR basis functions and less dependency on the knowledge of the true system poles than using only TM basis functions.
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PDF链接：
https://arxiv.org/pdf/1805.03853