基于数据的机器学习是信息处理中的重要技术，并已成为信息科学的研究热点之一。系统辨识是现代控制理论的一个重要分支，Szego核和Takenaka-Malmquist(T-M) 基在系统辨识领域发挥着非常重要的作用。本项目将构造以Szego核或T-M基为激活函数的复值学习算法，结合极限学习机和稀疏贝叶斯算法的思想，得到Hardy-2空间上解析函数的稀疏逼近，并将所构造的算法用于频率域的系统辨识。本质上，该算法可以看作是自适应傅里叶分解（AFD）算法的一个扩充。本项目涉及数学、信息科学、计算机科学和工程等多个学科，是一个富有挑战性的研究课题。

The machine learning based on data is an important technology in information processing and has become one of the hot research topics in information science.System identification is an important branch of modern control theory, where Szego and Takenaka-Malmquist (T-M) play a very important role in frequency domain identification. In this project, we will construct complex-valued learning machines based on the T-M bases or Szego kernel. Combining the Extreme Learnings Machine and Sparse Bayesian learning, we obtain a sparse approximation of analytic function in Hardy-2 space. The proposed learning machines will be applied to frequency domain identification. In essence, the proposed algorithms can be regarded as an extension of adaptive Fourier decomposition (AFD) algorithm. This project related to mathematics, information science, computer science and engineering, is a challenging research topic.