论文标题
ESPRIT与Espira重建短余弦总和及其应用
ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application
论文作者
论文摘要
在本文中，我们介绍了两种新算法，用于稳定近似值，并恢复短余弦总和。使用的信号模型包含具有任意实际正频率参数的余弦项，因此强烈概括了通常的傅立叶总和。所提出的方法两者都采用一组等距信号值作为输入数据。余弦总和的ESPRIT方法是一种类似于Prony的方法，并且应用了Toeplitz+Hankel矩阵的矩阵铅笔，而ESPIRA方法基于DCT数据的理性近似，并且可以理解为用于特殊LoeWner矩阵的矩阵铅笔方法。与已知的指数总和恢复的数值方法相比，所考虑的新算法的设计直接利用了信号模型的特殊真实结构，因此通常为噪声输入数据提供真实的参数估计值，而在这种情况下，已知的一般恢复算法对于复杂的指数总和倾向于产生复杂参数。
In this paper we introduce two new algorithms for stable approximation with and recovery of short cosine sums. The used signal model contains cosine terms with arbitrary real positive frequency parameters and therefore strongly generalizes usual Fourier sums. The proposed methods both employ a set of equidistant signal values as input data. The ESPRIT method for cosine sums is a Prony-like method and applies matrix pencils of Toeplitz+Hankel matrices while the ESPIRA method is based on rational approximation of DCT data and can be understood as a matrix pencil method for special Loewner matrices. Compared to known numerical methods for recovery of exponential sums, the design of the considered new algorithms directly exploits the special real structure of the signal model and therefore usually provides real parameter estimates for noisy input data, while the known general recovery algorithms for complex exponential sums tend to yield complex parameters in this case.
