指数样条作为多项式样条的推广，在函数逼近论和系统理论中发挥着基础性作用，指数样条有很多令人满意的逼近性质，而且利用指数样条我们可以建立一个完整而且独立的信号处理系统，而且还把连续信号处理和离散信号处理紧密联系在一起。2008年提出的自适应信号分解方法- - 基于算子的零空间追踪算法近些年来受到了广泛关注，该算法通过定义一些参数化的微分或积分算子，把一个复杂信号分解成若干简单信号(局部窄带信号)的和，而这些简单信号在所定义的算子的零空间中。本项目研究内容包括指数样条的逼近理论研究和指数样条在信号分解领域的应用研究，把指数样条和基于算子的自适应信号分解方法相结合，通过对上述基于算子的自适应信号分解方法进行推广，把复杂信号分解为若干指数样条信号，再对指数样条信号进行处理，此研究内容是自适应信号分解领域的新的尝试，也是基于算子的自适应信号分解的推广。

As the generalization of polynomial splines,exponential splines play a fundamental role in approximation theory and system theory. Exponential splines have many satisfactory approximation properties,and we can build a complete and self-contained signal processing formulation of exponential splines .The exponential spline present a unifying continuous and discrete approach to signal processing. Null space pursuit an operator-based approach to adaptive signal separation which was proposed in 2008 have received extensive attention in recent years. The operator-based signal separation approach uses an adaptive differential or integral operator to separate a complex signal into additive subcomponents of simple (local narrowband)signals, these simple signals are in the null space of the operator. The research of this project is the approximation theory of exponential spline and combining the exponential splines with the operator-based signal separation approach. First, we separate a complex signal into additive subcomponents of exponential splines, then we process these exponential splines. This project is a new attempt in the field of adaptive signal separation and a promotion of operator-based signal separation approach.