信号分析中的正交变换

Orthogonal linear transformation in signal analysis

信号分析的主要目的是寻找一种简单有效的信号变换方法,以便突出信号中的重要特性、简化运算的复杂程度,其中希尔伯特(Hibert)空间中的正交变换得到了广泛的应用。投影定理在平稳时间序列的预报及函数逼近研究中起着重要的作用。本文从数学分析的角度推证了正交变换与投影定理的内在联系,通过信号分析中典型正交变换的应用进行了验证,从而揭示了正交变换的内在本质。

The main purpose of signal analysis is to seek a simple effective method of signal transformation, which give prominence to important property of signal and predigest complexity degree of operation, such as orthogonal linear transformation widely used in Hilbert space. Theorem of projection is more important in the study of prediction of stationary discrete-time sequence and function approximating. The relationship between orthogonal linear transformation and theorem of projection is demonstrated in the angle of mathematics analysis meanwhile validating its correctness through analyzing typical applications of transformation. So the essence of orthogonal linear transformation is exposed.