Unified study on the decomposition for deterministic signals and stationary random signals

Abstract

The unified decomposition theories and methods for deterministic signals and stationary random signals were deeply studied.According to the stability theory of linear systems,the unified results of signal decomposition under both regular stable and boundary stable conditions were given respectively.The unified results of signal decomposition under both orthogonal projection and self projection conditions were also provided based on the linear space projection theory.The former is clear and definite in its physical meaning,and the latter is clear in its mathematical and geometrical meanings.They are both complement with each other.

Keywords

• signal decomposition;linear system;regular stability;boundary stability;linear space;orthogonal projection;self projection