Differential Operator In The Application Of Null Space Pursuit

Digital signal Processing involves very extensive in theory, so it has very profound mathematical background, as well as many research directions and the project. While in Digital Signal Processing, the approach of signal model representation and separation has been the fundamental problem in many researches, which can directly affect the later method of signal processing and the final results of experiment. However, the representation and separation of signals seem the same problem in the research. So far, most of the signals model s researched by many scholars is expressed as a simple set of single component signals. Therefore, on the one hand, the algorithm of signal separation and the results depend on the definition of a single component in the signals model; on the other hand, the single component in the different signals’model define differently in every algorithm of signal separation. The algorithm of signal separation based on operator is in this article, whose signal component is defined as the function of the Null Space of the operator corresponding to this cluster.In2008, adaptive signal separation based on linear differential operator was proposed by Peng and Hwang. Good adaptability and characteristics of fully data-driven make adaptive signal separation algorithm attract the widespread attention. And then they put forward the Null Space Pursuit algorithm. In2011, Null Space Pursuit algorithm based on the differential operator is not effective for AM-FM signal. So Dr Hu improved Null Space Pursuit algorithm, which expanded the scope of signals. In this article, we will further improve the Null Space Pursuit algorithm. Firstly, we improve the algorithm to use a fourth-order linear differential operator, and conduct experiments simulation to verify the practicability of the new algorithm. Secondly, the fourth-order Runge-Kutta algorithm is integrated into NSP based on fourth-order linear differential operator, similarly, conducting the experiments simulation. Finally, the two algorithms are compared.