Approximation Of Multidimensional Weak Sense Stationary Stochastic Processes By Sampling Series

Signal processing is a process to transform or deal with the signal,and its purposeis to weaken the extra content in the signal, remove mixed noise and interference, orconvert the signal into another form of being easy to analyse and recognize, that isconvenient for estimation and selection of its parameters. Study on signal processinginvolves calculus, probability and statistics, stochastic process, optimization theory,functional analysis and so on. The Shannon sampling theorem is the cornerstone of thesignal processing, and it has been widely used in the digital telemetry system, telemetrysystem, information processing, digital communication, control theory and other fields.In the light of the importance of sampling theorem,the study on sampling theoremhas never stopped. However,there are still some troubles in application of the classicalsampling series. For example, it’s tedious to deal with the sinc function occurring in thesampling series. Moreover it’s the stochastic signal more common,and there are manyfactors afecting its accuracy. Therefore it’s necessary to approximate the sinc functionby the finite sum of its Taylor series expansion to improve the processing method ofone-dimensional random signal sampling series. At last, this result is extended to highdimensional signal, and the error analysis of the improved sampling series is carried out.