采样级数对高维平稳过程的逼近

Approximation of Multidimensional Stochastic Processes by Sampling Series

香农采样定理是信号处理的基石,现实中的信号多是高维随机的,采样时也会有诸多干扰因素,并且经典采样级数中对sinc函数的处理也是比较繁琐的,为此,用sinc函数的Taylor展式对其进行逼近,对变动后的高维随机过程采样级数进行了误差分析,得到了时间扰动误差的误差上界。

Shannon sampling theorem is the cornerstone of signal processing. However it＇s the multidimensional stochastic signal more common. Besides, there are many factors affecting its accuracy, in addition, it＇s tedious to deal with the sinc function occurring in the sampling se- ries. With regards to this, in this paper the sinc function is approximated by the finite sum of its Taylor series expansion, and then the error analysis of the improved sampling series is car tied out.