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Sampling Approximation of Stationary Stochastic Processes and Its Estimate of Truncation Error

Author: FangYang
Tutor: SongZhanJie
School: Tianjin University
Course: Applied Mathematics
Keywords: Sampling Theorem Local average Stationary process Truncation error
CLC: TN911.7
Type: Master's thesis
Year: 2007
Downloads: 62
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Abstract


Well known, in order to obtain useful information , the efficient processing of large amounts of signal data . For a long time , whether it is in the signal processing community , or in mathematics , people are looking for can represent any signal . Nearly 30 years , due to advances in computer technology , signal processing technology has been rapid development . In order to use the computer for quick calculation , must signal discretization . Discretized key signal sampling , the sampling process to follow the rules , known as the sampling theorem . Sampling theorem illustrates the relationship between the sampling frequency of the signal spectrum , it is 1928 by U.S. telecommunications engineers H.Nyquist [ 1 ] first proposed to the 1949 founder of information theory CEShannon [2] this theorem clearly and formally referenced as a theorem , it is known as the Shannon sampling theorem . After this , Shannon sampling theorem to get a wide range of applications . Conditions in practice , in general we can not get the exact value of the sampling points , observations of actual Integral to do local averaging theory on the local mean rapid development in recent years . The local average based on the sampling theory , the signal can be restored . Using sampling theory , however , the sampled values ??on the infinite time is required , and we can not be obtained all of these sampled values ??, it can only use the limited observation value of the signal approximation , which requires truncation error discussed . This thesis is the use of the local average sampling theory of stationary random signal approximation error estimation and approximation signal .

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