修正采样定理与周期现象的实验研究方法

信号与系统理论中的采样定理,要求采样时区无限宽,采样数据无限多,这是一种理想化情况.实际采样时区宽度和采样数据量只能有限,采样定理难以用来探索物理量随时间变化的规律.结合物理学实验研究的需要,我们提出了修正采样定理.利用修正采样定理和周期物理量的有限多个采样数据,可以准确捕获周期物理量的演化规律.方法是,取尽可能小的采样周期Ts和尽可能多的观测次数N.观测周期物理量产生N个采样数据,先找出物理量的周期T.然后通过重复观测来调整Ts和N,使NTs/T等于整数.计算采样数据的频谱Xs(f),利用修正采样定理和Xs(f),快速得到周期物理量的频谱X(f).依据X(f)重建周期物理量随时间变化的规律.以大摆角单摆为例,展示研究周期现象规律的方法和过程.

Revising sampling theorem and experimental research method of cycle phenomenon

The sampling theorem in signa l and system theory,demands sample the time zone limitlessly widely,amount of d ata sampled is many limitlessly.This is a kind of idealized situation.It can o nly be limited to sample the width of time zone and amount of data sampled actua lly.Therefore,it is difficult for the sampling theorem to use and explore the law that the physical quantity evolved with time.The need of combining the phys ics experiment and studying,we propose the revising sampling theorem for utili z ing limited sampled data and revising sampling theorem,which can catch the evo l ution law of cycle physical quantity accurately.The method is,fetch the time i nterval Ts as smal l as possible,fetch the number of times of observation as large as possible, to observe cycle physical quantity N times.We analyze the sampled data and find out cycle T of the physical quantity,adjust Ts and N by observing repeatedly,make NT s/T equal to the integer.We c alculate spectral Xs(f) which samples the data,utilize the revising sampling th eo rem and Xs(f),and get spectral X(f) o f cy cle physical quantity fast.According to X(f),we rebuild law that the cycle physical quantity evolved with time.As an example,large tilt angle simple pendulum as the research object,we show the method and process of cycle phenomenon law.