海洋调查方法之采样

海洋调查方法之采样程灵巧上海海洋大学曲线上某点的斜率：采样所得相邻两点间的斜率：现实：连续型采样：离散型RealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequency理想：采样所获的信息尽量接近现实情况尽量减小△t，使得：（1）（2）

Taylorseries:尽量小RealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequencyTaylorseries:两边同除以量级U/T后，切断误差为：RealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequency理想：采样所获的信息尽量接近现实情况现实：1、观测仪器分解率有限2、计算机内存有限3、现场观测时间有限...等。CTD（Sea-bird911plus）：24Hz有其它办法吗？RealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequency（4）（5）（4）式-（5）式，centereddifferenceapproximationForwardBackwardRealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequency例子：当ω△t≈O(1)，误差的量级为1，所以有100%的误差。对于二次有限差分，ω△t≤0.8，使得误差小于10%。△t≤T/8RealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequency一般化假设利用泰勒展开RealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequencyRealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequency同样利用泰勒展开只需满足条件RealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequencyRealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequencywhatabout...例子：相对高频以为频率的信号无法与以为频率的信号区分开来。混叠现象（Aliasing）RealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequency貌似只有间的信息是可以被获取。另外由于采样频率至少是信息频率的两倍。Nyquistfrequency香农采样定理RealmotionandsamplingIdealsolutionHigher-ordermethodsAliasingandNyquistfrequency对于一个给定的采样间隔，能分