Data Analysis Tutorial : Synthetic time series

1.2 Synthetic time series

$\includegraphics{figs/uandv.eps}$

Figure 1: Synthetic series $u$ and $v$

The following in intended to be a simple tutorial introducing basic concepts of data analysis for oceanographers and coastal engineers. Examples are given using two synthetic time series:

$\begin{equation} \label{eq:u1} u=1.+\sin {(\pi k/5)}+\cos {(\pi k/20)}+(rand(1,N_ t)-0.5); \end{equation}$

(1)

$\begin{equation} \label{eq:u1} v=0.5+0.75\cos {(pi*k/5)}+0.5\cos {(\pi k/20)}+(rand(1,N_ t)-0.5); \end{equation}$

(2)

where $k$ is an index running $1:N_ t$ and rand is a random number sequence, intended to make the synthetic series behave a little more like real observations. For these exmples $N_ t=1024$ . All programs are written in Octave 3.0, and ought to run without change in Matlab.