4 Simulation

The following numerical experiment illustrates the theory presented above. We chose the times as

$$t_{\rm k} = \frac{ \lfloor 1000 \cdot \mbox{rnd} \rfloor }{100}, k=1,~\ldots, 20$$ (3)

where rnd are random numbers uniformly distributed on [0,1[. Then, we built up a signal as follows $f(t_{i})=3 \sin(2\pi \nu_{0} t_{i})$, with $\nu_{0}=43$ (period = .0233...).

The smallest time interval is s=0.05, so $\nu_{0}$ is well above 1/2s, but p is 0.01. As expected, we observe that the Nyquist frequency is at 50, and that there is no strong aliasing peak before $\nu = 100$ (Fig. 1).

If we had rounded the times $t_{\rm k}$ to 0.001 in the above example and had p at 0.001, we would have found $\nu_{\mbox{\tiny Ny}}$ at 500.

  

Figure 1: Spectral window GN and power spectrum FN for the simulation described in the text. Both functions are clearly symmetrical around $\nu_{\mbox{\tiny Ny}}=1/2p=50$. No peak appears for $G_{N}(\nu)$ at $\nu=1/s$