6 Application

Actually, most data are obtained at approximately equal time intervals. The fact that there is some randomness may raise substantially the Nyquist frequency. As a conspicuous example, we can cite Minniti et al. (1998) who are able to find periods for $\delta$ Scuti stars with MACHO observations of bulge fields. Indeed, the data are separated by about one day and the periods found are of few hours. We give an example for the $\delta$ Scuti star 162.25348.3066. The histogram of the time intervals is given in Fig. 2, its Fourier transform is shown in Fig. 3, and finally the folded curve is presented in Fig. 4, it leaves no doubts that the period is the right one. The detection limit is dominated by the exposure time (150 s), that is about $\nu_{\mathrm{max}}=$ 192 $\mbox{days}^{-1}$ if $\kappa=3$ ($P_{\mathrm{min}}=7.5 \; \mbox{min}$).

  

Figure 2: Histogram of the time intervals. The smallest is around 0.8 days. In total, 122 measurements were available

  

Figure 3: Spectral window GN and power spectrum FN of the $\delta$ Scuti star 162.25348.3066 from MACHO. Although there are rather strong aliasing peaks, the frequency of $1/0.0854259\; \mbox{days}^{-1}$ is unambiguous

  

Figure 4: The folded curve of the $\delta$ Scuti star 162.25348.3066 from MACHO (period = 0.0854259 days)

With the HIPPARCOS mission the smallest time interval is 20 minutes. A search for shorter periods was undertaken (Eyer 1998). Unfortunately no results came out. We can invoke that often the spectral window is nearly symmetric around 1/40 $\mbox{min}^{-1}$ (this is due to the fact that observations are often found in sequences, inducing strong aliasing peaks), or that short periods are rarely stable over three years (either period change or phase shift can occur).