8 Conclusions

We have realised and experimented a new method for spectral analysis for unevenly sampled signals based on three phases: preprocessing, extraction of principal eigenvectors and estimate of signal frequencies. This is done, respectively, by input normalization, nonlinear PCA neural networks, and the Multiple Signal Classificator algorithm. First of all, we have shown that neural networks are a valid tool for spectral analysis.

However, above all, what is really important is that neural networks, as realised in our neural estimator system, represent a new tool to face and solve a problem tied with data acquisition in many scientific fields: the unevenly sampling scheme.

Experimental results have shown the validity of our method as an alternative to Periodogram, and in general to classical spectral analysis, mainly in presence of few input data, few a priori information and high error probability. Moreover, for unevenly sampled data, our system offers great advantages with respect to P. First of all, it allows us to use a simple and direct way to solve the problem as shown in all the experiments with synthetic and Cepheid's real signals. Secondly, it is insensitive to the frequency interval: for example, if we expand our interval in the SU Cygni light curve, while our system finds the correct frequency, the Lomb's P finds many spurious frequencies, some of them greater than the confidence threshold, as shown in Figs. 33 and 34.

  

Figure 33: n.e. estimate of SU Cygni with enlarged window

  

Figure 34: Lomb's P of SU Cygni with enlarged window

Furthermore, when we have a multifrequency signal, we can use our system also if we do not know the frequency number. In fact, we can detect one frequency at each time and continue the processing after the cancellation of the detected periodicity by IIR filtering.

A point worth of noting is the failure to find the right frequency in the case of eclipsing binary for both our method and Lomb's P. Taking account of the morphology of eclipsing light curve with two minima, this fact can not be of concern because in practical cases the important thing is to have a first guess of the orbital frequency. Further refinement will be possible through a wise planning of observations. In any case we have under study this point to try to find a method to solve the problem.

Acknowledgements

The authors would like to thank Dr. M. Rasile for the experiments related to the model selection and an unknown referee for his comments who helped the authors to improve the paper.