High-resolution spectral analysis of unevenly spaced data using a regularization approach

The problem of estimating the power spectrum of unevenly spaced time series is considered. Indeed, this problem is quite common in ground-based astronomy, and the use of classical methods leads to aliased frequency detection. Moreover, the spectral resolution is limited by the observation time (Shannon-Nyquist law). We propose a regularized method to estimate the power spectrum of such irregular time series. We also show that with this approach, one can achieve high resolution. The method is described in detail and applied to simulated data as well as helioseismic velocities. A fast algorithm is also presented for the numerical implementation. The results show that accurate frequency estimation can be obtained from short, noisy and irregularly sampled signals.