  Independent component analysis (ICA) is a blind source separation method to
recover source signals of interest from their mixtures. Most existing ICA
procedures assume independent sampling. Second-order-statistics-based source
separation methods have been developed based on parametric time series models
for the mixtures from the autocorrelated sources. However, the
second-order-statistics-based methods cannot separate the sources accurately
when the sources have temporal autocorrelations with mixed spectra. To address
this issue, we propose a new ICA method by estimating spectral density
functions and line spectra of the source signals using cubic splines and
indicator functions, respectively. The mixed spectra and the mixing matrix are
estimated by maximizing the Whittle likelihood function. We illustrate the
performance of the proposed method through simulation experiments and an EEG
data application. The numerical results indicate that our approach outperforms
existing ICA methods, including SOBI algorithms. In addition, we investigate
the asymptotic behavior of the proposed method.
