Separation of system dynamics and line spectra via sparse representation

The purpose of this work is to explore the use of sparse representation in the context of system identification and, in particular, to address the important problem of identifying spectral lines in the presence of colored noise. To this end we formulate an ℓ₁ optimization problem, similar to Lasso, to incorporate an AR-model that accounts for the noise-color dynamics with contribution of sinusoids drawn out of an over-complete basis (dictionary). A suitable generalization for correlated time series sharing common components is also considered.