  Non-stationary source separation is a well-established branch of blind source
separation with many different methods. However, for none of these methods
large-sample results are available. To bridge this gap, we develop large-sample
theory for NSS-JD, a popular method of non-stationary source separation based
on the joint diagonalization of block-wise covariance matrices. We work under
an instantaneous linear mixing model for independent Gaussian non-stationary
source signals together with a very general set of assumptions: besides
boundedness conditions, the only assumptions we make are that the sources
exhibit finite dependency and that their variance functions differ sufficiently
to be asymptotically separable. The consistency of the unmixing estimator and
its convergence to a limiting Gaussian distribution at the standard square root
rate are shown to hold under the previous conditions. Simulation experiments
are used to verify the theoretical results and to study the impact of block
length on the separation.
