Does anyone know if there is a procedure as to separate the stationary and non stationary parts of a univariate signal. I have seen signal source separation and blind separation algorithms (all of them assuming that the signal is a linear superpossition of underlying hidden source signals where the signals are statistically independent - linearly independent - not sure if colored noises are linearly independent) where different signals are mixed in a single combined signal. For this several methods exist as to separate the sources mostly based on either orthogonality, correlation, variance and distances, however all of them based on having already multivariate variables:
Principal components analysis Singular value decomposition Independent component analysis Dependent component analysis Non-negative matrix factorization Low-complexity coding and decoding Stationary subspace analysis Common spatial pattern
My question is that if you could treat a single signal which is the combination of signal + uncorrelated stationary noise colors (white) + correlated noise colors (pink,brown,etc) as a source problem (implying that there is a mix of signals formed by the stationary noise, non stationary noise and signal) and thus apply a specific blind signal separation algorithm as to separate the sources statistically (for example as in stationary subspace analysis there is identification of the stationary and non stationary parts).
All blind signal separation algos I have seen can only be applied to multiple variables, my question is if there are there any blind separation algorithms that can be applied to univariate series where stationary and non stationary components can be separated as individual signal sources.
Following comments from LPT
I know the signal is spread across a wide range of frequencies from the Evoluionary power spectrum. I know uncorrelated stationary white noise affects the signal and that other unidentifed stationary correlated colors do as well but ignore their mix. My idea was to run a wavelet at one level decomposition as to have two range of frequencies and use this as to run one of the analysis above as to determine the stationary and non stationary parts. As the stationary parts will correspond to correlated and uncorrelated noise colors which I will assume to be non gausian and additive. As the nature of the signal is non stationary I would effectively have separated the signal from noise. Then from noise I will run wavelet thresholding as to eliminate white noise based on a MA MAD and remain with correlated noises which via FFT and their power relation understand the type dominating noise color or identify their mix.