Blind separation algorithm for sources with temporal structure based on contract transformation matrix

In the field of signal processing, there are many source signals with temporal structure, i.e. time signals or time series. In the procedure of dealing this blind source separation problem, there is a contractual relationship between the autocorrelation matrix of the source signals and the autocorrelation matrix of the observed signals under the linear instantaneous mixing model, in other words, the separation matrix is a contract transformation matrix which transforms the autocorrelation matrix of the observed signals into a diagonal matrix, which is corresponding to independent sources. Based on this relationship, we improve the Independent Component Analysis (ICA) algorithm of time signals, that is, the intersection of the contract transformation matrix sets under each delay is the required separation matrix. Finally, the simulation results for analog source signals and real sound signals show that the new algorithm is valid and efficient.