Analysis of signal separation and signal distortion in feedforward and feedback blind source separation based on source spectra

Source separation and signal distortion in three kinds of BSSs with convolutive mixture are analyzed. They include a feedforward BSS, trained in the time domain and in the frequency domain, and a feedback BSS, trained in the time domain. First, an evaluation measure of signal distortion is discussed. Second, conditions for source separation and distortion free are derived. Based on these conditions, source separation and signal distortion are analyzed. The feedforward BSS has some degree of freedom, and the output spectrum can be changed. The feedforward BSS, trained in the frequency domain, has weighting effect, which can suppress signal distortion. This weighting is, however, effective only when the source spectra are similar to each other. Since, the feedforward BSS, trained in the time domain, does not have any constraints on signal distortion free, its output signals can he easily distorted. A new learning algorithm with a distortion free constraint is proposed. On the other hand, the feedback BSS can satisfy both source separation and distortion free conditions simultaneously. Simulation results support the theoretical analysis.