Blind separation of audio signals using trigonometric transforms and Kalman filtering

This paper deals with the problem of blind separation of audio signals from noisy mixtures. It proposes the application of a blind separation algorithm on the Discrete Cosine Transform (DCT) or the Discrete Sine Transform (DST) of the mixed signals, instead of performing the separation on the mixtures in the time domain. Kalman Filtering of the noisy separated signals is recommended in this paper as a post-processing step for noise reduction. Both the DCT and the DST have an energy compaction property, which concentrates most of the signal energy in a few coefficients in the transform domain, leaving the rest of the transform-domain coefficients close to zero. As a result, the separation is performed on a few coefficients in the transform domain. Another advantage of signal separation in transform domains is that the effect of noise on the signals in the transform domains is smaller than that in the time domain due to the averaging effect of the transform equations. The simulation results confirm the effectiveness of transform-domain signal separation and the feasibility of the post-processing Kalman filtering step.