Blind Source Separation and Deconvolution of Fast Sampled Signals

In real world implementations of blind source separation and deconvolution, the mixing takes place in continuous time. In the models normally considered, discrete time sampling is implicitly assumed to provide a mixing filter matrix from a suitable demixing filter matrix which can be learned given an appropriate algorithm. In this paper, we consider the implications of trying to separate and deconvolve signals which may include some signals which are low frequency compared to the sample rate. It is shown that if a fast sampling rate is used to obtain the discrete time observed data, learning to solve blind source separation and deconvolution tasks can be very difficult. This is due to the data covariance matrix becoming almost singular. We propose a discrete time model based on alternative discrete time operators which is capable of overcoming the problems and giving significantly improved performance under the conditions described.