Activity Index Variance as an Indicator of the Number of Signal Sources

In this paper we introduce a novel technique that can be used as an indicator of the number of active signal sources in convolutive signal mixtures. The technique is designed so that the number of sources is estimated using only recorded signals and some marginal information, such as possible minimum and maximum triggering frequencies of sources, but no information on mixing matrix, other parameters of signal sources, etc. Our research is based on the convolution kernel compensation method (CKC), which is a blind source separation method. First, a correlation matrix of the recorded signals is estimated. Next, a measure of the global activity of the signal sources, called activity index, is introduced. The exact analytical model of the activity index variance was derived for the purpose of the estimation of the number of signal sources. Using the analytical model, the number of active signal sources can be estimated if some a priori marginal information is available. We evaluated these marginal parameter values in extensive simulations of compound signals. The number of sources, their lengths, signal-to-noise ratio, source triggerings, and the number of measurements were randomly combined in preselected ranges. By using the established marginal parameter values and increasing extension factors, the model of the activity index variance was deployed to estimate the number of signal sources. The estimation results using synthetic signal mixtures are very promising. Key-Words: Compound signals, estimation of the number of sources, correlation matrix, convolutive signal mixture, variance model, convolution kernel compensation.