Abstract: The same activation function is always used to separate all speech signals by means of the conventional natural gradient algorithm. Although blind source separation can be achieved， the separation effect is not ideal. To solve this problem， sub-band activation function was used based on Pearson system to improve natural gradient algorithm. By introducing Pearson system， the Pearson function with conventional activation function was combined. The appropriate activation function was selected according to the method of moments-estimating in each part. Then the selected activation function was brought into the separation matrix. This algorithm effectively overcomes the shortcomings and deficiencies of the conventional separation algorithm for speech signal. The simulation results showed that the performance of the improved algorithm is superior to that of the conventional natural gradient algorithm in the actual speech signal separation. In addition， the mean square error is reduced greatly and good convergence rate is maintained at the same time.

Key words: blind source separation, natural gradient, speech signal, Pearson system, activation function