Stability Analysis of the Separation of Sources Algorithm: Application to an Analogue Hardware

We present in our paper a stability analysis of the two-neuron Hérault-Jutten network for separation of two sources from a linear and instantaneous mixture. The non-linear functions used by the learning rule are chosen to be in the form f(x)=sinh(x/α) and g(x)=tanh(x/β), as we can easily implement them on analogue hardware. Based on simulation results and theoretical considerations, the influence of the non-linear functions and the statistical nature of the source signals on the stability of the algorithm, are pointed out. In order to determine the properties and the limitations of our analogue hardware, the behavior of the algorithm is derived finally for g(x)=signe(x), as it is actually implemented in our circuit.