Theoretical and computer simulation study of the "Correlofiltre" adaptative system for non stationary processes

The adaptative filter for real time noise cancelling applications is shown. The signal is corrupted by an additive noise which is a linear transformation of the noise "source" available as a reference input. To obtain the disturbing noise it is necessary to estimate this transformation. The difference between the input and the estimated noise gives an estimation of the signal. The system presented here is an open loop filter which is a different case from that proposed by Widrow. The theoretical study of the performance of the system (in the case where the disturbing noise is a non stationary process) is shown. To check the stationarity of the process we introduce a criterion which conpare the estimated transformation with the previous one (learning process) and decide if it is necessary or not to change the last estimated transformation. We studied typical cases of non stationarity as change of the power of the disturbing noise or in the impulse response of the linear system. The theoretical and computer calculated results are shown. We find a good agreement between the two approaches.