System identification using nonstationary signals

The conventional method for identifying the transfer function of an unknown linear system consists of a least squares fit of its input to its output. It is equivalent to identifying the frequency response of the system by calculating the empirical cross-spectrum between the system's input and output, divided by the empirical auto-spectrum of the input process. However, if the additive noise at the system's output is correlated with the input process, e.g., in case of environmental noise that affects both system's input and output, the method may suffer from a severe bias effect. We present a modification of the cross-spectral method that exploits nonstationary features in the data in order to circumvent bias effects caused by correlated stationary noise. The proposed method is particularly attractive to problems of multichannel signal enhancement and noise cancellation, when the desired signal is nonstationary in nature, e.g., speech or image.