Linear Time Invariant System Identification Using a Result of the Bussgang Theorem

摘要

This investigation applied the Bussgang theorem to the cross correlation method of linear, time invariant (LTI) system identification. In this procedure a Gaussian signal is passed through an LTI system and the output is cross correlated with a nonlinearly distorted version of the original Gaussian signal. If the Gaussian noise were white, the cross correlation would be equal to the impulse response of the LTI system within a constant of proportionality. With the use of bandlimited gaussian noise this relationship is only approximately satisified. The analysis compared the performance of the cross-correlation method with the nonlinearity to that of the cross correlation method without the nonlinearity. The experimental results indicate that the introduction of the nonlinearity degrades the performance of the method, but this can be improved by correcting for the effects of several quantities associated with the time varying statistics of the Gaussian noise.