Impulse response determination using derivatives of correlation function

In this short paper, a new method of system identification is proposed in which the impulse response of a system is determined from a linear combination of the derivatives of the cross-correlation function between an input and the corresponding output of the system. This method is particularly simple when the autocorrelation function of the input is an exponential or a triangular function of the variable tau. This method merely requires the autocorrelation function to be undifferentiable at some points in the sense of usual functions. Essentially, the method utilizes the δ-functions appearing when is differentiated in the sense of the distribution, or the generalized function proposed by Schwartz. Results of experiments by computer simulation showed good agreement with the theoretical considerations.