The experimental determination of system transfer functions from normal operating data

It is often not possible to remove a plant or system from service in order to measure its transfer function by the usual process of applying sinusoidal or impulse test signals. Use can, however, be made of statistical data of input and output when the system is operating in normal service, since in a linear system, undisturbed by noise, the cross-correlogram between the input and output signals is given by the convolution of the system weighting function and the autocorrelogram of the input. The experimental determination of the system transfer function or weighting function involves finding the function which, when convoluted with the auto correlogram of input, will most closely fit the cross-correlogram between the input and output signals. The paper discusses various methods of doing this, with particular emphasis on analogue methods.