Because the input x(t) is the sound pressure level, it has zero mean, thus nx ^ 0, and the average output of the linear filter H(s), will also be zero. Thus Equation 8.2-17 can be simplified:

x+ = E{x(t -T)y = b,z > 0} = bRxy (t)/oy + RxZCOV^/az 8.2-18

The statistic, x + , is a biased estimator of the cross-correlation function of the wideband Gaussian noise input, x(t), and the output, y(t), of H(s). Thus x+ can be used to estimate h(t).

It is also of interest to examine the error statistics associated with the computation of the TC function. Wu (1970) has shown:

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