The forgotten effect of the finite measurement time on various noise analysis techniques

The conventional noise analysis expressions for functions like the auto- and cross-correlation function, the variance to mean ratio, and the Rossi-ex formula, diverge when the reactor is critical. This problem arises because one pole of the zero-power reactor transfer function is zero. However, in a finite measurement time, a zero frequency cannot be measured and the divergence will not be found experimentally. New expressions for the expectation values of the experimental quantities of various pulse counting techniques are derived which also take into account the dead time of the detector. These expressions do not suffer from divergence at critical. A Feynman-ex experiment is simulated in two, neutronically different systems. The use of the conventional equations for the analysis of the experiments is seen to lead to a bias in the inferred reactivity value