Biological signal detection by the autocorrelogram and a recurrence frequency method

The signal detection property of the autocorrelation function (ACF) is conventionally derived on the assumption of two conditions that may not be present in biological time sequences: (1) the measured variable is assumed to be the sum of a noise and a signal function; (2) the signal function is assumed to continue throughout the sequence. In neuroelectric sequences of all-or-none responses the first assumption would not be appropriate if most of the elements seen by the recording electrode were accessible to the signal input. The sensitivity of the ACF was investigated in simulated sequences in which the random noise was entirely replaced by a periodic square wave signal function for a small number of repetitions and the results compared with a recurrence frequency function (RFF) developed during this work; under these conditions the ACF proved to be significantly inferior. Sensitivity of the ACF was the same for a pure signal function as for an additive function of signal and noise but sensitivity of the RFF was severely degraded for the latter. A variety of neuroelectric sequences was studied and many were found in which strong rhythmic processes revealed by RFF were not detected by the ACF. It is suggested that both methods be used when the signal function may be present during only a small part of the data-collection period and when it is not known to what degree the measured variable may be the sum of a noise and signal function. When an additive function is known to exist, the ACF will be the method of choice; for pure signal functions REF will be more sensitive.