Spectral analysis techniques of stationary point processes used for the estimation of cross-correlation: Application to the study of a neurophysiological system

In this work we apply spectral analysis techniques of bivariate stationary point processes for the estimation of the cross-correlation (CC). This is used for the study of a component of the neurophysiological system called muscle spindle. We are interested in the effect of different stimuli to the function of the muscle spindle by recording the response from the Ia sensory axon transferred to the spinal cord. The estimate of the cross-correlation, a measure of the association between the input and the output of the muscle spindle, is obtained using the periodogram statistic which is a function of the frequency domain. It is shown that the asymptotic distribution of the estimator is Normal. Thus approximate 95% pointwise confidence intervals for the estimates of the modified CC can be computed which show if the behaviour of the system is excitatory and/or inhibitory.