Normalized Auto- and Cross-Covariance Functions for Neuronal Spike Train Analysis

Abstract

The normalized auto- and cross-covariance functions of discrete-time stochastic point process, used for quantitatively analyzing neuronal spike trains, were derived from the corresponding functions of general stochastic process using Kronecker delta functions. The auto-correlation and cross-correlation properties can be described as numerical differences on a monotonic scale ranging from - 1 to + 1. A segmental integration method and a significance test for the normalized cross-covariance function estimate are suggested. Examples from real spike trains are illustrated, and Monte Carlo methods are used for controls and for testing the algorithms and computer programs.

Key Words:

• neural spike train analysis
• stochastic point process
• biological signal processing
• covariance function
• numerical representation of correlation
• cross-correlation test