Effects of stochastic phase spectrum differences on phase-only correlation functions: Part I: Statistically constant phase spectrum differences for frequency indices

This paper analyzes effects of stochastic phase spectrum differences on phase-only correlation (POC) functions. We assume phase spectrum differences between two signals are statistically constant for frequency indices. That is, they have identical probability density function for all frequency indices. We derive the general expressions of the expectation and variance of the POC functions. Relationships between the POC functions and the phase spectrum differences are formulated. This result mathematically guarantees the validity of the POC functions used for similarity measure in matching techniques.