Effects of stochastic phase-spectrum differences on phase-only correlation functions: Part II: Statistically proportional phase spectrum differences to frequency indices

This paper discusses properties of the phase-only correlation (POC) functions for stochastic phase spectrum differences. Assuming the phase spectrum differences between two signals to be random variables, we derive general expressions of the expectation and variance of the POC functions, and show that the expectation of the peak of the POC functions decreases and the variances of the POC functions increase as the phase spectrum differences increase. This property mathematically guarantees validity of the POC functions for evaluating similarity between two signals.