Variability of Behavior of Phase-Only Correlation Functions under Frequency Transformation of Signals

Abstract

This paper clarifies variability of behavior of Phase-Only Correlation functions under frequency transformation of continuous-time signals. The signals are classified into two categories: continuous time signals defined on a continuous time axis and discrete time signals defined on a discrete time axis. Continuous time signals are converted into discrete time signals by sampling at arbitrary periods when signal processing is performed. When a discrete-time signal is obtained by sampling a continuous-time signal with a constant sampling period, the phase defined by (-∞, ∞) in the continuous-time signal is restricted to (-π, π] in the discrete-time signal. It is necessary to consider the nature of the POC functions for continuous-time signals, which has been analyzed for discrete- time signals in previous studies.

In order to preserve the information in the phase spectrum at continuous time, it is necessary to suppress the changes in the phase spectrum that occur during the sampling of the signal. In this paper, we propose a nonlinear transformation of the phase spectrum using the projection method in continuous time.