## Abstract

This paper proposes statistical analysis of phase-only correlation functions based on linear statistics and directional statistics. We derive the expectation and variance of the phase-only correlation functions assuming phase-spectrum differences of two input signals to be probability variables. We first assume linear probability distributions for the phasespectrum differences. We next assume circular probability distributions for the phase-spectrum differences, considering phase-spectrum differences to be circular data. As a result, we can simply express the expectation and variance of phase-only correlation functions as linear and quadratic functions of circular variance of phase-spectrum differences, respectively.

Original language | English |
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Pages (from-to) | 2601-2610 |

Number of pages | 10 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E97A |

Issue number | 12 |

DOIs | |

Publication status | Published - 2014 Dec 1 |

## Keywords

- Circular probability distributions
- Circular variance
- Directional statistics
- Mean direction
- Phase-only correlation functions
- Von-Mises distribution

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics