Statistical Analysis of Phase-Only Correlation Functions Based on Directional Statistics

• YAMAKI Shunsuke

  Research and Development Divisions, Cyberscience Center, Tohoku University

• ABE Masahide

  Department of Electronic Engineering, Graduate School of Engineering, Tohoku University

• KAWAMATA Masayuki

  Department of Electronic Engineering, Graduate School of Engineering, Tohoku University

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 phase-spectrum 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.

Journal

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E97.A (12), 2601-2610, 2014

  The Institute of Electronics, Information and Communication Engineers

Keywords

• phase-only correlation functions
• directional statistics
• circular probability distributions
• mean direction
• circular variance
• von-Mises distribution

Details

• CRID: 1390282681287038208
• NII Article ID: 130004706427
• DOI: 10.1587/transfun.e97.a.2601
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E97.A/12/E97.A_2601/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed