Unitary Diagonalization of the Generalized Complementary Covariance Quaternion Matrices with Application in Signal Processing

Abstract

Let H denote the quaternion algebra. This paper investigates the generalized complementary covariance, which is the ϕ-Hermitian quaternion matrix. We give the properties of the generalized complementary covariance matrices. In addition, we explore the unitary diagonalization of the covariance and generalized complementary covariance. Moreover, we give the generalized quaternion unitary transform algorithm and test the performance by numerical simulation.

Keywords

• quaternion algebra
• covariance matrices
• <i>ϕ</i>-Hermicity
• signal processing