Convolution and Correlation Theorems for Quaternion Fourier Transformation Based on the Orthogonal Planes Split

Abstract

The quaternion Fourier transformation based on orthogonal planes split is an extension of the two-sided quaternion Fourier transformations using quaternion split. In the present paper we investigate its basic properties such as linearity, frequency-shift and time-frequency shift. We then study the convolution and correlation definitions for the quaternion Fourier transformation based on orthogonal planes split and obtain their convolution and correlation theorems.