I. Introduction
Traditionally, quaternion algebra [1], [2] has been extensively used in computer graphics [3] and aerospace applications [4], [5] due to its compact notation, moderate computational requirements and avoidance of singularities associated to 3×3 rotation matrices [3]. Moreover, the interest in quaternion signal processing has increased in the last years due to its applications in image processing [6]–[9], wind modeling [10], [11], and design (and processing) of space–time (and space–time-polarization [12]) block codes [13]–[17].