Quaternion Multiplier Inspired by the Lifting Implementation of Plane Rotations

A lifting-based structure for quaternion multipliers with unit-magnitude constant coefficients is proposed, whose development was inspired by the well-known implementation of a plane rotation (complex multiplication with a unit-magnitude coefficient) using three shears each of which corresponds to one real multiplication and addition. Our solution is mainly aimed at implementing quaternion transforms as dedicated multiplierless digital circuits. Compared to alternative schemes obtained using the most known general-purpose lifting factorizations, it needs 1/3-1/5 less lifting steps. On general-purpose hardware, it allows for saving 14% operations at the price of representing the hypercomplex coefficient indirectly using six, instead of four, real numbers.