A Unit Quaternion-based Spherical Trigonometry and

a New Two-carrier Phase quadrature Quaternion Modulation System 

 

A new Hyperspherical trigonometry based on Quaternion's Algebra is introduced.

Spatial curves on the surface of the unit-quaternion hypersphere are described in the

parametric form. A draft of a new Continuous Quaternion Modulation System is presented,

in which two modulation signals are used to drive paths in the normalized 4D-hypersphere.

The outline of a PLL-based demodulation is also sketched.