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Sociedade Brasileira de Telecomunicações

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.

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