Analytic Video (2D + t) Signals Using Clifford–Fourier Transforms in Multiquaternion Grassmann–Hamilton–Clifford Algebras

摘要: We present an algebraic framework for (2D+ t) video analytic signals and a numerical implementation thereof using Clifford biquaternions Clifford–Fourier transforms. Though the basic concepts of transforms are well known, sequences multiquaternion algebras does not seem to have been realized so far. After short presentation transforms, brief pedagogical review 1D 2D quaternion right Fourier is given. Then, biquaternion developed express (2D + in standard polar form constituted by scalar, pseudoscalar six phases. The phase extraction procedure fully detailed. Finally, discrete fast signal provided.