Real Clifford Algebra Cl(n,0), n=2,3(mod 4) Wavelet Transform

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We show how for n=2,3 (4) continuous Clifford (geometric) algebra (GA) Clₙ-valued admissible wavelets can be constructed using the similitude group SIM(n). We strictly aim for real geometric interpretation, and replace the imaginary unit i ∈ therefore with a GA blade squaring to -1. Consequences due to non-commutativity arise. We express the admissibility condition in terms of a Clₙ Clifford Fourier Transform and then derive a set of important properties such as dilation, translation and rotation covariance, a reproducing kernel, and show how to invert the Clifford wavelet transform. As an example, we introduce Clifford Gabor wavelets. We further invent a generalized Clifford wavelet uncertainty principle.