Dihedral Fourier Analysis
نویسنده
چکیده
The Fourier transforms x̂j = ∑ k xkω , k, j = 0, 1, . . . , n− 1 of a data vector x with scalar components xk indexed by n-fold planar rotations ω k define a n × n Hermitian matrix F with entries ωjk/√n, so that x̂ = √n Fx and the inverse Fourier transform is simply x = F∗x̂/√n. Here, the frequencies ω and their harmonics ω fully describe the set (Ĝ) of all n irreducible representations of the Abelian group Cn, each one in dimension of one. Indicating by φk the permutation matrix representing the regular action ω k → ω of Cn, then
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