Hartley transform and the use of the Whitened Hartley spectrum as a tool for phase spectral processing

Dual-Root Lattice Discretization of Weyl Orbit Functions

“…Similarly, the action of Γ M on M F Q , described by (32), assigns to each element γ M ∈ Γ M its permutation matrix corresponding to γ ∈ Γ, provided by isomorphism (30). Consequently, the action of Γ M also induces, independently on M , the identical representation matrices A(γ),…”

“…Assuming Weyl symmetric or antisymmetric boundary conditions in mechanical graphene eigenvibrations model [5] or in quantum field lattice models [8] potentially yields novel Weyl invariant solutions and dispersion relations in terms of four types of extended Weyl orbit functions. Realvalued multivariate Hartley-Weyl versions of the transforms augment the application potential of discrete Hartley transforms in pattern recognition [4], geophysics [23], signal processing [30,31], optics [25] and measurement [33]. The unitary matrices of the derived transforms also permit the construction of novel analogues of the Kac-Peterson matrices from the conformal field theory [17].…”