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

Paraskevas, Ioannis; Barbarosou, Maria; Chilton, E.

doi:10.1049/joe.2014.0350

Cited by 4 publications

(2 citation statements)

References 24 publications

(29 reference statements)

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“…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),…”

Section: Dual Affine Weyl Groupsmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

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Dual-Root Lattice Discretization of Weyl Orbit Functions

Hrivnák

Motlochová

2019

J Fourier Anal Appl

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Four types of discrete transforms of Weyl orbit functions on the finite point sets are developed. The point sets are formed by intersections of the dual-root lattices with the fundamental domains of the affine Weyl groups. The finite sets of weights, labelling the orbit functions, obey symmetries of the dual extended affine Weyl groups. Fundamental domains of the dual extended affine Weyl groups are detailed in full generality. Identical cardinality of the point and weight sets is proved and explicit counting formulas for these cardinalities are derived. Discrete orthogonality of complex-valued Weyl and real-valued Hartley orbit functions over the point sets is established and the corresponding discrete Fourier-Weyl and Hartley-Weyl transforms are formulated.

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Section: Dual Affine Weyl Groupsmentioning

confidence: 99%