| Abstract: |
Existing approaches towards discrete fractional Fourier analysis rely
upon the furnishing of a basis of eigenvectors for the DFT or its centered
version. This fundamental problem, however, does not have a unique solution
and several approaches that claim to furnish a basis of eigenvectors
for the DFT exist. In the hope of answering the question of uniqueness,
using concepts inspired by quantum mechanics in finite dimensions, we
present an approach that provides a discrete version of the Gauss-Hermite
(G-H) differential operator. In addition to serving up an orthogonal basis
of eigenvectors, the commuting matrix developed here possesses an eigenvalue
spectrum that very closely resembles the integer valued spectrum of
the G-H operator and converges to the G-H operator in the limit, features
that are not shared by the existing approaches.
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