Abstract

Based on the coherence property under the Fourier transform, we introduce two types of coherent states into the finite discrete oscillator model of ${\sf su}(2)$ algebra, and show that they are stable under the fractional Fourier–Kravchuk transform. Using the set of discrete coherent states of this model as biorthonormal bases, we propose two discrete transforms. The first transform maps $f \in {\mathbb{C}^N}$ functions to the unit circle, and the second transform maps the same functions to Bargmann space; both transforms have analytic inverses. These transformations establish a connection between Fourier and Bargmann expansions, respectively, with the basis of Kravchuk symmetric functions. They also provide a framework for the study of finite-dimensional systems in a periodic or complex continuous space. We give some examples of applications to qudit systems.

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