In this paper, we present a method based on generating matrices for constructing number-theoretic transform (NTT) eigenvectors. We provide a specific generating matrix and, using it, we demonstrate how to construct an orthogonal basis of Hermite–Gaussian-like NTT eigenvectors, which can be used to define a fractional number-theoretic transform (FrNTT). We discuss the main aspects of the referred eigenbasis, present an example and suggest a potential application for the corresponding FrNTT.

Additional Metadata
Keywords Fractional transforms, Generating matrices, Hermite–Gaussian-like eigenvectors, Number-theoretic transforms
Persistent URL dx.doi.org/10.1016/j.sigpro.2018.05.018
Journal Signal Processing
Citation
de Oliveira Neto, J.R. (José R.), Lima, J.B. (Juliano B.), & Panario, D. (2018). A generating matrix method for constructing Hermite–Gaussian-like number-theoretic transform eigenvectors. Signal Processing, 152, 189–196. doi:10.1016/j.sigpro.2018.05.018