A robust eigenbasis generation system for the discrete Fourier transform

We have developed a systematic approach to construct an intelligible real eigenbasis for discrete Fourier transforms (DFT) by directly utilizing the eigenbases of some specific types of discrete sine and cosine transforms (DST and DCT). This methodological advancement not only enhances the comprehension of DFT spectra but also leads to a significant outcome: the identification of an explicit discrete analogue of Hermite-Gaussian functions within the context of DFT. By capitalizing on the inherent structure present in DST and DCT eigenbases, our approach facilitates a seamless transition to the domain of discrete Hermite-Gaussian functions, thereby opening up new avenues for related applications.