The discrete Fourier transform: A canonical basis of eigenfunctions

We exhibit a canonical basis of eigenvectors for the discrete Fourier transform (DFT). The transition matrix from the standard basis to defines a novel transform which we call the discrete oscillator transform (DOT for short). Finally, we describe a fast algorithm for computing in certain cases.

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Shamgar Gurevich, Ronny Hadani, Nir A. Sochen
• Keywords: Canonical Basis, CORR 2008, Discrete Fourier Transform, Discrete Oscillator, Education