On the diagonalization of the discrete Fourier transform
| dc.creator | Gurevich, Shamgar | |
| dc.creator | Hadani, Ronny | |
| dc.date | 2008-08-24 | |
| dc.date | 2008-12-27 | |
| dc.date.accessioned | 2026-07-07T12:22:07Z | |
| dc.date.available | 2026-07-07T12:22:07Z | |
| dc.description | The discrete Fourier transform (DFT) is an important operator which acts on the Hilbert space of complex valued functions on the ring Z/NZ. In the case where N=p is an odd prime number, we exhibit a canonical basis of eigenvectors for the DFT. The transition matrix from the standard basis to the canonical basis defines a novel transform which we call the discrete oscillator transform (DOT for short). Finally, we describe a fast algorithm for computing the discrete oscillator transform in certain cases. | |
| dc.description | Accepted for publication in the journal "Applied and Computational Harmonic Analysis": Appl. Comput. Harmon. Anal. (2009), doi:10.1016/j.acha.2008.11.003. Key words: Discrete Fourier Transform, Weil Representation, Canonical Eigenvectors, Oscillator Transform, Fast Oscillator Transform | |
| dc.identifier | https://arxiv.org/abs/0808.3281 | |
| dc.identifier | http://arxiv.org/abs/0808.3281 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213542 | |
| dc.subject | Information Theory | |
| dc.subject | Discrete Mathematics | |
| dc.subject | Representation Theory | |
| dc.title | On the diagonalization of the discrete Fourier transform | |
| dc.type | text |