On the diagonalization of the discrete Fourier transform

Details On the diagonalization of the discrete Fourier transform On the diagonalization of the discrete Fourier transform

2008-08-24

arxiv.org/abs/0808.3281v2

Computer Science

Information Theory

Accepted for publication in the journal "Applied and Computational Harmonic Analysis": Appl. Comput. Harmon. Anal. (2009), d

Scientific paper

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.

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