The discrete Fourier transform: A canonical basis of eigenfunctions

Details The discrete Fourier transform: A canonical basis of eigenfunctions The discrete Fourier transform: A canonical basis of eigenfunctions

2008-08-23

arxiv.org/abs/0808.3214v1

Computer Science

Information Theory

To appear in the proceeding of the 2008 European Signal Processing Conference (EUSIPCO-2008), Lausanne, Switzerland; MSC class

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 DOT in certain cases.

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