Application of the Weil representation: diagonalization of the discrete Fourier transform
نویسندگان
چکیده
We survey a new application of the Weil representation to construct a canonical basis Φ of eigenvectors for the discrete Fourier transform (DFT). The transition matrix Θ from the standard basis to Φ defines a novel transform which we call the discrete oscillator transform (DOT for short). In addition, we describe a fast algorithm for computing Θ in certain cases.
منابع مشابه
On the diagonalization of the discrete Fourier transform
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 Φ of eigenvectors for the DFT. The transition matrix Θ from the standard basis to Φ defines a novel transform which we call the discrete oscillator transform (DOT for short). Final...
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عنوان ژورنال:
- CoRR
دوره abs/0902.0668 شماره
صفحات -
تاریخ انتشار 2009