The fractional Fourier transform over finite fields |
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| Authors: | J.B. Lima R.M. Campello de Souza |
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| Affiliation: | a Polytechnic School of Pernambuco, University of Pernambuco, Rua Benfica, 455, CEP 50750-470, Recife, Brazil
b Department of Electronics and Systems, Federal University of Pernambuco, C.P. 7800, Recife, Brazil |
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| Abstract: | The central contribution of this paper is the definition of the fractional Fourier transform over finite fields (GFrFT). In order to introduce the GFrFT, concepts related to trigonometry in finite fields are reviewed and some new ideas put forward. In particular, graphic representations of elements in a finite field are suggested and analogies with real and complex numbers are discussed. A modified version of the finite field Fourier transform is given and its eigenstructure is analyzed. This allows us to develop GFrFT theory and investigate its main characteristics. Some illustrative examples are also given throughout the paper. |
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| Keywords: | Fractional Fourier transform Finite field Eigenvalue Eigenvector |
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